exponential smoothing: 11e4effect of initial...

"EXPONENTIAL SMOOTHING: 11E4EFFECTOF INITIAL VALUES AND LOSS FUNEMZONSON POST—SAMPLE FORECASTING ACM:WADY'

by

Spyros MAKRIDAKIS"and

Michele HIBON"

N° 90/46/TM

Research Professor of Decision Sciences and Information Systems,INSEAD, Boulevard de Constance, Fontainebleau, 77300 Cedex, France

Research Associate at INSEAD, Boulevard de Constance, Fontainebleau,77300 Cedex, France

Printed at INSEAD,Fontainebleau, France

EXPONENTIAL SMOOTHING: THE EFFECT OF INITIAL VALUES AND LOSS

FUNCTIONS ON POST-SAMPLE FORECASTING ACCURACY

1

Spyros MAKRIDAKIS and Michele HIBON

INSEAD Fontainebleau France

EXPONENTIAL SMOOTHING: THE EFFECT OF INITIAL VALUES AND LOSS

FUNCTIONS ON POST-SAMPLE FORECASTING ACCURACY

ABSTRACT

This paper describes an empirical investigation aimed atmeasuring the effect of different initial values and loss functions(both symmetric and asymmetric) on the post-sample forecastingaccuracy. The 1001 series of the M-competition are used andthree exponential smoothing methods are employed. The resultsare compared over various types of data and forecasting horizonsand validated with additional data.

Exponential smoothing methods are widely used in many industrial applications

including production planning, production scheduling and inventory control (Brown,

1959; Brown, 1963; Brown, 1967; Gardner, 1985; Holt et al., 1960; Johnson and

Montgomery, 1974; Makridakis and Wheelwright, 1989). Although extremely simple

and easy to model, such methods have been found to be as accurate as more complex

and statistically sophisticated alternatives (Groff, 1973; Chatfield, 1978; Koehler and

Murphree, 1988; Makridakis and Hibon, 1979; Makridakis et al., 1982; Martin and Wit,

1989). Furthermore exponential smoothing methods are robust, easy to program and

require a minimum of historical data. In addition, forecasting systems based on these

methods can be easily maintained while the cost of running them on the computer is the

smallest of all available alternatives.

The purpose of this paper is to empirically investigate the effect of various

initial values and loss functions on the post-sample forecasting accuracy of three (Single,

Holt's and Dampened) exponential smoothing methods. The first part of the paper

2

3

reviews the literature and provides the reasoning for undertaking this study. The second

part describes the methodology used and formulates various hypotheses to be studied.

The third part presents and analyses the results. There is a concluding section which

discusses the implications of the findings, validates such findings with another set of data

provided by Fildes (1989) and presents possible avenues for further research.

LITERATURE REVIEW AND REASONS FOR UNDERTAKING THIS STUDY

Exponential smoothing methods were first proposed by Brown (1959) and Holt

(1960) and were extended by Brown (1963), Winters (1960) and others (Harrison 1967;

Gardner and McKenzie, 1985). Since their introduction the question of how to initialize

the first smoothed value(s) has always been posed (Cogger, 1973; McClain, 1981; Taylor,

1981; Wade, 1967). Several alternatives have been proposed in the literature. The most

common among them are the following (see Appendix for more details):

1. Least Square Estimates: The historical data available is used to estimate

ordinary least square estimates of the initial value(s) (Brown, 1959). In practice this is

the most widely used approach for computing them.

2. Backcasting: The data is inverted and forecasting starts using the most recent

data and going backwards forecasting the less recent ones. The forecast, or smoothed

values, at period 1 are then used as initial values to start the usual forecasting (Ledolter

and Abraham, 1984).

3. Training Set: The data is divided into two parts. The first part (usually the

smaller of the two) is used to estimate the initial values for the exponential smoothing

4

equation(s) used with the second part where the final forecasts (see Makridakis et al.,

1983) are being based.

4. Convenient Initial Values: Some convenient values can be used to initialize the

smoothing equation(s). For instance, the first data value can be used to initialize the

level, while the difference between the first and the second actual value (or the average

of the second minus the first and third minus the fourth) can be used to initialize the

trend. (Makridakis and Wheelwright, 1978).

5, 6 and 7 Zero Values: The initial values can be all set to zero, or alternatively

one can he set to zero and the other(s) can be initialized using one of the alternatives

described above. This set of values(s) can be used as benchmarks to judge the improved

accuracy of approaches 1 to 4 above.

Because of the widespread applications of exponential smoothing methods even

small reductions in their forecasting errors can bring big improvements in terms of lower

costs and/or better customer services (Gardner, 1990a). At present few guide-lines and

no empirical evidence exist to help users decide upon the best initialization procedure

(see Gardner, 1985). The present study aims to provide such empirical evidence and

propose guide-lines, if any exist, for selecting appropriate initialization approaches.

Forecasting and, in general, statistical models can be optimized using a number

of loss functions such as linear, quadratic, or higher order. As in the case of initial

values there is not much help or empirical evidence to guide the choice of the best loss

function to optimize a model's parameters (Granger, 1969; Montgomery and Johnson,

1976), although, in practice the great majority of computer programs employ a quadratic

loss that minimizes the sum of square errors when a model is fitted to historical data.

However, little is known about the influence of alternative loss functions on the post-

5

sample forecasting accuracy (Cogger, 1979). The aim of this paper is to study such an

influence as far as the three exponential smoothing methods utilized in the present study

are concerned. The obvious purpose of interest is whether or not post-sample

forecasting accuracy can be improved by the appropriate choice of a loss function.

Finally, the effects of non-symmetric loss-functions are investigated as the cost

of negative errors (i.e., underestimating demand) is usually considered more critical

than that of positive ones (i.e., overestimating demand). The purpose of such

investigation is to find out the influence of non-symmetric losses on the post-sample

forecasting errors and suggest guide-lines, if any exist, in using non-symmetric loss

functions to balance the cost of negative versus positive errors.

EXPERIMENTAL DESIGN AND METHODOLOGY

The three (Single, Holt's and Dampened) most commonly used exponential

smoothing method were selected for the study (see Appendix for a description of the

models involved). Seven types of initial values (see last section and Appendix) were

used for Holt's and Dampened smoothing and five for Single. In addition eight

optimization criteria (loss functions) were employed. They range from a linear to a

fourth power one (see Appendix). The optimization of the model parameter(s) was

done using a grid search algorithm which found the optimal smoothing constants through

finer and finer searches around a global optimum initially identified through the grid

search.

Table 1 shows the 56 possibilities tested for each of the three smoothing

methods (with the exception of Single where possibilities 6 and 7 were not tested). A

non-symmetric loss function was also applied by weighting positive errors less than

6

negative ones. Such weighting was clone at five levels (.35, .50, .65, .80, .95) while

computing the model fitted errors. Consequently the post sample forecasting accuracy

of each horizon and method was recorded and compared to that of symmetric

optimization.

INSERT TABLE 1 ABOUT HERE

The methodology employed consisted of using the 1001 series of the M-

Competition (see Makridakis et al., 1982) for each of the possibilities listed in Table 1.

For each series and experimental case the optimal model parameters were estimated

and subsequently used to forecast for periods 1, 2, ... , m (where m=6 for yearly data,

m=8 for quarterly data and m=18 for monthly data). These forecasts were then

compared to the actual values (known but obviously not used in developing the

forecasting model) so as to compute the post-sample forecasting errors for each of the m

forecasting horizons. Three post-sample accuracy measures were computed from such

errors: the Mean Absolute Deviations (MAD), the Mean Absolute Percentage Errors

(MAPE) and the Mean Square Errors (MSE). These accuracy measures were

calculated separately for yearly, quarterly and monthly data and were also summarized

for all data and forecasting horizons. Similarly, the same accuracy measures were also

computed when a non-symmetric loss function was used to optimize the parameter(s) in

the model fitting phase.

The approach used in this study is not different to that of real life applications

where m forecasts are made at period t (present) even though their accuracy can only be

found in the future when the actual data becomes available.

The hypotheses to be tested were the following:

A. If yo is the average post-sample accuracy when the initial values are found by

ordinary least squares (prevalent approach) and when the optimization is done

by a quadratic loss function (prevalent approach), then

H =Ho • o 1

HA /4A +ici

where yi is the average post-sample accuracy of an alternative initialization procedure.

B. If yo is the average post-sample accuracy when a quadratic loss function

(prevalent approach) is used to obtain optimal model parameters and when ordinary

least squares (prevalent approach) is employed to initialize the first value(s), then

H0 : = ,u•o o j

HA :#A+//j

where Aej is the average post-sample accuracy of an alternative loss function.

C. If yo is the average post-sample accuracy when the initial values are found by

ordinary least squares and the optimization is done through a quadratic loss

function, then

H = p••o • o

HA :14A+

7

8

where denotes post sample accuracies for specific forecasting horizons, averages of

such horizons (e.g., short, medium, long), specific types of data (e.g., monthly, quarterly,

yearly) or length of the time series.

