Short-Run Forecasting Models ofBeef Prices

Ronald A. Oliveira, Carl W. O'Connor and Gary W. Smith

This paper reports on the development of autoregressive-integrated-moving-average (ARIMA) forecasting models for selected cattle price series and the nearby livecattle futures price. The ARIMA models are fitted to weekly data by employing theBox-Jenkins time series modeling procedure. Relatively accurate short-run forecasts areobtained with the estimated models, with the Midwest price models performing betterthan Northwest price models, and the nearby futures model being considerably moreaccurate for longer forecasting horizons.

A major characteristic of agricultural mar-kets in the past decade is the volatile natureof their prices. Livestock prices have beenaffected by many diverse factors; for exam-ple, cyclical building and depletion of herds,unprecedented changes in feed prices,droughts, blizzards, consumer boycotts, andseasonal factors of supply and demand. Someof these events may occur randomly and onlyonce during a person's lifetime, while othersmay be cyclical in nature. Regardless of thecircumstances, forecasting beef prices, espe-cially on a weekly basis, is not usually an easyprocess.

However, the importance of price forecast-ing, especially in times of increased uncer-tainty, is obvious when one considers theproduction, investment, and marketing deci-sions which must be made by producers,processors, and suppliers in the beef trade.Many forecasting methods are discussed inthe livestock literature, [Helmers and Held;

Ronald A. Oliveira and Carl W. O'Connor are AssistantProfessors of Agricultural and Resource Economics, andGary W. Smith is Research Assistant, Oregon State Uni-versity. Thanks is extended to Joseph Alber, Kofi Apraku,Diane Farrow, Marie Rietmann, Adisak Rithikrivong,and Carol Whitley for computational assistance. Helpfulreview comments were received from Peter J. Barry, RayBrokken, Richard J. Crom, and Gene Nelson.

Oregon Agricultural Experiment Station Technical PaperNo. 4909.

Nelson and Spreen], but to be effective, thespecific techniques must be tailored to fit therequirements and set of resources that areunique to an individual firm, researcher, orboth.

The broad range of alternative forecastingmethods offers a wide degree of flexibility indetermining a particular forecasting system.Some of the more specific criteria to considerin developing a forecasting system include: 1)Choose the simplest, least cost methodsavailable to deliver the degree of accuracydesired. The forecasting system must fit thedata and the personnel involved. 2) Theplanning period needs to be specified beforethe forecasting technique is chosen. Themethods used to project next week's pricemay be very different from those needed toproject next quarter's price. 3) Avoid un-necessary detail. Each specific forecastingpurpose will dictate the needed data. 4)Provide a system to check the accuracy of theforecast. This process should reveal anybiases in a forecasting technique.

The specific purpose of this paper is to in-vestigate the potential of a relatively newtime series analysis technique, namely theBox-Jenkins autoregressive-integrated-moving-average (ARIMA) technique, in thedevelopment of weekly forecasting modelsfor various cattle prices. More specific objec-tives are to develop alternative short-runforecasting models, based exclusively on time

45

Western Journal of Agricultural Economics

series for cash-cattle and futures prices, andto test the accuracy of these models for vari-ous short-run forecasting horizons.

ARIMA Models

Various techniques have been used toforecast cattle prices. Several researchershave developed econometric models of vari-ous livestock markets and then employedthese models in forecasting [Hayenga andHacklander; Langemeier and Thompson;Reutlinger]. Forecasting prices witheconometric models requires forecasts of therelevant exogenous and lagged endogenousvariables. While forecasts of lagged endogen-ous and exogenous variables can be obtainedin a recursive manner, forecasts of exogenousvariables often present problems foreconometric model users.

An alternative price-forecasting procedureis the specification and estimation of ARIMAmodels as presented by Box and Jenkins.ARIMA models may be called self-determining since they are based upon cur-rent and past observations of the particulardata series in question and no exogenous var-iables are included. Thus, causal structuresimplied by economic theory are not includedin univariate ARIMA models. For this rea-son, the authors are not suggesting thatARIMA models should replace traditionaleconometric models; rather, they should beconsidered as a supplementary forecastingprocedure.

