feasibility study about tribeco company

Jeekeshen Chinnappen Taylors ID: 0308104 UniSA ID: 110107264

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1.0 Executive Summary

This report is a feasibility study about Tribeco Company who wishes to expand their

operations in the Adelaide Market. The study is to analyse Adelaide market and more

specifically their unemployment rate, their average weekly earnings and recreational

goods retail turnover.

The analysis also encompasses the forecasting of the Recreational Good Retail

Turnover (RGRT) in 2014 which will act as a reference for Tribeco forecasted sale in the

Adelaide’s market.

Objective

To forecast the sales in 2014 for Tribeco.

Results

RGRT has been forecasted to be $4656.3 Million in the first quarter of 2014.

RGRT is more affected by the Unemployment Rate in Adelaide than the workers

weekly earnings.

A 1% decrease in Unemployment Rate will lead to $719.44 Million increase in

Recreational Goods Retail Turnover (RGRT).

A unit increase in Average Weekly will raise the RGRT by $799.09 Million.

A 1% rise in unemployment rate and average weekly earnings will reduce RGRT

to an equilibrium value of $145.6 Million.


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2.0 Introduction

Our aim is to perform a feasibility study for Tribeco who wants to expand in the Adelaide

Market. The purpose of the analysis is forecast its sales for 2014 through the prediction

of the Recreational Goods Retail Turnover (RGRT).

Research Objectives

To forecast the Recreational Goods Retail Turnover (RGRT) in 2014.

To understand the relation of Unemployment Rate (UR) on RGRT.

To understand the relation of Average Weekly Earnings (AWE) of people in

Adelaide on RGRT.


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3.0 Justifications & Discussions of Methodologies

Data Description

Recreational Goods Retail Turnover (RGRT) refers to the products related to leisure

activities, sports and entertainment such as sport and camping equipment, media

retailing, toy and game retailing which are being sold in the Adelaide Market.

Unemployment Rate (UR) refers to the percentage of people living in Adelaide without

an income.

And Average Weekly Earnings (AWE) is the income per week of people working in

Adelaide.

Methodologies

Autoregressive Models (AR) – A tool to analyse the relationships of a variable

and its own lags.

Autocorrelation Matrix – A tool used to find the correlation of a variables and its

own lagged variables to determine the stationarity properties of the series.

Autoregressive Distributed Lag (ADL) -

Dickey-Fuller Test – A method used to test whether a data series has unit roots

by comparing the t-statistics on ρ and the DF critical value.

Engle Granger – A method to test for cointegration between data that have unit

roots by running regression on residuals.


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Data Frequency

Recreational Good Retail Turnover (RGRT) was converted into quarterly series by

summing the 3 consecutive months respectively while the unemployment rate (UR) was

converted to quarterly series by averaging the rate of the 3 consecutive months

accordingly.

Below is the data set transformed into quarterly series to match the frequency of

Average Weekly Earnings (AWE).

Note: See Appendix for Calculation


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4.0 Evaluation of Results & Limitations

Empirical Results for Recreational Goods Retail Turnover (RGRT)

Below is the Autocorrelation Matrix performed on Recreational Goods Retail Turnover

(RGRT) lagged till twelve periods to test for RGRT stationarity properties. As per the

Autocorrelation Chart, there are high correlations between RGRT ($) and its 12 lags.

Therefore, we have to perform an autocorrelation matrix for the ∆RGRT and its lags.

0.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

LAG 1 LAG 2 LAG 3 LAG 4 LAG 5 LAG 6 LAG 7 LAG 8 LAG 9 LAG10

LAG11

LAG12

Autocorrelation for RGRT

Autocorrelation


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Below is the Autocorrelation Matrix performed on the change of Recreational Goods

Retail Turnover (∆RGRT) lagged till twelve periods to test for ∆RGRT stationarity

properties. As per the Correlogram, ∆RGRT is not highly correlated with its lags and is

more stationary. Therefore, ∆RGRT should be used to run the regression instead of

original RGRT.