PRESENTATION AND ANALYSIS OF THE RESULTS

Table 2 shows the MAPE of the best and worst initialization alternatives

together with that of least square estimates (the most widely used approach) for various

forecasting horizons. The optimization alternative used was that of minimizing a

symmetric quadratic (MSE) loss function. As it can be seen in Table 2 the differences in

forecasting accuracy between the best and worst alternatives are extremely small, and

statistically non-significant for Single and Dampened exponential smoothing as well as

for short (periods 1 to 6) forecasting horizons for Holt's. The same results can be

observed in Table 3 which shows the MAPE of the best and worst symmetric

optimization alternative together with that of the MSE (the most widely used approach)

for various forecasting horizons when the initialization approach employed was that of

ordinary least squares. None of the differences are statistically significant except for

those of Holt's for longer than six forecasting horizons.

INSERT TABLES 2 AND 3 ABOUT HERE

In conclusion, there is no evidence from the empirical results to reject the null

hypotheses stated in A and B except in the case of Holt's smoothing for periods longer

than six horizons.

9

The same conclusions can be drawn when the data is separated into yearly,

quarterly and monthly. All of the observed differences when various initial approaches

and loss functions are used are extremely small and none are statistically significant at

the 5% level or below except in the case of Holt's smoothing for periods longer than six

horizons. Table 4, for instance, shows the results of an analysis of variance for yearly

data (m=6 for such data) when Dampened smoothing was used. None of the

differences between initialization procedures (columns), optimization criteria (rows) or

their interaction is statistically significant (the smallest P-value is equal to 0.34). When

the same analysis of variance is conducted for Holt's smoothing the only statistically

significant difference comes from the horizon effect.


Table 5 summarizes the MAPE for the best and worst alternatives for the

various initialization values and loss functions. 'B' on the top right corner of each box

means 'Best' among the horizontal alternatives (i.e., optimization criteria) while 'W'

signifies 'Worst'. Similarly, 'B' and 'W' on the left, lower corner of each box means 'Best'

and 'Worst' alternative among the vertical ones (i.e., initialization values). Table 5(a)

presents the results of Single smoothing, 5(b) presents those of Holt's while 5(c) presents

those of Dampened.

The differences in Table 5(a) are extremely small (the largest is only 0.3%) and

none of them are statistically significant. Moreover, none of the alternatives perform

consistently "best" or "worst" in terms of the initialization and optimization alternatives

experimented with.

The differences in Table 5(b) are considerably bigger than those in Table 5(a).

Moreover, almost all differences between the best and worst alternatives are statistically

1 0

significant (at least at the 5% level). In addition the median is consistently the worst

optimization approach while power 1.5 or 2 (MSE) is consistently the best. Among the

different initialization alternatives the best results are found when both initial values are

set to zero, except in one case where the best result is when only one of the two is set to

zero.

Differences in Table 5(c) are less consistent than those in Table 5(b). The loss

function which does best most of the time is that of MAPE while the corresponding

'best' for initialization is that of least square estimates and convenient values.

Furthermore, the great majority of differences are not statistically significant.

There are no consistent results that hold across Tables 5(a), 5(b), and 5(c).

Thus, hypotheses C cannot be rejected from the experimental findings. In Single

smoothing, Table 5(a), the best results are found when the loss function is the median

and the worst the fourth power. There is no best initialization procedure although the

worst is when the first value is set to zero. However, it must be emphasized that all

differences are extremely small and statistically no significant. In Holt's smoothing,

Table 5(b), the worst loss function is the median (the opposite of Table 5(a)) and the

best is the 1.5 power in all but one case when the 2nd power (MSE) provides the best

results. In terms of initial values the best post-sample accuracies are found when the

first values are both set to zero, except in one case when only one of the two is set to

zero. The worst results are when convenient values are used to initialize.

For Dampened smoothing, Table 5(c), the results are closer to those of Single.

Thus the worst loss function is the fourth power (although not in all cases), the worst

initialization is with zero values (not in all cases) while the best is found with convenient

values (again not in all cases). The great majority of differences are extremely small and

11

statistically non-significant (in Single smoothing the differences are even smaller and

none are statistically significant).

Tables 6 shows results similar to those of Table 5 except the post-sample

accuracy is that of MAD instead of MAPE. Concerning Single smoothing the

differences in post-sample MADs are extremely small and statistically non-significant as

was the case in Table 5(a). However, there are no other consistent patterns between

Tables 5(a) and 6(a). For instance, in Table 6(a) there is a consistent improvement in

post-sample MAD when the model parameters are optimized through higher power

(2.5, 3, or 4) loss functions while in Table 5(a) this is not the case. Similarly, the initial

values that provide the most accurate results are not the same in Tables 5(a) and 6(a).

In Holt's smoothing the differences in MADs are bigger, however higher power

loss functions do not improve the results. Moreover, the median continues to be the

worst optimization alternative while the 1.5 or 2 power the best. There is also

consistency in initialization procedures where the results of Table 5(b) and 6(b) are

similar. Thus, setting both initial values at zero provides the best results most of the

time while the worst results are found when the initialization is done through a training

set.

Finally, there is little consistency between Tables 5(c) and 6(c) - Dampened

smoothing. In Table 6(c) the best optimization criterion is power 1.5 in all but one case,

while in Table 5(c) the best was MAPE (in all but two cases). Finally, there is no

initialization procedure which is consistently best in Table 6(c) while the best in 5(c) was

that of convenient values (in all but two cases).

Thus, it can be concluded that few consistent results can be reported between

Tables 5 (a) and 5 (c) and 6 (a) and 6 (c). That is whatever, if anything, influences post-

12

sample MAPEs does not consistently influence MADs. This is not, however, the case

with Tables 5 (b) and 6 (b) - referring to Holt's smoothing - where the results are fairly

consistent.


Post-sample forecasting accuracies were also computed with MSE. The values

found were, however, large and extremely unstable. The averages were often reduced

by a factor of 10,000 by excluding as few as six series. Given the large number of series

and forecasting horizons involved (almost 14,000 in total) such large fluctuations make

the use of MSE inappropriate as a comparative measure (see Chatfield, 1988).

Furthermore, no consistent or insightful results could be deduced by examining the

various tables of post-sample MSE values even when large errors were excluded. This is

why such tables are not reported in this paper.

The non-symmetric optimization was done using ordinary least square estimates

for initial values and a quadratic (MSE) loss function. Five levels of non-symmetric

losses were used by adding to the sum 35%, 50%, 65%, 80% or 95% of the square error

at period t, when such error was positive while adding the entire square error when it

was negative (see Appendix for more details). As usual the parameter(s) that

minimized the sum of square errors were chosen and were used to make m forecasts and

subsequently compute the post-sample accuracies.

The differences in post-sample accuracies when a non-symmetric loss function

was used were extremely small for all three exponential smoothing methods. In Single

smoothing the great majority of such differences were in the second decimal. In Holt's

smoothing there were some small improvements in post-sample accuracies for longer

than twelve forecasting horizons when the non-symmetric loss function, at the 35% level,

13

was used. However, such differences were not statistically significant while the best

overall results were still obtained when a symmetric loss function was employed. In

Dampened smoothing the best overall results were found with a non-symmetric loss

function at the 50% level. Furthermore, for twelve or longer forecasting horizons the

improvements were considerably larger than those of Single or Holt's smoothing and

consistent; however, they were not statistically significant.

DISCUSSION

If the median and the fourth power are excluded as loss functions to base the

optimization of model parameters few consistent or statistically significant differences

can be found in post-sample forecasting accuracies whether such accuracies are

measured in terms of MAPE, MAD or MSE. Moreover, no consistent patterns could be

found when MAPEs, MADs or MSEs criteria were used to optimize the model's

parameters and MAPEs, MADs or MSEs measures were employed to compute post-

sample accuracies. Thus, there was no correspondence between the type of loss function

used during the model fitting and the accuracy measure employed to compute the post-

sample errors.

These results are surprising. In the forecasting literature the initialization

procedure and the optimization criteria have been considered to influence post-sample

forecasting accuracies. It has been also advocated that there must be a correspondence

between the loss function used in the model fitting and the corresponding post-sample

accuracy used to measure forecasting errors (Zellner, 1986).

From a practical point of view the prevalent approaches of using MSE as a loss

function and ordinary least square estimates to initialize the starting values seems

adequate as the differences between such approaches and the best of the alternatives

14

are small and statistically non-significant, in the great majority of cases. Furthermore, as

these approaches (MSE as the loss function and least square estimates for initialization)

are easy to program and require little computer time to apply there is no motivation to

change them. On the other hand, it makes no sense to consider more elaborate

alternatives such as backcasting for initial values or medians for optimizing the model's

parameter(s) since such alternatives are more difficult to program and require more

computer time when used to obtain forecasts.

In addition to the various results reported in the last section several other

hypotheses were tested during our study. For instance we found that sample size did not

exhibit any consistent influence on the magnitude of post-sample forecasting errors or the

choice of the best initialization or optimization alternatives. In addition, if frequency

distributions of the differences in post-sample errors between the various approaches

were made it was found that the great majority of them were less than 1% - this was in

particular true with Single and Dampened smoothing. Furthermore, no obvious

patterns of such differences could be deduced and no important factors could be found

that could explain the larger than 1% errors.

Another hypothesis tested was whether a specific set of initial values or loss

functions was best for yearly, quarterly or monthly data. But again no consistent

conclusion that hold among the three methods could be reached. Similarly, no

forecasting horizons could be better predicted than others by the appropriate choice of

specific initial values or loss functions.