Several authors have recently applied theBox-Jenkins procedure to selected data se-ries. Examples include Leuthold, et. al., tohog prices, Rausser and Oliveira to recrea-tion data and, most recently, Oliveira, Buon-giorno and Kmiotek to lumber prices. Thefindings of these studies suggest the potentialbenefits of applying this technique to fore-casting cattle prices. Before going into theresults of this application, however, the basicelements of the ARIMA model will be out-lined. More detailed discussions of theARIMA procedures can be found in Nelsonor Box and Jenkins.

46

The ARIMA model is based exclusivelyupon the past behavior of the data series ofinterest and, as the name implies, upon au-toregressive (AR) and moving average (MA)models, which are a "powerful" class of sta-tionary time series models useful in describ-ing a wide variety of stationary time seriesvariables.' Independently, the AR model isdefined as

(1) Zt = (IAlZ_ + (2Zt-2 + * *+ (IpZtp + at,

where Zt is a finite linear sum of its pastvalues; at is a random shock or white noiseterm assumed to be independently and iden-tically distributed N(O, o02); (i, (i = 1, * * , p)are the parameters of the model; and Zt isassumed to be stationary.

The MA model is defined as

(2) Zt = 0 , + at -,- at- - - qat-q,

where Zt is linearly dependent upon theweighted sum of the current and past valuesof the random shock series; the Oj, (j = 1,... , q) are the moving average parameters;and Oo indicates a constant trend patternwithin the data. In economic applications o0is often assumed to be zero, thereby prevent-ing forecasts from increasing regardless ofthe behavior of the series.

AR and MA models may also be extendedto analyze nonstationary time series by theuse of successive differencing of a suitabledegree or by expressing the series in terms oflogarithms. For example, if the series Zt isreduced to stationarity by incorporating a dif-ferencing of degree one, i.e., AZt = Zt -Zt-,, the AR model (1) can be written in theform

(3) AZt -(i-AZt _- -(pAZt-p= at.

1A stationary series is said to "have a mean and variancethat do not change through time, and the covariancebetween values of the process at two time points willdepend only on the distance between these time pointsand not on time itself," [Granger and Newbold, p. 4]. Inother words, the generating mechanism or filter of astationary process is time-invariant.

July 1979

Oliveira, O'Connor, and Smith

The process of transforming a nonstationaryseries to a stationary one is signified by theword "integrated" in the ARIMA model.

Combining the AR and MA models, as-suming the appropriate degree of differenc-ing is one, and omitting the trend param-eters, we may express Zt in the form of ageneral ARIMA model as follows:

(4) AZt-L AZ- AZ ...- < pAZp=at - Olat l - .- Oqatq.

Conventionally, the ARIMA model is ex-pressed in a more summary fashion using thebackward shift operator B, where BdZt =

Zt-d, (1-B)Zt = AZt = Zt - Zt-1, and(1-B)dZt = Zt- Zt-d. Therefore, assumingthe necessary degree of differencing is d, thegeneral ARIMA (p,d,q) model may be ex-pressed as2

(5) (1 - (1 B - ( 2B2 . .. pBP)

(1 -B)Zt = (1 - 0B - 0 2B2 -

... - qB)at.

In order to "fit" an ARIMA model to a dataseries, one should have at least 50 and pref-erably over 100 observations. Given this datarequirement, the procedure for modeling adata series with the general ARIMA formconsists of a three-step sequence. (1) ModelIdentification: Having duly concluded thattime series analysis is appropriate for thesample data, the alternative process (AR,MA, ARMA, or ARIMA) which generates thedata series must be identified. Identificationentails a comparison of the sample autocorre-lation values and sample partial autocorrela-tion values with the known values for varioustheoretical ARIMA models. (2) Parameter Es-timation: From a nonlinear least squares al-gorithm the maximum likelihood estimates ofthe parameters are calculated for the tenta-tively selected model. (3) Diagnostic Confir-mation: If the original data series has beencorrectly modeled, the estimated residual se-

2A more general ARIMA model may also contain sea-sonal differencing, i.e., (1 - BS)D, where s = order ofthe season difference and D = the number of seasonaldifferences.

ries should then be reduced to a "whitenoise" series as defined in (1). One can em-ploy the sum of the residual autocorrelationsin a chi-square test statistic to see if the re-sidual series is "close" to white noise. If theestimated residual series does not appear tobe white noise or if some parameters are in-significant, steps (1), (2), and (3) are repeatedas needed. After this modeling sequence, theresulting model may then be used for fore-casting.