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

LAG 1 LAG 2 LAG 3 LAG 4 LAG 5 LAG 6 LAG 7 LAG 8 LAG 9 LAG 10LAG 11LAG 12

Autocorrelation for ∆RGRT

Autocorrelation


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Testing for Stationarity (Unit Root): Dickey- Fuller Test

Below is the Dickey-Fuller Test performed on ∆ RGRT.

The general model before performing Dickey-Fuller Test is:

∆Yt = α + ρYt-1 +γ1∆Yt-1+ . . . + γρmax -1 ∆Yt- ρmax +1 δt + ℯt

(T = Time Index/Deterministic Trend, ∆Y = ∆RGRT)

Since, the number of observations is more than 50, Dickey-Fuller test can be

performed.


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AR(p) Variables P-Value

AR(13) ∆Yt-12 0.14082089 Insignificant AR(12) ∆Yt-11 0.201493802 Insignificant AR(11) ∆Yt-10 0.929289032 Insignificant AR(10) ∆Yt-9 0.547102183 Insignificant AR(9) ∆Yt-8 0.006935036 Significant

We first estimated AR(13) with deterministic trend and found the coefficient of ∆Yt-12 to

be insignificant as shown in the table above. We then dropped to AR(12) with

deterministic trend and found the coefficient of ∆Yt-11 to be insignificant. We then

dropped each variable one by one by running different multiple regressions for each as

shown in the table above, and found that the coefficient for ∆Yt-8 to be significant.


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We then tested for the significance of the deterministic trend variable and found it was

significant. Therefore, we had to keep the deterministic trend variable (Time Index).

Dickey-Fuller Test Conclusion

After settling on AR(9) where ∆Yt-8 was significant with the deterministic trend variable,

the Dickey-Fuller critical value is approximately -3.45. And since the t-stat on ρ is less

negative than -3.45, we need to conclude that the series has a unit root and is non-

stationary.


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Empirical Results for Unemployment Rate (UR)

Below is the Autocorrelation Matrix performed on Unemployment rate (UR) lagged till

twelve periods to test for UR stationarity properties. As seen on the Correlogram, there

are high correlations between UR and its 12 lags.

Therefore, we have to perform an autocorrelation matrix for the ∆UR and its lags.

0.75

0.8

0.85

0.9

0.95

1


LAG11

LAG12

Autocorrelation for Unemployment Rate (UR)

Autocorrelation


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Below is the Autocorrelation Matrix performed on change of Unemployment Rate (∆UR)

lagged to twelve periods to test for ∆UR stationarity properties. As seen on the

Correlogram, ∆UR is not highly correlated with its lags and is more stationary.

Therefore, ∆UR should be used to run the regression instead of original UR.

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

LAG 1 LAG 2 LAG 3 LAG 4 LAG 5 LAG 6 LAG 7 LAG 8 LAG 9 LAG 10LAG 11LAG 12

Autocorrelation for ∆ UR

Autocorrelation


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Below is the Dickey-Fuller Test performed on ∆UR.



(T = Time Index/Deterministic Trend, ∆Y = ∆UR)


performed.


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AR(13) ∆Yt-12 0.269711438 Insignificant AR(12) ∆Yt-11 0.874725229 Insignificant AR(11) ∆Yt-10 0.892613833 Insignificant AR(10) ∆Yt-9 0.680654741 Insignificant AR(9) ∆Yt-8 0.019649771 Significant

We first estimated AR(13) with deterministic trend and found the coefficient of ∆Yt-12 to

be insignificant. We then dropped to AR(12) with deterministic trend and found the

coefficient of ∆Yt-11 to be insignificant. We then dropped each variable one by one by

running different multiple regressions for each as shown in the above table, and found

that the coefficient for ∆Yt-8 to be significant.


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We then tested for the significance of the deterministic trend variable and found it was

0.06394 which is greater than the significance level. Therefore, we had to drop the

deterministic trend variable (Time Index).


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After settling on AR(9) where ∆Yt-8 was significant without the deterministic trend

variable, the Dickey-Fuller critical value is approximately -2.89. And since the t-stat on

ρ is less negative than -2,89 we need to conclude that the series has a unit root and

is non-stationary.