The practical implications of our study suggest that there are few benefits, if

any, in attempting to find optimal ways to initialize the values of exponential smoothing

15

methods (at least the three we studied). Moreover, the choice of a best loss function is

of no consequence as long as the median and the fourth power are excluded. As

Gardner (1990 b) explained "the reason that starting values and loss functions don't

make any difference is that the optimal smoothing parameter(s) found compensate for

various starting values and different loss functions".

These findings mean that the prevalent approach of initializing by ordinary least

squares and optimizing by a quadratic loss (MSE) function provide satisfactory results

which cannot be improved in any consistent way that holds constant across methods,

data types, forecasting horizons or sample sizes. These conclusions are both good and

bad news. The good news is that exponential smoothing methods (and in particular

simple and Dampened) are easy, accurate and robust forecasting techniques that can be

used across a wide range of actual forecasting applications. The bad news is that

theoretical expectations do not seem to hold empirically for reasons that are not always

clear. Thus, research efforts must concentrate on better understanding such reasons and

in developing alternative methods and approaches that can more accurately predict real

life time series. Somehow it must be possible to beat Single smoothing for longer

forecasting horizons and Dampened for shorter and medium ones. Moreover, research

efforts must be directed in better understanding the effects of one-period-ahead versus

two, three, ... , m-period optimization and their consequence on post-sample forecasting

accuracy (Makridakis, 1990). Finally, more research needs to be done to better

understand the lack of consistency between various loss functions used in model

optimization and the resulting post-sample accuracies. For instance, one would have

expected a correspondence between the type of loss function used in model fitting and

the best results found when post-sample accuracies were measured in the same fashion;

however, none were found in our study.

16

An interesting question in all types of empirical work is whether or not the

results found can be generalized and can also hold with other types of data. In order to

validate the generality of the findings it was therefore decided, after the present results

were found, to test all the 56 possibilities listed in Table 1 with the data of Fildes (1989)

Such data are not at all similar to those of the M-Competition. They consist of 261

monthly series all coming from a Single source (AT&T). Moreover, all series exhibit a

strong negative trend and include little or no seasonality.

The similarities in the results between the two data sets is striking as far as

Single and Holt's smoothing are concerned (see Table 7). That is the magnitude of the

difference between the various experimental cases is very similar while the best and the

worst alternatives are practically the same. With Dampened smoothing the best

initialization procedure, most of the time, was that of the least squares (this was not so

with the M-Competition data) while there was no loss function which provided in a

consistent way the best or the worst results as it was also the case with the M-

Competition data (see Table 7)

Conclusion

This study has shown few differences in post sample forecasting accuracies

when different initialization values and optimization (loss) functions have been used. In

addition non-symmetric loss functions did not change in any statistically significant

fashion the post-sample results. Apart from the conclusion that the median and the

fourth power produced inferior results, no other pervasive finding holds across the

experimental possibilities tested. Finally, concerning the differences observed the

biggest ones were for longer than six forecasting horizons and were mostly concentrated

to Holt's exponential smoothing. All differences between the various experimental cases

17

in Single smoothing were small and statistically insignificant while the magnitude of

those very few of Dampened which were statistically significant was a small fraction of

those of Holt's.

The practical implications of this study suggest dropping existing concerns about

initial values and loss functions and instead concentrating on more important issues

affecting post-sample forecasting accuracy such as optimizing for more than one-step-

ahead forecasting horizons and using actual post-sample measures to base the model

selection process.

To allow replication and/or extensions of the present study both the M-

Competition and the Fildes data can be obtained at no cost by writing to Spyros

Makridakis at INSEAD.

References

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18

Holt, C. C., et al., Planning Production, Inventories, and Work Force, Englewood Cliffs,NJ: Prentice-Hall, 1960, Chapter 14.

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19

- 1 -

APPENDIX

A.Exponentjal Methods Used

Single

et = X t - Ft

where Xt is the actual data at period t andFt is the one-step-ahead forecast at period t-1 for period t.

St = St-1 + aet

where a is the smoothing constant whose value is 0 a 1

and F t+i = S t = 1, 2, 3, ... , m

where m = 6 for yearly data, m = 8 for quarterly and m = 18 for monthly

fiott's Smoothing

et = X t - Ft

St S t_i + Tt_i + aet

Tt = Tt-1 Oet

where p is a smoothing constant whose value is 0 13 1and Ft+i = S t + iTt

Damoened Trend

et = Xt - Ft

S t = + OT t . 1 + aet

Tt = OTt-1 Ret

F i+m = S t + y, OLrt1=1

-2-

B.jnitial values used

1. least Square

For Single exponential smoothing the initial value Si was found as :

Xt

Si — t=in

where n is the number of historical data available.

For Holt's and dampened exponential smoothing S 1 and T 1 are found as :

n nnE tXt - E tY, Xt

t=1 t=1 t=1n

112

nE t2t=1 ,=t

n n

EX t E tS 1 = 'in

This initialization approach is referred to as the ''prevalent" one as it is the mostwidely used in forecasting applications.

2. j3 ackcastinp

The data is inverted and the most recent data value becomes period 1 while theleast recent (i.e., period 1) becomes the last one (i.e., period n). Consequently thevalues of S 1 , or S 1 and T 1 are found as above and the appropriate equation(s) is(are)used to forecast. The last values of Sn, or Sn and Tn are used for initial estimates in theregular forecastings except that the sign of the value of Tn is reversed. Thus, in Singlesmoothing

S 1 = Sn

while in Holt's and Dampened

Si = SnT1 =0 - Tn

T1 –

and

-3-

3 . Training set

The data is separated into two sets (the first set makes up one third of thehistorical data while the second makes up the remaining two thirds). The initial valuesfor S1 or S 1 and T 1 for the training set are found as in 1 above.

If f is the last period of the training (first) set then the values of the S t or S 1 andTi for the remaining data are found as:

= Sfor

SI SfTI Tf

4. Convenient values

The value of S 1 or S i and T 1 are simply set as follows :

S i =XIor

S =XIT1 = (X2 - X1 + X4 - X3) / 2

5. Zero values

The initial values are set as follows:

S = 0or

S1 = 0T1 = 0

6 . Zero Value (for Holt's and Dampened smoothing only)

S 1 = 0T 1 = Least square estimate (see 1 above).

7 . Zero value (for Holt's and Dampened smoothing only)

S 1 = Least square estimate (see 1 above)T 1 =0

-4-

C.Symmetric Loss Functions

The one-period-ahead forecasting errors e t were computed as :

et = Xt - Ft

Consequently the smoothing parameters a, a and 0, or a, j3 and cl) were chosenin such a way as to minimize the corresponding model fitting loss function outlinedbelow :

I Mean Absolute Deviation (MAD)

N- I ett=1

II Mean Absolute Percentage Error (MAPE)

vn et I X

t=1t

n

III Median Absolute Percentage Error (Median)

The smoothing parameter(s) corresponding to the middle value (median) whenall absolute percentage errors were arranged from the smallest to the largest waschosen.

IV I.5th Power

I et 11.5

t=1

V Mean Square Error (MSE)

Et=i

-5-

VI 2.5th Power

VII 3th Power

Eiett.i

VIII 4th Power

4t=i

D.Non-Svmmetric Loss Functions

The prevalent initialization procedure (least square estimates see 1 above) and theprevalent optimization function (MSE, I above) were used with the following non-symmetric loss functions.

n

where 141= 1 when e t > 0

and tv=c when et

TABLE 1: INITIAL VALUES AND LOSS FUNCTIONS

Symmetric loss functions

InitialValues I II HI IV V VI VII VIII

MAD MAPE MEDIAN 1.5th MSE 2nd 2.5th Cubic 4thpower power power power power

1 Least square Single Single Single Single Single Single Single Singleestimates Holt's Holt's Holt's Holt's Holt's Holt's Holt's Holt's

Dampened Dampened Dampened Dampened Dampened Dampened Dampened Dampened

2 Backcasting Single Single Single Single Single Single Single SingleHolt's Holt's Holt's Holt's Holt's Holt's Holt's HolesDampened Dampened Dampened Dampened Dampened Dampened Dampened Dampened

3 Training set Single Single Single Single Single Single Single SingleHolt's Holt's Holt's Holt's Holt's Holt's Holt's Holt'sDampened Dampened Dampened Dampened Dampened Dampened Dampened Dampened

4 Convenient Single Single Single Single Single Single Single Singlevalues Holt's Holt's Holt's Holt's Holt's Holt's Holt's Holt's


5 s =0, or Single Single Single Single Single Single Single Singles=0 and t=0 Holt's Holt's Holt's Holt's Holt's Holt's Holt's Holt's


6 s =0 Holt's Holt's Holt's Holt's Holt's Holt's Holt's Holt'st =least square Dampened Dampened Dampened Dampened Dampened Dampened Dampened Dampened

7 s = least square Holt's Holt's Holt's Holes Holt's Holt's Holt's Holt'sT=0 Dampened Dampened Dampened Dampened Dampened Dampened Dampened Dampened

TABLE 2

COMPARISON OF INITIALIZATION

OPTIMIZATION BY MSE

1 3

FORECASTING HORIZONS

6 8 12 18 Average(All horizons)

All SINGLE Least Squares (1) 8.7 13.3 19.7 18.0 16.9 26.1 17.0Data Best: Convenient (4) 8.5 13.1 19.4 17.9 16.9 26.1 16.9