Cattle Price ARIMA Models

The data set for this study consisted ofweekly observations for six cattle cash-marketprice series and the Chicago Mercantilelive-cattle nearby futures price series. De-scriptions and sources for the series are givenin Table 1. The sample or estimation periodfor the weekly price series was from January1972 through December 1976, resulting in260 observations. The test, or forecast periodwas January 1977 to August 1977, resulting in32 post-sample period observations.

The final ARIMA models selected for thevarious price series are presented in Table 2,along with the approximate standard errorsof the estimated coefficients and thestandard error of the estimates, O-a. This lat-ter statistic, which is actually the samplestandard deviation for the estimated residualseries, is one indication of how well eachmodel "fits" the observations over the sampleperiod. The relative standard error, i.e., 0 -a,

divided by the sample mean of the price se-ries, gives a comparison of the accuracy ofeach model relative to the mean price.Another accuracy measure is the sum ofsquared residuals divided by the degrees offreedom for estimation. Also presented inTable 2 is a chi-square statistic for testing thehypotheses that the residual series of theARIMA model has been reduced to "whitenoise."

As one would expect, the Box-JenkinsARIMA model fitting procedure often resultsin more than one acceptable model for agiven time series. Three criteria were used toselect the final models shown in Table 2: (a)

47

Forecasting Beef Prices

Western Journal of Agricultural Economics

TABLE 1. Identification of Data Seriesa

Series Title and Description

NW Steer.............

NW Heifer ............

NW Feeder ...........

Omaha Steer .........

Omaha Heifer.........

K.C. Feeder ..........

Near Futures..........

Northwest steer cash price; weekly average in dollars per 100 pounds (900-1,100pounds, F.O.B. feedlot, 4 percent shrink, average of Washington, Oregon, andIdaho). SOURCE: Federal-State Market News Service, Livestock Division, USDA.

Northwest heifer cash price; weekly average in dollars per 100 pounds (900-1,100pounds, F.O.B. feedlot, 4 percent shrink, average of Washington, Oregon, andIdaho). SOURCE: Federal-State Market News Service, Livestock Division, USDA.

Northwest feeder cash price; weekly average in dollars per 100 pounds (600-700pounds, Portland auction market). SOURCE: USDA Agricultural Marketing Service,Livestock Division.

Omaha steer cash price; weekly average in dollars per 100 pounds (F.O.B. Omaha,Choice, 2-4 yield, 900-1,100 pounds). SOURCE: Livestock-Meat-Wool MarketNews, Weekly Summary and Statistics, USDA.

Omaha heifer cash price; weekly average in dollars per 100 pounds (F.O.B. Omaha,Choice, 2-4 yield, 900-1,100 pounds). SOURCE: Livestock-Meat-Wool MarketNews, Weekly Summary and Statistics, USDA.

Kansas City feeder cash price; weekly average in dollars per 100 pounds (F.O.B.Kansas City, Choice, 600-700 pounds). SOURCE: Livestock-Meat-Wool MarketNews, Weekly Summary and Statistics, USDA.

Nearby fat cattle futures price; weekly closing price in dollars per 100 pounds,nearby live futures contract, Chicago Mercantile Exchange. SOURCE: ChicagoMercantile Exchange Yearbook, Market News Department, Chicago.

aThe estimation data consisted of weekly observations for the period Jan. 8, 1972 - Dec. 25, 1976.The forecasting (or post sample) data was for the period Jan. 1, 1977 - Aug. 6, 1977.

low standard error of the estimates implyinga good fit over the sample period, (b) signifi-cance, in terms of an approximate t-test, ofmost coefficients at the 95 percent confi-dence interval, and (c) as few coefficients aspossible ("parsimony" rule). In many cases,some relatively less parsimonious modelswere maintained to test if gains in forecastingaccuracy could be obtained with these"larger" models.

If one employs 0 'a or the relative standarderror as a criterion for choosing betweenmodels, it is evident from Table 2 that largermodels (in terms of the number and order ofparameters) do not necessarily perform bet-ter. For instance, Model 2 for the KansasCity Feeder price gives the best fit of the fourmodels listed. The addition of 2nd and 29thorder AR terms in Model 4 did not result in asmaller relative sum of squared errors or asmaller oa. For other price series, however,the addition of higher order terms did resultin a better fit, but the decrease in o-a wasusually not large.