Empirical Results for Average Weekly Earnings (AWE)

Below is the Autocorrelation Matrix performed on Average Weekly Earnings (AWE)

lagged till twelve periods to test for AWE stationarity properties. As seen on the

Correlogram, there are high correlations between AWE and its 12 lags.

Therefore, we have to perform an autocorrelation matrix for the ∆AWE and its lags.

0.965

0.97

0.975

0.98

0.985

0.99

0.995

1


LAG11

LAG12

Autocorrelation for AWE

Autocorrelation


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Below is the Autocorrelation Matrix performed on change of Average Weekly Earnings

(∆AWE) lagged till twelve periods to test for ∆AWE stationarity properties. As seen on

the Correlogram, ∆AWE is not highly correlated with its lags and is more stationary.

Therefore, ∆AWE should be used to run the regression instead of original AWE.

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25


LAG11

LAG12

Autocorrelation ∆AWE

Autocorrelation


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Below is the Dickey-Fuller Test performed on ∆AWE.



(T = Time Index/Deterministic Trend, ∆Y = ∆AWE)


performed.


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AR(13) ∆Yt-12 0.970280034 Insignificant AR(12) ∆Yt-11 0.060251745 Insignificant AR(11) ∆Yt-10 0.643007772 Insignificant AR(10) ∆Yt-9 0.439593477 Insignificant AR(9) ∆Yt-8 0.398740404 Insignificant AR(8) ∆Yt-7 0.367358821 Insignificant AR(7) ∆Yt-6 0.612968271 Insignificant AR(6) ∆Yt-5 0.182044324 Insignificant AR(5) ∆Yt-4 0.796172324 Insignificant AR(4) ∆Yt-3 0.419179623 Insignificant AR(3) ∆Yt-2 0.312379828 Insignificant AR(2) ∆Yt-1 0.207203081 Insignificant

We estimated AR(13) till AR(2) where we ran out of lags, and found they were all

insignificant with a deterministic trend as shown below.


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We found that the deterministic trend variable was also insignificant and therefore had

to drop it.


After settling on AR(1) without the deterministic trend variable, the Dickey-Fuller critical

value is approximately -2.89. And since the t-stat on ρ is less negative than -2.89, we

need to conclude that the series has a unit root and is non-stationary.


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5.0 Final Model

Engle Granger Test (Cointegration)

Since RGRT, UR and AWE have unit roots then the usual regression will be misleading

and lead to spurious regression problem. We therefore need to test for cointegration

through Engle-Granger test.

After running regression of RGRT on UR & AWE, the following residual output were

obtained.


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Dickey-Fuller strategy

Dickey-Fuller test was carried out by regressing ∆u on ut-1 and ∆ut-1 till ∆ut-12 as

shown below.

The regression results shown below, was then obtained.


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Cointegration Conclusion

Since the t-stat on ut-1 is -3.07259 which is more negative than the Dickey-Fuller critical

value of -2.89, it means we can reject the unit root hypothesis and conclude that RGRT

is cointegrated to UR and AWE.

ADL Model

Though the data have unit roots, but since they are cointegrated which means the unit

roots in Y and X will cancel out each other. Thefore, ADL Model (Autoregressive

Distributed Lag) can be used. ADL(2,2) model were estimated using OLS as shown

below.

Dependent Variable (Y) = RGRT

Independent Variables (X) = UR and AWE

ADL Model:

∆RGRT = α + δt + ρRGRTt-1 + γ1∆RGRTt-1+ ѲURt + w1∆URt + z1∆URt-1 + QAWEt +

x1∆AWEt + L1∆AWEt-1


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Regression Analysis

A 1% decrease in Unemployment Rate will lead to $719.44 Million increase in

Recreational Goods Retail Turnover (RGRT).

A unit increase in Average Weekly will raise the RGRT by $799.09 Million.

Long Run Multiplier = -Ѳ/ρ = - (-77.7855/-0.5270) = - 145.6 and it means that if

unemployment rate and average weekly earnings increase by 1%, the

equilibrium value of RGRT will decrease by $145.6 Million.