Worst: zero (5) 8.8 13.2 19.6 18.4 16.9 25.8 17.0

All HOLT Least Squares (1) 8.7 12.9 21.3 22.7 21.3 33.6 19.8Data Best: Both zero (5) 8.6 12.5 19.4 20.6 19.4 34.8 18.7

Worst: Convenient (4) 8.8 13.4 22.1 25.4 26.0 42.5 22.8

All DAMPEN Least Squares (1) 8.5 12.4 18.5 18.1 17.2 27.4 17.0Data Best: Convenient (4) 8.4 12.5 18.7 18.2 17.2 27.5 17.0

Worst: Both zero (5) 8.7 12.9 19.2 18.8 17.2 27.1 17.3

TABLE 3

COMPARISON OF OPTIMIZATION

INITIALIZATION BY PREVALENT VALUES

1 3

FORECASTING HORIZONS

6 8 12 18 Average(All horizons)

All SINGLE MSE 8.7 13.3 19.7 18.0 16.9 26.1 17.0Data Best: MEDIAN

Worst: etMEDIA 8.6

8.713.013.4

19.419.8

17.918.0

16.816.9

25.926.1

16.917.0

All HOLT MSE 8.7 12.9 21.3 22.7 21.3 33.6 19.6Data Best: et 1.5 8.6 12.6 20.5 22.1 20.9 34.0 19.4

Worst: MEDIAN 9.5 15.5 24.6 28.3 33.0 50.0 27.6

All DAMPEN MSE 8.5 12.4 18.5 18.1 17.2 27.4 17.0Data Best: MAPE 8.7 12.2 18.6 17.8 17.5 24.8 16.8

Worst: MEDIAN 8.5 12.4 19.1 19.3 17.9 26.7 17.4

TABLE 4: TWO-WAY ANALYSIS OF VARIANCE

Source Sum of d.f. Mean Computed

Squares Square F-value p-value

Columns 2266. 5. 453. .87 .498

Rows 2940. 5. 587. 1.13 .340

Row X Col 1199. 25. 47. .09 1.000

Error 3062580. 5904. 519.

TOTALS 3068990. 5939.

165 series of yearly data with DAMPEN-Trend Method

Average Error on 6 Forecasting Horizons

Horizontal values: Errors for each OPTIMIZATION criteria

Vertical values: Errors for each STARTING VALUE

THE DIFFERENCES ARE NOT STATISTICALLY SIGNIFICANT

TABLE 5(a): SINGLE SMOOTHING, AVERAGE MAPE FOR ALL FORECASTING HORIZONS AND TIME SERIES


InitialValues I II III IV V VI VII VIII

MAD MAPE MEDIAN 1.5thpower

MSE 2nd 2.5thpower power

Cubicpower

4thpower

Least square 16.9Bestimates

16.9B w16.9B 16.9B w17.0W w17.0W 17.0W B17.0W

2 Backcasting 16.9 816.8 B16.7B B16.8 B16.9 w17.0W 17.0W B17.0W

3 Training set 16.9 B16.8B 16.8B 16.9 w17.0 w17.0 w17.1 w17.1W

4 Convenient B16.8Bvalues

B16.8B 16.8B 16.88 B16.9 B16.9 B16.9 B17.0W

5 s=0, or w17.0s=0 and t=0

w17.1W w16.9B w17.0 w17.0 w17.0 17.0 B17.0

6 s = 0t =least square

7 s = least squareT=0

TABLE 5(b): HOLTS SMOOTHING, AVERAGE MAPE FOR ALL FORECASTING HORIZONS AND TIME SERIES

InitialValues


I H III IV V VI VII VIII



Cubicpower

4thpower

1 Least squareestimates

19.8 19.9 27.6W 19.4B 19.8 20.1 20.3 22.7

2 Backcasting 20.7 21.5 27.8W 20.2B 20.3 21.8 21.6 26.7

3 Training set 21.4 22.8 30.5W 20.5 B 20.8 21.3 22.5 24.0

4 Convenientvalues

w23.5 w23.6 w29.6W w23.0 w22.8B w24.4 w24.8 w25.7

5 s =0, ors=0 and t=0

B19.0 B18.9 27.0W B 18.4B B18.7 B19.2 B19.7 B21.0

6 s =0t = least square

19.1 19.1 27.1W 18.8B 18.9 19.4 B19.7 21.2

7 s =least squareT=0

19.2 19.3 B26.8W 18.6B 21.8 21.1 23.5 25.0

TABLE 5(c): DAMPENED SMOOTHING, AVERAGE MAPE FOR ALL FORECASTING HORIZONS AND TIME SERIES



MAD MAPE MEDIAN 1.5thPower

MSE 2nd 2.5thPower Power

CubicPower

4thPower

1 Least square 16.9estimates

16.8B 17.4W B 16.9 B17.0 B17.0 B172 B17.4W

2 Backcasting 17.0 B16.7B 17.4 B16.9 17.1 17.1 17.3 17.5W

3 Training set 17.0B 17.0B 17.4 17.1 17.3 17.3 17.4 18.4W

4 Convenient B 16.8values

B16.7B 17.4 B16.9 B17.0 17.1 B172 w19.0W

5 s =0, or w17.3s=0 and t=0

w17.2B w17.7" w17.2B w17.3 17.3 17.4 B17.4

6 s =0 17.1Bt = least square

w17.2 17.6W 17.1 B 17.1B 17.1B B 17.2 17.5

7 s =least square 16.9BT=0

17.1 B173 17.0 17.2 w17.4 w17.5 17.9W

"B" at the upper, right hand side of each box signifies Best while "W" signifies Worst accuracy."B" at the lower, left hand side of each box signifies Best, while "W" signifies Worst accuracy.

TABLE 6(a): SINGLE SMOOTHING, AVERAGE MAD FOR ALL FORECASTING HORIZONS AND TIME SERIES(Values have been divided by 1000)

Loss functions




Cubicpower

4thpower


15.5W 15.3 15.4 W 15 .4 15.2B w 15 .4 15 2BW •

2 Backcasting 15.4W 15.4W B15.1 15.4W 15.3 B15.1 B15.08 15.1

3 Training set B 15.3W 13 15.2 15.3W B 15.3W B15.2 B15.1 B15.0 14.9B

4 Convenient 15.5Wvalues

15.4 15.5W 15.4 15.3 B15.1 B15.0 B14.88

5 s =0, or w15.6Ws=0 and t=0

w15.6W w15.6W w15.6W w15.4 w15.3 15.1 14.9B

6 s =0t =least square

7 s =least squareT=0

TABLE 6(b): HOLTs SMOOTHING, AVERAGE MAD FOR ALL FORECASTING HORIZONS AND TIME SERIES(Values have been divided by 1000)

InitialValues

Loss functions

I II III IV V VI VII VIII



Cubicpower

4thpower

1 Least squareestimates

12.4 13.2 B173W 12.4 12.4 12.3B 15.1 15.2

2 Backcasting 11.9 B12.7 21.9W 11.6B 11.8 11.8 w15.8 15.5

3 Training set w15.5 w18.7 w28.1W w13.0B w14.3 w14.6 14.9 15.1

4 Convenientvalues

13.6 15.6 23.5W 12.8 11.7B 11.8 14.4 w15.7

5 s = 0, ors = 0 and t =0

B11.3B 12.9 20.4w B 11.3B B11.5 /311.6 B13.9 14.9

6 s =0t = least square

12.2B 13.6 22.8W 12.2B 12.2B 12.2B 14.7 15.1

7 s = least squareT =0

13.0B 13.9 18.6W w13.0B 13.6 13.1 B13.9 B14.1

TABLE 6(c): DAMPENED SMOOTHING, AVERAGE MAD FOR ALL FORECASTING HORIZONS AND TIME SERIES(Values have been divided by 1000)