48

During the initial stages of this analysis itwas anticipated that the ARIMA models forcomparable price series would be somewhatsimilar. For example, a priori it was expectedthat the ARIMA model for NW Feederwould be similar, in terms of order and esti-mated coefficients, to the resulting model forKansas City Feeder. Obviously the modelspresented in Table 2 do not support theseprior expectations. Apparently the Midwestcattle price series are characterized by differ-ent time series patterns than those for theirNorthwest counterparts. 3

Forecasting Analysis

Post-sample period forecasts were madefor forecasting horizons of 1, 4, 6, 8, 12, 16,20, and 24 weeks. Forecasting origins, de-

3In order to explain these structural differences in timeseries, one would need to introduce explanatory var-iables and extend the analysis to dynamic regression(transfer function) models. For example, see Pierce.

Abbreviation

July 1979

Oliveira, O'Connor, and Smith

fined as the point in time from which a fore-cast is made, were spaced at approximatelymonthly intervals throughout the post-sample period, resulting in eight forecastingorigins. For example, from forecasting origin3, which was observation 269 on February26, 1977, 1-week, 4-week, , 24-weekforecasts were made for each price series byemploying the appropriate ARIMA model.As an illustration, the 95 percent forecastconfidence limits for two forecast origins,along with the actual price series, are shownfor Model Omaha Heifer. 1 in Figure 1. Theforecasting accuracy of each model wasevaluated by computing the percentage errorfor different forecasting horizons. Then themean absolute percentage errors for eachmodel and forecast horizon were computedby averaging across the various origins. Themean absolute percentage errors for selectedforecasting horizons are presented in Table 3.

The results presented in Table 3 indicatethat more accurate forecasts were obtainedwith the Midwest price models. In otherwords, lower mean absolute percentage er-rors were obtained for all forecast horizonswith the "best" Midwest price models. Theseresults suggest a more consistent time seriespattern in the Midwest price series relativeto the Northwest series. One possible expla-nation is that the Pacific Northwest is a deficitfed-beef market, and a relatively small mar-ket for feeder calves relative to the Midwest.

It is also interesting to note that, comparedto the cash series forecasts, the nearby fu-tures forecasts were less accurate for veryshort-run horizons, but much more accuratefor longer term horizons. Again, this resultmay suggest a more stationary and predictivenature of the nearby futures price series rela-tive to the cash series. A tentative explana-tion for our findings is that the futures marketmay reflect a national market for live cattlerather than localized supply and demandconditions.

In order to assess the relative accuracy ofthe ARIMA models, forecasts were also com-puted for each series by using the followingsimple naive or no change model [Chisholm

and Whitaker, Chapter 2]:

(6)

where Zf, t + I is the forecast price for I weeksahead, and Zt is the actual price for week t. Inactuality, the ARIMA forecasts also may becalled naive since they are based solely onhistorical values of variables to be forecast.Dent and Swanson have, in fact, labeledARIMA models as being "super-sophisticatednaive." Nevertheless, we consider model (6)to be relatively simple and naive compared tothose models in Table 2. Model (6) requiresno statistical analysis and assumes a constanttime relationship across all lags. The forecastsobtained from (6) could also be obtained froma random walk model, which is defined as Zt- Zt1 = at [Leuthold]. The mean absolutepercentage forecasting errors for model (6)are shown in Table 3 for each series.

As indicated by Table 3, the forecastingability of the naive model is as good as, andoften superior to, that of the ARIMA modelsfor the shorter forecasting horizons, i.e., 1-8weeks.4 For the 16- and 20-week forecasthorizons, the ARIMA models are slightlymore accurate in terms of mean absolute per-centage errors. Obviously, a practitionerwould need to weigh the cost of estimatingthe ARIMA models versus their small gain inaccuracy over a simple naive model.

The potential usefulness of short-run timeseries forecasting models is illustrated withtwo examples. First, consider a feedlot ownerfacing a buying decision. He may forwardcontract for feeders now or speculate on thecash price two months (8 weeks) from now.Feedlot operators making 8-week forecastswith the above ARIMA models would haveexpected absolute errors of five and six per-cent for the Midwest and Northwest, respec-tively.