Final Model

∆RGRT = 797.23 + 3.07t -0.5270 RGRTt-1+ 0.08644∆RGRTt-1 -77.79URt -

70.42∆URt + 178.49∆URt-1 + 1.86AWEt + 1.54∆AWEt -1.39 ∆AWEt-1

Forecast for the Quarter February 2014

RGRT = 4558.40 + ∆RGRT = 4558.40 + 97.9459 = $ 4656.3 Million

Note: See Appendix for Calculation


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Limitations

The statistical information shows the model is not accurate due to some

explanatory variables being insignificant such as Average Weekly Earnings.

Microsoft Excel do not allow more than 16 independent variables to be used in

multiple regression and two independent variables lagged to 12 periods can

already come up to 24 variables in total which limits our analysis.

All the data sets had long memory behavior.

After the Autoregressive Models, we found that all the variables had unit roots.

This model has been created based on nominal prices which include inflationary

factors and therefore this might lead to an improper model. The model should

have been build using real data instead to convey results without inflationary

pressures.

The analysis shows that Unemployment Rate and Average Weekly Earnings are

not time series data as the deterministic trend variables was insignificant which in

real practice is not true.

There is omitted variable bias as there are many other independent variables like

inflation that will surely affect the Recreational Goods Retail Turnover which has

not been taken into consideration.


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6.0 Conclusions

Based on our analysis, Tribeco should go forward with expanding their business into the

Adelaide market as the forecasted Recreational Goods Retail shows a promising

turnover of $ 4656.3 Million. This is an increase of $97.9 Million in the February 2014–

Quarter compared to the previous November 2013-Quarter.

We also found that the Unemployment Rate in Adelaide has the biggest impact on

Recreational Goods Retail Turnover compared to Average Weekly Earnings.

Recreational Goods Retail Turnover seemed to be done affected much by the weekly

income of the workers in Adelaide.

Words: 1151


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7.0 Appendix

The frequency for Recreational Good Retail Turnover (RGRT) was transformed into

quarterly series by summing the 3 months respectively as shown below. The sum

function was used in excel for RGRT.


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The frequency for Unemployment Rate (UR) was transformed into quarterly series by

average the 3 months respectively as shown below. The average function in excel was

used for UR.


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Autocorrelation on RGRT

Below is how the Autocorrelation function has been performed whereby the first step

was to lag RGRT from one period to twelve periods.

Autocorrelation Matrix on RGRT


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Below is how the Autocorrelation function on ∆ RGRT has been performed whereby the

first step was to lag ∆RGRT from one period to twelve periods.

Autocorrelation on ∆RGRT


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Dickey-Fuller Test on RGRT

Below are the periods being lagged up to twelve before adding the deterministic trend

variable (Time Index).

Autocorrelation on UR

Below is how the Autocorrelation function has been performed whereby the first step

was to lag UR(%) from one period to twelve periods.


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Autocorrelation Matrix on UR

Below is how the Autocorrelation function on ∆ UR has been performed whereby the

first step was to lag ∆UR from one period to twelve periods.

Autocorrelation Matrix on ∆UR


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Dickey-Fuller Test on UR



Autocorrelation on AWE

Autocorrelation Matrix on AWE


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Below is how the Autocorrelation function on ∆ AWE has been performed whereby the

first step was to lag ∆AWE from one period to twelve periods.

Autocorrelation Matrix on ∆AWE


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Dickey-Fuller Test on AWE



Forecast for Quarter February 2014

Note: The Coefficients were obtained from the Regression shown in the report earlier.

While the values used to forecast February 2014 were obtained using the last data

which is November 2013 lagged to one period and same method has been applied for

the other values obtained for this model.

∆RGRT = 797.23 + 3.07t -0.5270 RGRTt-1+ 0.08644∆RGRTt-1 -77.79URt -70.42∆URt +

178.49∆URt-1 + 1.86AWEt + 1.54∆AWEt -1.39 ∆AWEt-1

= 797.23 + 3.07 (77.0) – 0.5270(4558.4) + 0.08644(223.6) -77.7(6.6) -

70.42(0.21) + 178.49(0.21) + 1.86(1037.50) + 1.54(51) -1.39(51)

∆RGRT = 97.9459

Therefore, RGRT at time, t = 77.0 is ∆RGRT + 4558.40 = 4656.3 Million Dollars.

feasibility study about tribeco company

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