Loss functions




Cubicpower

4thpower


14.9W 14.2 B 10.8B B12.2 B12.7 12.9 w13.5

2 Backcasting 13.3 14.3 14AW 12.5 B 12.8 13.2 w13.2 13.1

3 Training set 13.5 813.2 15.8W 12.7B 13.1 13.1 13.1 812.7

4 Convenient B 13.2values

14.3 w18.7W 11.8 B 12.9 13.1 w132 13.1

5 s=0, or 13 .6s=0 and t=0

W I -5 .6W 15.1 11.9B 12.4 13.0 12.9 13.1

6 s =0 13.9t = least square

14.8 B15.0W 11.7B 12.6 12.9 B124 12.9

7 s = least squarew15.0T=0

15.3W B15.0 w15.0 w14.1 w14.2 13.0B 13.0B

TABLE 7(a): SINGLE SMOOTHING, AVERAGE MAPE FOR ALL FORECASTING HORIZONS AND TIME SERIES

InitialValues

FILDES DATA

I II III IV V VI VII VIII


MSE 2ndpower

2.5thpower

Cubicpower

4thpower

Least squareestimates

18.1 18.1 18.1 18.1 18.2 18.2 18.2 18.2

2 Backcasting 18.1 18.1 18.2 18.1 18.1 18.2 18.2. 18.3

3 Training set 18.1 17.9 18.1 18.1 18.1 18.1 18.1 18.2

4 Convenientvalues

18 . 1 17.9 18.2 18.1 18.1 18.2 18.2 18.2

5 s =0, ors=0 and t=0

18.1 18.1. 18.1 18.1 18.1 18.1 18.1 18.1

6 s =0t =least square

7 s = least squareT=0

TABLE 7(b): HOLVS SMOOTHING, AVERAGE MAPE FOR ALL FORECASTING HORIZONS AND TIME SERIES

FILDES DATA

InitialValues I H III IV V VI VII VIII



Cubicpower

4thpower


12.4W B11.5 8.9B 9.7 10.2 10.4 10.5

2 Backcasting 8.8B 12.5 17.1W 8.9 9.2 9.9 10.3 10.8

3 Training set 8.9B 10.2 18.0W 9.6 10.1 10.2 10.7 11.1

4 Convenient 9.6Bvalues

w12.7 w20.0W 10.0 10.3 10.0 10.5 10.9

5 s =0, or w18.1s=0 and t=0

11.6B 16.9 w18.9 w18.9 w19.0 w19. w19.1W

6 s = 0 B7.3Bt = least square

9.3 15.4W B7.8 B8.2 B8.6 B8.8 B8.9

7 s= least square 10.4T=0

B9.0 17.7W 8.013 8.9 9.8 9.6 9.5

TABLE 7(c): DAMPENED SMOOTHING, AVERAGE MAPE FOR ALL FORECASTING HORIZONS AND TIME SERIES

FILDES DATA


MAD MAPE MEDIAN 1.5thPower

MSE 2nd 2.5thPower Power

CubicPower

4thPower


13.4 13.6W B 10A B10.4 B10.5 B9.4B B10.1

2 Backcasting B 12.5 813.2. 13.8W 12.6 12.6 13.2 13.5 12.1B

3 Training set 14..3W 13.9 W 14 3 W13.6 13.3 13.4 10.8B 11.2

4 Convenient 13.4W.values

8 13.2 B 13.1 12.3 12.3 13.0 13.4W 11,6

5 s=0, or w18.0s=0 and t=0

w17.4 13.9E w18.1 W w18.1W w18.1 W 18.0 18.0

6 s =0 w18.0t = least square

w17.4 13.9E W 18.1. w18.1 w18.1 w18.2 w18.3W

7 s = least square 15.0WT=0

14.3 B13.1 12.6 12.6 11.3 11.5 11.5

"B" at the upper, right hand side of each box signifies Best while "W" signifies Worst accuracy."B" at the lower, left hand side of each box signifies Best, while "W" signifies Worst accuracy.

INSEAD VOREING PAPERS SERIES

1986

86/01 Arnoud DE MEYER

86/02 Philippe A. NAERTMarcel VEVERBERGHand Guido VERSVIJVEL

86/03 Michael BRIMS

86/04 Spyros MAKRIDAKISand Michele HIBON

86/05 Charles A. VYPLOSZ

86/06 Francesco CIAVAllI,Jeff R. SHEEN andCharles A. VYPLOSZ

"The R 6 D/Production interface".

"Subjective estimation in integratingcommunication budget and allocationdecisions: a case study", January 1986.

"Sponsorship and the diffusion oforganizational innovation: a preliminary viev".

"Confidence intervals: an empiricalinvestigation for the series in the M-Competition" .

"A note on the reduction of the vorkveek",July 1985.

"The real exchange rate and the fiscalaspects of a natural resource discovery",Revised version: February 1986.

86/16 B. Espen ECKBO andHerwig M. LANGOHR

86/17 David B. JEMISON

86/18 James TEBOULand V. MALLERET

86/19 Rob R. VEITZ

86/20 Albert CORHAY,Gabriel HAVAVINIand Pierre A. MICHEL

86/21 Albert CORHAY,Gabriel A. HAVAVINIand Pierre A. MICHEL

86/22 Albert CORHAY,Gabriel A. HAVAVINIand Pierre A. MICHEL

"Les primes des offres publiques, la noted'information et le marche des transferts decontrele des societes".

"Strategic capability transfer in acquisitionintegration", May 1986.

"Towards an operational definition ofservices", 1986.

"Nostradamus: a knowledge-based forecastingadvisor".

"The pricing of equity on the London stockexchange: seasonality and size premium",June 1986.

"Risk-premia seasonality in U.S. and Europeanequity markets", February 1986.

"Seasonality in the risk-return relationshipssome international evidence", July 1986.

86/07 Douglas L. MacLACHLANand Spyros MAKRIDAKIS

86/08 Jose de la TORRE andDavid H. NECKAR

86/09 Philippe C. HASPESLAGH

86/10 R. MOENART,Arnoud DE MEYER,J. BARGE andD. DESCHOOLMEESTER.

86/11 Philippe A. NAERTand Alain BULTEZ

86/12 Roger BETANCOURTand David GAUTSCHI

86/13 S.P. ANDERSONand Damien J. NEVEN

"Judgmental biases in sales forecasting",February 1986.

"Forecasting political risks forinternational operations", Second Draft:March 3, 1986.

"Conceptualizing the strategic process indiversified firms: the role and nature of thecorporate influence process", February 1986.

"Analysing the issues concerningtechnological de-maturity".

"From "Lydiametry" to "Pinkhamization":■isspecifying advertising dynamics rarelyaffects profitability".

"The economics of retail firms", RevisedApril 1986.

"Spatial competition a la Cournot".


86/24 David CAUTSCHIand Vithala R. RAO

86/25 H. Peter GRAYand Ingo WALTER

86/26 Barry EICHENGREENand Charles VYPLOSZ

86/27 Karel COOLand Ingemar DIERICKX

86/28 Manfred KETS DEVRIES and Danny MILLER

86/29 Manfred KEYS DE VRIES

86/30 Manfred KETS DE VRIES


"An exploratory study on the integration ofinformation systems in manufacturing",July 1986.

"A methodology for specification andaggregation in product concept testing",July 1986.

"Protection", August 1986.

"The economic consequences of the FrancPoincare", September 1986.

"Negative risk-return relationships inbusiness strategy: paradox or truism?",October 1986.

"Interpreting organizational texts.

"Vhy follow the leader?".

"The succession game: the real story.

"Flexibility: the next competitive battle",October 1986.

"Comparaison Internationale des marges brutesdu commerce", June 1985.

"How the managerial attitudes of firms withFMS differ from other manufacturing firms:survey results", June 1986.

86/31 Arnoud DE MEYER,Jinichiro NAKANE,Jeffrey G. MILLERand Kasra FERDOVS

86/32 Karel COOLand Dan SCHENDEL

"Flexibility: the next competitive battle",Revised Version: March 1987

Performance differences among strategic groupmembers", October 1986.

86/14 Charles VALDMAN

86/15 Mihkel TOMBAK andArnoud DE MEYER

86/33 Ernst BALTENSPERGERand Jean DERMINE

86/34 Philippe HASPESLAGHand David JEMISON

86/35 Jean DERMINE

86/36 Albert CORHAY andGabriel HAVAVINI

86/37 David GAUTSCHI andRoger BETANCOURT

86/38 Gabriel HAVAVINI

86/39 Gabriel HAVAVINIPierre MICHELand Albert CORHAY

86/40 Charles VYPLOSZ

86/41 Kasra FERDOVSand Wickham SKINNER

86/42 Kasra FERDOWSand Per LINDBERG

86/43 Damien NEVEN

86/44 Ingemar DIERICKXCarmen MATUTESand Damien NEVEN

1987


87/02 Claude VIALLET

87/03 David GAUTSCHIand Vithala RAO

87/04 Sumantra GHOSHAL andChristopher BARTLETT

87/05 Arnoud DE MEYERand Kasra FERDOWS

"The role of public policy in insuringfinancial stability: a cross-country,comparative perspective", August 1986, RevisedNovember 1986.

"Acquisitions: myths and reality",July 1986.

"Measuring the market value of a bank, aprimer", November 1986.

"Seasonality in the risk-return relationship:some international evidence", July 1986.

"The evolution of retailing: a suggestedeconomic interpretation".

"Financial innovation and recent developmentsin the French capital markets", Updated:September 1986.

"The pricing of common stocks on the Brusselsstock exchange: a re-examination of theevidence", November 1986.

"Capital flows liberalization and the EMS, aFrench perspective", December 1986.

"Manufacturing in a new perspective",July 1986.

"FMS as indicator of manufacturing strategy",December 1986.

"On the existence of equilibrium in hotelling'smodel", November 1986.

"Value added tax and competition",December 1986.

"Prisoners of leadership".

"An empirical investigation of Internationalasset pricing", November 1986.

"A methodology for specification andaggregation in product concept testing",Revised Version: January 1987.

"Organizing for innovations: case of themultinational corporation", February 1987.

"Managerial focal points in manufacturingstrategy", February 1987.

"Customer loyalty as a construct in themarketing of banking services", July 1986,

"Equity pricing and stock market anomalies",February 1987.

"Leaders who can't manage", February 1987.

"Entrepreneurial activities of European MBAs",March 1987.

"A cultural view of organizational change",March 1987

"Forecasting and loss functions", March 1987.

"The Janus Bead: learning fro, the superiorand subordinate faces of the manager's job",April 1987.

"Multinational corporations as differentiatednetworks", April 1987.

"Product Standards and Competitive Strategy: AnAnalysis of the Principles", May 1987.