4In the opinion of the authors, these results should notbe considered as evidence of random walks in cattleprices as discussed by Leuthold. Certainly the randomwalk model was not sufficient in terms of "fitting" thedata series over the sample period. It appears, how-ever, that the ARIMA models need to be altered for thepost-sample period data.

49

Forecasting Beef Prices

Zf, t + I Zt,

July 1979 Western Journal of Agricultural Economics

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Oliveira, O'Connor, and Smith Forecasting Beef Prices

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July 1979 Western Journal of Agricultural Economics

TABLE 3. Mean Absolute Percentage Forecasting Errors for Selected Forecast Horizonsa

Forecast Horizon (weeks)

Series & Model 1 4 8 16 20

NW Steer.1 ................. 1.24 3.99 5.03(1.79) (2.97) (3.99)

NW Steer.2 ................. 1.13 4.69 5.85(0.76) (2.87) (3.69)

NW Steer.3 ................. 1.16 4.72 5.54(0.67) (2.63) (3.55)

NW Steer.N ................ 1.22 3.45 4.73(1.00) (2.58) (3.70)

NW Heifer.1 ................ 1.50 4.51 5.82(0.76) (3.85) (5.46)

NW Heifer.2 ................. 1.58 4.59 6.33(0.98) (4.91) (6.89)

NW Heifer.N................. 1.47 4.15 5.62(0.83) (3.79) (5.52)

NW Feeder.1 ................ 1.58 5.27 7.28(1.23) (4.22) (4.65)

NW Feeder.2 ................ 1.89 5.25 5.93(1.18) (4.14) (5.40)

NW Feeder.3 ................ 1.79 5.47 5.97(1.18) (4.11) (5.63)

NW Feeder.N................ 1.59 5.37 7.23(1.22) (4.24) (4.59)

Omaha Steer .............. 1.31 4.42 5.02(0.85) (2.54) (1.94)

Omaha Steer.2 .............. 1.21 3.20 5.42(0.97) (3.18) (3.92)

Omaha Steer.3 .............. 1.20 3.17 5.40(0.96) (3.13) (3.78)

Omaha Steer.N .............. 1.22 3.24 5.35(0.89) (3.02) (3.523)

Omaha Heifer1 .............. 1.01 3.24 4.31(0.73) (2.24) (1.74)

Omaha Heifer.2.............. 0.97 2.98 4.78(0.56) (2.71) (3.25)

Omaha Heifer.3.............. 1.02 3.19 4.77(0.54) (2.82) (2.90)

Omaha Heifer.4............. 1.00 3.12 4.58(0.61) (2.63) (3.10)

Omaha Heifer.N ............. 1.06 2.52 4.33(0.66) (2.68) (3.20)

52

7.95(2.79)

7.77(3.83)

7.77(3.68)

7.97(3.45)

9.24(1.56)

10.88(4.64)

9.27(1.10)

10.86(1.36)

9.76(1.30)

9.84(1.45)

10.87(0.94)

3.11(1.36)

6.07(4.10)

6.03(4.07)

5.98(4.00)

2.47(1.78)

6.22(3.06)

5.27(3.50)

5.57(3.15)

6.28(3.15)

10.41(1.97)

10.24(2.60)

10.09(2.59)

10.29(1.48)

8.69(4.66)

9.70(5.51)

9.00(4.19)

13.50(0.76)

12.17(1.66)

12.31(1.75)

13.35(0.44)

2.52(0.29)

6.20(2.37)

6.15(2.40)

5.89(2.43)

1.46(0.96)

6.49(1.51)

6.56(0.84)

6.42(1.19)

6.44(1.23)

.... . I_ .

Oliveira, O'Connor, and Smith

K.C. Feeder.1 ...............

K.C. Feeder.2 ...............

K.C. Feeder.3 ...............

K.C. Feeder.4 ...............

K.C. Feeder.N ...............

Near Futures.1 ..............

Near Futures.2 ..............

Near Futures.3 ..............

Near Futures.N ..............

1.01(0.79)

1.19(0.88)

1.31(0.81)

1.18(0.68)

1.35(1.08)

3.39(3.31)

2.00(1.46)

1.58(1.08)

1.55(1.01)

4.11(2.17)

4.07(2.54)

3.41(1.72)

3.44(1.76)

4.54(1.86)

5.86(4.77)

5.73(5.26)

5.88(5.32)

5.67(5.62)

6.07(3.59)

6.04(3.76)

4.74(3.97)

4.93(3.34)

6.21(3.85)

6.37(3.59)

6.18(5.27)

6.97(5.44)

7.70(5.31)

6.81(6.22)

6.71(6.25)

5.10(4.37)

5.27(4.32)

6.84(6.47)

2.13(0.93)

3.60(2.15)

4.21(2.71)

4.58(3.75)

7.89(6.10)

7.69(6.52)

5.42(5.40)

5.59(5.30)

8.14(6.11)

3.58(0.27)

3.87(2.34)

4.27(1.76)

4.88(0.53)

aThe numbers in parentheses are the sample standard deviations of the respective absolute percentage errors.bThe naive model for each series is denoted by an upper case N.

4+

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+

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FEB MAR APRI I 270 I i

270MAY JUN JUL AUG

280 2900 I 0

300 310 WEEKS

OBSERVATION AND MONTH

Figure 1. Omaha heifer cash series: Actual 1977 values and 24-week forecasts for selectedforecast origins, December 25, 1976 and May 14, 1977.

53

++

50

40

30

202 JAN

060

+++

.. . . ..I I i·.

Forecasting Beef Prices

+4+

.a

Western Journal of Agricultural Economics

Another example is a cow-calf operatorchoosing whether to sell a 400 pound feedernow or feed it five more months for sale at600 pounds. If this feeder is in the Midwest,an ARIMA price forecast could be made withan expected absolute error of 5.5 to 7.5 per-cent. Alternatively, a Northwest feeder couldexpect a 12 percent absolute error. These twoexamples illustrate that the potential for errorincreases greatly as the forecast horizon in-creases, and that ARIMA models may differin accuracy among regions. In reality, eachdecision-maker would also employ other in-formation in making short-run forecasts andsale decisions. Thus, an obvious extension ofthese univariate models would be the de-velopment of mulitvariate time series, (i.e.,transfer function) models for short-term priceforecasting [Pierce].

SummaryVarious ARIMA models were used to fore-

cast prices for alternative forecasting periods.In general, the models for cash prices wererelatively more accurate for shorter timehorizons, and the forecasts for commodity fu-ture prices were more accurate for longertime horizons. In addition, there appeared tobe little gain in accuracy from developingARIMA models with more parameters orfrom using an ARIMA model instead of anaive model.

This analysis is based on data from 1972-1976 and forecasts for 1977. The primary dataperiod (1972-1976) experienced severalexogenous shocks, which included the impactof the Russian Grain Deal on prices andsupplies of feed grain, and a significant ad-justment of the national cow herd, creating amajor shift in production and the beginningof a new cattle cycle. In addition, the valida-tion portion of this analysis utilized eightmonthly origins for forecasts. Weekly originslikely would have provided more accurateforecasts, but the management of such a sys-tem was too expensive for this analysis. Po-tential users of this forecasting techniqueshould evaluate the results of this report inlight of these conditions and their specificresearch needs and resources.

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In light of the above analysis, what are theconclusions regarding ARIMA forecastingmodels? Once one has become familiar withthe notation and model building procedure,ARIMA models are relatively easy to pro-duce. Given the current availability of timeseries software at most major universities, anexperienced practitioner can "fit" an ARIMAmodel within six computer "runs" for mostseries. As illustrated above, however, themodels produced may not always forecastwell. Thus, one is not advised to solely relyupon ARIMA model forecasts, but perhaps tocombine these forecasts with those from aneconometric model, as discussed by Rausserand Oliveira.

Since an econometric model was not em-ployed in this paper, we cannot directlycompare the forecasting abilities of ourARIMA models with those of a weekly beefeconometric model. This type of comparisonhas been presented in detail for other datasets by Naylor, et. al., and Leuthold, et. al. 5

There is no clear consensus on the best fore-casting technique. An appropriate conclusionis perhaps best obtained by quoting fromNaylor, et. al., (p. 136):

Of course, the forecasting and computa-tional advantages of Box-Jenkins methodshave to be weighed against their inherentshortcomings: (1) they are void of explana-tory power; (2) they are not based on eco-nomic theory; and (3) they are essentiallysophisticated smoothing techniques and noteconomic models.