"METAFORECASTING: Rays of improvingForecasting. Accuracy and Usefulness",May 1987.

"Takeover attempts: what does the language tellus?, June 1987.

"Managers' cognitive maps for upward anddovnvard relationships", June 1987.

"Patents and the European biotechnology lag: astudy of large European pharmaceutical firms",June 1987.

"Why the EMS? Dynamic games and the equilibriumpolicy regime, May 1987.

"A new approach to statistical forecasting",June 1987.

"Strategy formulation: the impact of nationalculture", Revised: July 1987.

"Conflicting ideologies: structural andmotivational consequences", August 1987.

"The demand for retail products and thehousehold production model: new views oncomplementarity and substitutability".

87/06 Arun K. JAIN,Christian PINSON andNaresh K. MALHOTRA

87/07 Rolf BANZ andGabriel HAVAVINI


87/09 Lister VICKERY,Mark PILKINCTONand Paul READ

87/10 Andre LAURENT

87/11 Robert FILDES andSpyros MAKRIDAKIS

87/12 Fernando BARTOLOMEand Andre LAURENT

87/13 Sumantra GHOSHALand Nitin NOHRIA

87/14 Landis GABEL

87/15 Spyros MAKRIDAKIS

87/16 Susan SCHNEIDERand Roger DUNBAR

87/17 Andre LAURENT andFernando BARTOLOME

87/18 Reinhard ANGELMAR andChristoph LIEBSCHER

87/19 David BEGG andCharles VYPLOSZ


87/21 Susan SCHNEIDER


87/23 Roger BETANCOURTDavid GAUTSCHI


87/33 Yves DOZ andAmy SHUEN

87/34 Kasra FERDOWS andArnoud DE MEYER

87/35 P. J. LEDERER andJ. F. THISSE

"German, French and British manufacturingstrategies less different than one thinks",September 1987.

"A process framework for analyzing cooperationbetween firms", September 1987.

"European manufacturers: the dangers ofcomplacency. Insights from the 1987 Europeanmanufacturing futures survey, October 1987.

"Competitive location on netvorks underdiscriminatory pricing", September 1987.

87/36 Manfred KETS DE VRIES 'Prisoners of leadership", Revised versionOctober 1987.

87/24 C.B. DERR andAndre LAURENT

"The internal and external careers: atheoretical and cross-cultural perspective",Spring 1987.

87/41 Gavriel HAVAVINI and "Seasonality, size premium and the relationshipClaude VIALLET betveen the risk and the return of French

common stocks", November 1987

87/29 Susan SCHNEIDER andPaul SHRIVASTAVA

"The robustness of !IDS configurations in theface of incomplete data", March 1987, Revised:July 1987.

"Demand complementarities, household productionand retail assortments", July 1987.

"Is there a capital shortage in Europe?",August 1987.

"Controlling the interest-rate risk of bonds:an introduction to duration analysis andimmunization strategies", September 1987.

"Interpreting strategic behavior: basicassumptions themes in organizations", September1987

87/42 Damien NEVEN andJacques-F. THISSE

87/43 Jean GABSZEWICZ andJacques-F. THISSE

87/44 Jonathan HAMILTON,Jacques-F. THISSEand Anita WESKAMP

87/45 Karel COOL,David JEMISON andIngemar DIERICKX

87/46 Ingemar DIERICKXand Karel COOL

"Combining horizontal and verticaldifferentiation: the principle of max-mindifferentiation", December 1987

"Location", December 1987

"Spatial discrimination: Bertrand vs. Cournotin a model of location choice", December 1987

"Business strategy, market structure and risk-return relationships: a causal interpretation",December 1987.

'Asset stock accumulation and sustainabilityof competitive advantage", December 1987.

87/25 A. K. JAIN,N. K. MALNOTRA andChristian PINSON

87/26 Roger BETANCOURTand David GAUTSCHI

87/27 Michael BURDA


87/30 Jonathan HAMILTON

"Spatial competition and the Core", August

W. Bentley MACLEOD

1987. 1988and J. F. THISSE

87/31 Martine OUINZII andJ. F. THISSE

87/37 Landis GABEL


87/40 Carmen MATUTES andPierre REGIBEAU

"On the optimality of central places*,September 1987.

"Privatization: its motives and likelyconsequences", October 1987.

"Strategy formulation: the impact of nationalculture", October 1987.

"Product compatibility and the scope of entry",November 1987

88/01 Michael LAWRENCE andSpyros MAKRIDARIS

88/02 Spyros MARRIDAKIS

88/03 James TEBOUL


88/05 Charles VYPLOSZ

88/06 Reinhard ANGELMAR

88/07 Ingemar DIERICKXand Karel COOL

88/08 Reinhard ANGELMARand Susan SCHNEIDER

88/09 Bernard SINCLAIR-DESGAGN6



"Factors affecting judgemental forecasts andconfidence intervals", January 1988.

"Predicting recessions and other turningpoints", January 1988.

"De-industrialize service for quality", January1988.

"National vs. corporate culture: implicationsfor human resource management", January 1988.

"The swinging dollar: is Europe out of step?",January 1988.

"Les conflits dans les canaux de distribution",January 1988.

"Competitive advantage: a resource basedperspective", January 1988.

"Issues in the study of organizationalcognition", February 1988.

"Price formation and product design throughbidding", February 1988.

"The robustness of some standard auction gameforms", February 1988.

"Vhen stationary strategies are equilibriumbidding strategy: The single-crossingproperty", February 1988.

87/39 Manfred KETS DE VRIES "The dark side of CEO succession", November1987


"Business firms and managers in the 21stcentury", February 1988

88/13 Manfred KETS DE VRIES "Alexithymia in organizational life: theorganization man revisited", February 1988.

88/14 Alain NOEL "The interpretation of strategies: a study ofthe impact of CEOs on the corporation",March 1988.

88/15 Anil DEOLALIKAR andLars-Hendrik ROLLER


88/17 Michael BURDA

88/18 Michael BURDA

88/19 M.J. LAWRENCE andSpyros MAKRIDAKIS

88/20 Jean DERMINE,Damien NEVEN andJ.F. THISSE

88/21 James TEBOUL

88/22 Lars-Hendrik ROLLER

88/23 Sjur Didrik FLAMand Georges ZACCOUR

88/24 B. Espen ECKBO andHerwig LANGOHR

88/25 Everette S. GARDNERand Spyros MAKRIDAKIS

"The production of and returns from industrialinnovation: an econometric analysis for adeveloping country", December 1987.

"Market efficiency and equity pricing:international evidence and implications forglobal investing", March 1988.

"Monopolistic competition, costs of adjustmentand the behavior of European employment",September 1987.

"Reflections on "Wait Unemployment" inEurope", November 1987, revised February 1988.

"Individual bias in judgements of confidence",March 1988.

"Portfolio selection by mutual funds, anequilibrium model", March 1988.

"De-industrialize service for quality",March 1988 (88/03 Revised).

"Proper Quadratic Functions with an Applicationto AT&T", May 1987 (Revised March 1988).

"P.quilibres de Nash-Cournot dans le marcheeuropken du gaz: un cas on les solutions enboucle ouverte et en feedback coincident",Mars 1988

"Information disclosure, means of payment, andtakeover premia. Public and Private tenderoffers in Prance". July 1985, Sixth revision,April 1988.

"The future of forecasting", April 1988.

88/26 Sjur Didrik FLANand Georges ZACCOUR

88/27 Murugappa KRISHNANLars-Hendrik ROLLER

88/28 Sumantra GHOSHAL andC. A. BARTLETT

"Semi-competitive Cournot equilibrium inmultistage oligopolies", April 1988.

"Entry game with resalable capacity",April 1988.

"The multinational corporation as a network:perspectives from interorganizational theory",May 1988.

88/29 Naresh K. MALHOTRA,Christian PINSON andArun K. JAIN

88/30 Catherine C. ECKELand Theo VERMAELEN

88/31 Sumantra GHOSHAL andChristopher BARTLETT

88/32 Kasra FERDOWS andDavid SACKRIDER

88/33 Mihkel M. TOMBAK

88/34 Mihkel M. TOMBAK

88/35 Mihkel TOMBAK

88/36 Vikas TIBREWALA andBruce BUCHANAN

88/37 Murugappa KRISHNANLars-Hendrik ROLLER



88/40 Josef LAKONISHOK andTheo VERMAELEN

88/41 Charles WYPLOSZ

88/42 Paul EVANS

88/43 B. SINCLAIR-DESGAGNE

88/44 Essam MAHMOUD andSpyros MAKRIDAKIS

88/45 Robert KORAJCZYKand Claude VIALLET

88/46 Yves DOZ andAmy SHUEN

"Consumer cognitive complexity and thedimensionality of multidimensional scalingconfigurations", May 1988.

"The financial fallout frog Chernobyl: riskperceptions and regulatory response", May 1988.

"Creation, adoption, and diffusion of

innovations by subsidiaries of multinationalcorporations", June 1988.

"International manufacturing: positioningplants for success", June'1988.

"The importance of flexibility inmanufacturing", June 1988.

"Flexibility: an important dimension inmanufacturing", June 1988.

"A strategic analysis of investment in flexiblemanufacturing systems", July 1988.

"A Predictive Test of the HBO Model thatControls for Non-stationarity", June 1988.