In summary, if one is primarily interestedin forecasting, the Box-Jenkins methodsmay have considerable appeal. But there issome risk with Box-Jenkins methods. Ifthey yield poor forecasts, we may be at acomplete loss to explain "Why?", since theyhave no underpinnings in economic theory.Furthermore, if our goal is to "explain" thebehavior of an economic system and notmerely to grind out forecasts, then Box-

5 Econometric and ARIMA forecasting models have alsobeen compared by Nelson, Bechter and Rutner, Rausserand Oliveira, and Oliveira and Rausser. The latter twostudies, however, do not present a true test of theeconometric models since actual values of the exogenousvariables were employed for the forecasts.

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Oliveira, O'Connor, and Smith

Jenkins methods may be totally unaccept-able. Since they are void of economictheory, they cannot be used to test hypoth-eses and establish confidence intervals forcomplex economic phenomena.

References

Bechter, D. M., and J. L. Rutner. "Forecasting WithStatistical Models and a Case Study of Retail Sales."Economic Review. 63(1978): 3-11.

Box, G. E. P. and G. M. Jenkins. Time Series Analysis:Forecasting and Control. 2nd edition. San Francisco:Holden-Day, 1976.

Chen, Dean T. "The Wharton Agricultural Model:Structure, Specifications, and Some Simulation Re-sults." American Journal of Agricultural Economics.59(1977): 107-116.

Chishold, R. K., and G. R. Whitaker, Jr. ForecastingMethods. Homewood, Illinois: Richard D. Irwin,Inc., 1971.

Granger, C. W. J. and P. Newbold. Forecasting Eco-nomic Time Series. New York: Academic Press, 1977.

Hayenga, M. and D. Hacklander. Short-Run LivestockPrediction Models. Research Bulletin 25, MichiganState University, 1970.

Helmers, G. A. and L. J. Held. "Comparison of Live-stock Price Forecasting Using Simple Techniques,Forward Pricing, and Outlook Information." WesternJournal Agricultural Economics. 1(1977): 157-160.

Langemeier, L. and R. A. Thompson. "Demand, Sup-ply, and Price Relationships for Beef Sector, Post-World War II Period." Journal of Farm Economics.49(1967): 169-183.

Leuthold, R. M. "Random Walk and Price Trends: TheLive Cattle Futures Market." Journal of Finance.27(1972): 879-889.

Leuthold, R. M., A. J. A. MacCormick, A. Schmitz,and D. C. Watts. "Forecasting Daily Hog Prices andQuantities: A Study of Alternative Forecasting Tech-niques." Journal of the American Statistical Associa-tion. 65(1970): 90-107.

Naylor, T. G., T. G. Seaks, and D. W. Wichern. "Box-Jenkins Methods: An Alternative to EconometricModels." Inst. Stat. Rev. 40(1972): 123-137.

Nelson, C. R. Applied Time Series Analysisfor Manage-rial Forecasting. San Francisco: Holden-Day, 1973.

."The Prediction Performance of the FRB-MIT-PENN Model of the U.S. Economy." AmericanEconomic Review. 62(1972): 902-917.

Nelson, Glenn, and Thomas Spreen. "Monthly Steerand Heifer Supply." American Journal of AgriculturalEconomics. 60(1978): 115-125.

Oliveira, R. A., J. Buongiorno, A. M. Kmiotek. "TimeSeries Forecasting Models of Lumber Cash, Futures,and Basis Prices." Forest Science 23(1977): 268-280.

Oliveira, R. A., and G. C. Rausser. "Daily Fluctuationsin Campground Use: An Econometric Analysis."American Journal of Agricultural Economics.59(1977): 283-293.

Pierce, D. A. "Fitting Dynamic Time Series Models:Some Considerations and Examples." In: Proceedingsof the Fifth Annual Symposium on the Interface ofComputer Science and Statistics, 1971: 45-53.

Rausser, G. C. and R. A. Oliveira. "An EconometricAnalysis of Wilderness Area Use." Journal of theAmerican Statistical Association. 71(1976): 276-285.

Reutlinger, S. "Short-Run Beef Supply Response."Journal of Farm Economics. 48(1966): 909-919.

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