"Regulating Price-Liability Competition ToImprove Welfare", July 1988.

"The Motivating Role of Envy : A ForgottenFactor in Management, April 88.

"The Leader as Mirror : Clinical Reflections",July 1988.

"Anomalous price behavior around repurchasetender offers", August 1988.

"Assymetry in the EMS: intentional orsystemic?", August 1988.

"Organizational development in thetransnational enterprise", June 1988.

"Group decision support systems implementBayesian rationality", September 1988.

"The state of the art and future directionsin combining forecasts", September 1988.

"An empirical investigation of internationalasset pricing", November 1986, revised August1988.

"Prom intent to outcome: a process frameworkfor partnerships", August 1988.

88/47 Alain BULTEZ,Els GIJSBRECHTS,Philippe NAERT andPiet VANDEN ABEELE

88/48 Michael BURDA

88/49 Nathalie DIERKENS

88/50 Rob WEITZ andArnoud DE MEYER

88/51 Rob VEITZ

88/52 Susan SCHNEIDER andReinhard ANGELMAR


88/54 Lars-Hendrik ROLLERand Mihkel M. TOMBAK

88/55 Peter BOSSAERTSand Pierre HILLION

88/56 Pierre HILLION

88/57 Vilfried VANHONACKERand Lydia PRICE

88/58 B. SINCLAIR-DESGAGNEand Mihkel M. TOMBAK

8R/59 Martin KILDUFF

88/60 Michael BURDA

88/61 Lars-Hendrik ROLLER

88/62 Cynthia VAN HULLE,Theo VERMAELEN andPaul DE WOUTERS

"Asymmetric cannibalism between substituteitems listed by retailers", September 1988.

"Reflections on 'Wait unemployment' inEurope, II", April 1988 revised September 1988.

"Information asymmetry and equity issues",September 1988.

"Managing expert systems: from inceptionthrough updating", October 1987.

"Technology, work, and the organization: theimpact of expert systems", July 1988.

"Cognition and organizational analysis: who'sminding the store?", September 1988.

"Whatever happened to the philosopher king: theleader's addiction to power, September 1988.

"Strategic choice of flexible productiontechnologies and welfare implications",October 1988

"Method of moments tests of contingent claimsasset pricing models", October 1988.

"Size-sorted portfolios and the violation ofthe random walk hypothesis: Additionalempirical evidence and implication for testsof asset pricing models", June 1988.

"Data transferability: estimating the responseeffect of future events based on historicalanalogy", October 1988.

"Assessing economic inequality", November 1988.

"The interpersonal structure of decisionmaking: a social comparison approach toorganizational choice", November 1988.

"Is mismatch really the problem? Some estimatesof the Chelvood Cate II model with US data",September 1988.

"Modelling cost structure: the Bell Systemrevisited", November 1988.

"Regulation, taxes and the market for corporatecontrol in Belgium", September 1988.

88/63 Fernando NASCIMENTOand Vilfried R.VANHONACKER

88/64 Kasra FERDOWS

88/65 Arnoud DE MEYERand Kasra FERDOVS

88/66 Nathalie DIERKENS

88/67 Paul S. ADLER andKasra FERDOWS

1989

89/01 Joyce K. BYRER andTavfik JELASSI

89/02 Louis A. LE BLANCand Tavfik JELASSI

89/03 Beth H. JONES andTavfik JELASSI

89/04 Kasra FERDOVS andArnoud DE MEYER

89/05 Martin KILDUFF andReinhard ANGELMAR

89/06 Mihkel M. TOMBAK andB. SINCLAIR-DESGAGNE

89/07 Damien J. NEVEN

89/08 Arnoud DE MEYER andHellmut SCHUTTE

89/09 Damien NEVEN,Carmen MATUTES andMarcel CORSTJENS

89/10 Nathalie DIERKENS,Bruno GERARD andPierre BILLION

"Strategic pricing of differentiated consumerdurables in a dynamic duopoly: a numericalanalysis", October 1988.

"Charting strategic roles for internationalfactories", December 1988.

"Duality up, technology dovn", October 1988.

"A discussion of exact measures of informationassymetry: the example of Myers and Majlufmodel or the importance of the asset structureof the firm", December 1988.

"The chief technology officer", December 1988.

"The impact of language theories on DSSdialog", January 1989.

"DSS software selection: a multiple criteriadecision methodology", January 1989.

"Negotiation support: the effects of computerintervention and conflict level on bargainingoutcome", January 1989."Lasting improvement in manufacturingperformance: In search of a new theory",January 1989.

"Shared history or shared culture? The effectsof time, culture, and performance oninstitutionalization in simulatedorganizations", January 1989.

"Coordinating manufacturing and businessstrategies: I", February 1989.

"Structural adjustment in European retailbanking. Some view from industrialorganisation", January 1989.

"Trends in the development of technology andtheir effects on the production structure inthe European Community", January 1989.

"Brand proliferation and entry deterrence",February 1989.

"A market based approach to the valuation ofthe assets in place and the growthopportunities of the firm", December 1988.

89/11 Manfred KETS DE VRIESand Alain NOEL

89/12 Vilfried VANHONACKER




89/16 Untried VANHONACKER,Donald LEHMANN andFareena SULTAN

89/17 Gilles AMADO,Claude FAUCHEUX andAndre LAURENT

89/18 Srinivasan BALAK-RISHNAN andMitchell KOZA

89/19 Wilfried VANHONACKER,Donald LEHMANN andFareena SULTAN

89/20 Wilfried VANHONACKERand Russell VINER

89/21 Arnoud de MEYER andKasra FERDOVS

89/22 Manfred KETS DE VRIESand Sydney PERZOV

89/23 Robert KORAJCZYK andClaude VIALLET

89/24 Martin KILDUFF andMitchel ABOLAFIA

89/25 Roger BETANCOURT andDavid GAUTSCHI

89/26 Charles BEAN,Edmond MALINVAUD,Peter BERNHOLZ,Francesco GIAVAll1and Charles WYPLOSZ

"Understanding the leader-strategy interface:application of the strategic relationshipinterview method", February 1989.

"Estimating dynamic response models when thedata are subject to different temporalaggregation", January 1989.

"The impostor syndrome: a disquietingphenomenon in organizational life", February1989.

"Product innovation: a tool for competitiveadvantage", March 1989.

"Evaluating a firm's product innovationperformance", March 1989.

"Combining related and sparse data in linearregression models", February 1989.

"Changement organisationnel et realitèsculturelles: contrastes franco-americains".March 1989.

"Information asymmetry, market failure andjoint-ventures: theory and evidence",March 1989

"Combining related and sparse data in linearregression models",Revised March 1989

"A rational random behavior model of choice",Revised March 1989

"Influence of manufacturing improvementprogrammes on performance", April 1989

"Vhat is the role of character inpsychoanalysis? April 1989

"Equity risk premia and the pricing of foreignexchange risk" April 1989

"The social destruction of reality:Organisational conflict as social drama"April 1989

"Two essential characteristics of retailmarkets and their economic consequences"March 1989

"Macroeconomic policies for 1992: thetransition and atter", April 1989

89/27 David KRACKHARDT andMartin KILDUFF

89/28 Martin KILDUFF

89/29 Robert GOGEL andJean-Claude LARRECHE

89/30 Lars-Hendrik ROLLERand Mihkel M. TOMBAK

89/31 Michael C. BURDA andStefan GERLACH

89/32 Peter HAUG andTavfik JELASSI

89/33 Bernard SINCLAIR-DESGAGNE

89/34 Sumantra GHOSHAL andNittin NOHRIA

89/35 Jean DERMINE andPierre HILLION

89/36 Martin KILDUFF


89/38 Manfrd KETS DE VRIES

89/39 Robert KORAJCZYK andClaude VIALLET

89/40 Balaji CHAKRAVARTHY

89/41 B. SINCLAIR-DESGAGNEand Nathalie DIERKENS

89/42 Robert ANSON andTavfik JELASSI

89/43 Michael BURDA

89/44 Balaji CHAKRAVARTHYand Peter LORANGF

89/45 Rob VEIT7. andArnoud DE MEYER

"Friendship patterns and cultural attributions:the control of organizational diversity",April 1989

"The interpersonal structure of decisionmaking: a social comparison approach toorganizational choice", Revised April 1989

"The battlefield for 1992: product strengthand geographic coverage", May 1989

"Competition and Investment in FlexibleTechnologies", May 1989

"Intertemporal prices and the US trade balancein durable goods", July 1989

"Application and evaluation of a multi-criteriadecision support system for the dynamicselection of U.S. manufacturing locations",May 1989

"Design flexibility in monopsonisticindustries", May 1989

"Requisite variety versus shared values:managing corporate-division relationships inthe M-Form organisation", May 1989

"Deposit rate ceilings and the market value ofbanks: The case of Prance 1971-1981", May 1989

"A dispositional approach to social networks:the case of organizational choice", May 1989

"The organisational fool: balancing a leader'shubris", May 1989

"The CEO blues", June 1989

"An empirical investigation of internationalasset pricing", (Revised June 1989)

"Management systems for innovation andproductivity", June 1989

"The strategic supply of precisions", June 1989

"A development framework for computer supportedconflict resolution", July 1989

"A note on firing costs and severance benefitsin equilibrium unemployment", June 1989

"Strategic adaptation in multi-business firms",

June 1989

"Managing expert systems: a framework and casestudy", June 1989

89/46

89/47

Marcel CORSTJENS,Carmen MATUTES andDamien NEVEN

Manfred KETS DE VRIESand Christine MEAD

"Entry Encouragement", July 1989

"The global dimension in leadership andorganization: issues and controversies",

89/64(TM)

89/65(TN,AC, PIN)

Enver YUCESAN andLee SCHRUBEN

Soumitra DUTTA andPiero BONISSONE

"Complexity of simulation models: A graphtheoretic approach", November 1989

"MARS: A mergers and acquisitions reasoningsystem", November 1989

April 1989

Damien NEVEN andLars-Hendrik ROLLER

"European integration and trade flows",August 1989

89/66 B. SINCLAIR-DESGAGNE(TH,EP)

"On the regulation of procurement bids",November 1989

Jean DERMINE "Home country control and mutual recognition",July 1989

89/67 Peter BOSSAERTS and(PIN) Pierre BILLION

"Market microstructure effects of governmentintervention in the foreign exchange market",December 1989

Jean DERMINE "The specialization of financial institutions,the EEC model", August 1989

89/48

89/49

89/50




89/54 S. BALAKRISHNANand Mitchell KOZA

89/55 H. SCHUTTE

89/56 Vilfried VANHONACKERand Lydia PRICE

89/57 Taekwon KIM,Lars-Hendrik ROLLERand Mihkel TOMBAK

89/58 Lars-Hendrik ROLLER(EP,TM) and Mihkel TOMBAK

89/59 Manfred KETS DE VRIES,(08) Daphna ZEVADI,

Alain NOEL andMihkel TOMBAK

89/60 Enver YUCESAN and(TM) Lee SCHRUBEN

89/61 Susan SCHNEIDER and(All) Arnoud DE MEYER

89/62 Arnoud DE MEYER(TM)

89/63 Enver YUCESAN and(TM) Lee SCHRUBEN

"Sliding simulation: a new approach to timeseries forecasting", July 1989

"Shortening development cycle times: amanufacturer's perspective", August 1989

"Vhy combining works?", July 1989

"Organisation costs and a theory of jointventures", September 1989

"Euro-Japanese cooperation in informationtechnology", September 1989

"On the practical usefulness of meta-analysisresults", September 1989

"Market growth and the diffusion ofmultiproduct technologies", September 1989

"Strategic aspects of flexible productiontechnologies", October 1989

"Locus of control and entrepreneurship: athree-country comparative study", October 1989

"Simulation graphs for design and analysis ofdiscrete event simulation models", October 1989

"Interpreting and responding to strategicissues: The impact of national culture",October 1989

"Technology strategy and international R 6 Doperations", October 1989

"Equivalence of simulations: A graph theoreticapproach", November 1989

90/16 Richard LEVICH and "Tax-Driven Regulatory Drags European1990 FIN Ingo WALTER Financial Centers in the 1990's", January 1990

90/01TM/EP/AC

B. SINCLAIR-DESGAGNE "Unavoidable Mechanisms", January 1990 90/17FIN

Nathalie DIERKENS "Information Asymmetry and Equity Issues",Revised January 1990

90/02EP

Michael BURDA "Monopolistic Competition, Costs ofAdjustment, and the Behaviour of EuropeanManufacturing Employment", January 1990

90/18MKT

Wilfried VANHONACKER "Managerial Decision Rules and the Estimationof Dynamic Sales Response Models", RevisedJanuary 1990

90/03TM

Arnoud DE MEYER "Management of Communication in InternationalResearch and Development", January 1990

90/19 Beth JONES and "The Effect of Computer Intervention and TaskTM Tavfik JELASSI Structure on Bargaining Outcome", February

90/04 Gabriel HAVAVINI and "The Transformation of the European Financial 1990

PIN/EP Eric RAJENDRA Services Industry: Prom Fragmentation toIntegration", January 1990 90/20

TMTavfik JELASSI,

Gregory KERSTEN and"An Introduction to Group Decision andNegotiation Support", February 1990

90/05 Gabriel HAVAVINI and "European Equity Markets: Tovard 1992 and Stanley ZIONTSFIN/EP Bertrand JACOUILLAT Beyond", January 1990

90/06PIN/EP

Gabriel HAVAVINI and "Integration of European Equity Markets:Eric RAJENDRA Implications of Structural Change (or Key

90/21FIN

Roy SMITH and

Ingo WALTER"Reconfiguration of the Global SecuritiesIndustry in the 1990's" • February 1990

90/07

Market Participants to and Beyond 1992",January 1990

Gabriel HAVAVINI "Stock Market Anomalies and the Pricing of

90/22

FINIngo WALTER "European Financial Integration and Its

Implications for the United States", February1990

FIN/EP Equity on the Tokyo Stock Exchange', January1990

90/23 Damien NEVEN "EEC Integration towards 1992: SomeEP/Sli Distributional Aspects", Revised December 1989

90/08TM/EP

Tavfik JELASSI and "Modelling vith MCDSS: What about Ethics'",B. SINCLAIR-DESGAGNE January 1990 90/24 Lars Tyge NIELSEN "Positive Prices in CAPM", January 1990

FIN/EP

90/09 Alberto CIOVANNINI "Capital Controls and International Trade

EP/PIN and Jae VON PARK Finance", January 1990 90/25 Lars Tyge NIELSEN "Existence of Equilibrium in CAPM", JanuaryFIN/EP 1990

90/10 Joyce BRYER and "The Impact of Language Theories on DSSTM Tavfik JELASSI Dialog", January 1990 90/26 Charles KADUSHIN and "Why netvorking Pails: Double Binds and the

90/11TM

Enver YUCESAN "An Overviev of Frequency Domain Methodologyfor Simulation Sensitivity Analysis",

January 1990

OB/BP

90/27TM

Michael BRIM

Abbas FOROUGHI andTavfik JELASSI

Limitations of Shadow Networks", February 1990

"NSS Solutions to Major Negotiation StumblingBlocks", February 1990

90/12 Michael BURDA "Structural Change, Unemployment Benefits and

EP nigh Unemployment: A U.S.- European 90/28 Arnoud DE MEYER "The Manufacturing Contribution toComparison", January 1990 TM Innovation", February 1990

90/13 Soumitra DUTTA and "Approximate Reasoning about Temporal 90/29 Nathalie DIERKENS "A Discussion of Correct Measures ofTM Shashi SHEKHAR Constraints in Real Time Planning and Search',

January 1990

FIN/AC Information Asymmetry", January 1990

90/30 Lars Tyge NIELSEN "The Expected Utility of Portfolios of90/14 Albert ANCEHRN and "Visual Interactive Modelling and Intelligent FIN/EP Assets", March 1990TM Hans-Jakob LOTHI DSS: Putting Theory Into Practice',

January 1990

90/15 Arnoud DE MEYER, "The Internal Technological Reneval of a90/31MKT/EP

David GAUTSCHI andRoger BETANCOURT

"What Determines U.S. Retail Margins?",February 1990

TM Dirk DESCHOOLMEESTER, Business Unit with a Mature Technology",Rudy MOENAERT and January 1990Jan BARBE

90/32SM

Srinivasan BALAK-RISHNAN and

"Information Asymmetry, Adverse Selection andJoint-Ventures: Theory and Evidence",

Mitchell KOZA Revised, January 1990

90/33

OBCaren SIEHL,David BOWEN and

"The Role of Rites of Integration in ServiceDelivery", March 1990

Christine PEARSON

90/34 Jean DERMINE

"The Gains from European Banking Integration,

FIN/EP

a Call for a Pro-Active Competition Policy",

April 1990

90/35 Jae Won PARK

"Changing Uncertainty and the Time-VaryingEP

Risk Premia in the Term Structure of Nominal

Interest Rates", December 1988, Revised

March 1990


"An Empirical Investigation of ManufacturingTM

Strategies in European Industry", April 1990

90/37 William CATS-BARIL

"Executive Information Systems: Developing anTM/OB/SM

Approach to Open the Possibles", April 1990

90/38 Vilfried VANHONACKER "Managerial Decision Behaviour and theHKT

Estimation of Dynamic Sales Response Models",

(Revised February 1990)

90/39 Louis LE BLANC and

"An Evaluation and Selection Methodology forTM Taufik JELASSI

Expert System Shells", May 1990

90/40 Manfred KETS DE VRIES "Leaders on the Couch: The case of RobertoOB

Calvi", April 1990

90/41 Gabriel HAWAWINI, "Capital Market Reaction to the AnnouncementFIN/EP Itzhak SWARY and

of Interstate Banking Legislation", March 1990

Ik WAN JOG

90/42 Joel STECKEL and

"Cross-Validating Regression Models inMKT Wilfried VANHONACKER Marketing Research", (Revised April 1990)

90/43 Robert KORAJCZYK and "Equity Risk Premia and the Pricing of ForeignFIN Claude VIALLET

Exchange Risk", May 1990

90/44 Gilles AMADO, "Organisational Change and Cultural Realities:OH Claude FAUCHEUX and

Franco-American Contrasts", April 1990

Andre LAURENT

90/45 Soumitra DUTTA and

"Integrating Case Based and Rule BasedTM Piero BONISSONE

Reasoning: The Possibilistic Connection",

May 1990

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