In order to plan for the feasibility of the expansion, they needed to forecast their sales for the period. As a reference to their sales forecast, the Recreational Good Retail Turnover estimate for 2010 is required.
The Recreational Good Retail Turnover (RGRT) dataset is gathered starting April 1982 until the end of March 2010. Figure 1 is the graphical summary of the data per quarter of each year. It can be observed that the trend of RGRT is increasing every year with seasonal peaks by the fourth quarter of each year. Furthermore, it can be observed that a linear trend is visible starting from the year 2000 up to the present, thus, these dataset shall be significant.
Accompanying the RGRT is the Consumer Price Index (CPI) dataset is gathered from the start of September 1948 until the end of March 2010. The CPI is collected every quarter of the year. It can be observed that the CPI is also increasing through time.
The method used for forecasting RGRT in this paper is autoregression (AR) model of univariate analysis. Using Ordinary Least Squares (OLS), the AR(pmax) of RGRT is estimated. Lower order AR models are then determined until such time that Yp-1 is statistically significant or the P-value for testing Yp-1 = 0 is less than the chosen significance level of 0.05.
In order to corrIn order to correct for the seasonality of the RGRT dataset, a method of calculating seasonal index is applied, wherein, the average seasonal index for each period is used as a multiplier for the regression equation (Rowbotham, Galloway, & Azhashemi, 2007).
Other factors that can affect the RGRT are also checked for their statistical significance. These factors are unemployment rate, consumer price index and average weekly earnings of the population.
Evaluations of results
The unemployment rate, consumer price index and average weekly earnings are significant to the calculation for determination of RGRT forecast values. Appendix A shows the summary of fitted values for each factor. All factors show an increasing trend through time. This means that the increasing trend of RGRT is justified and it is safe to assume that there are no significant downward slope for the year to come.
The AR model for RGRT is determined to be in the first-order as estimated by OLS. The RGRT model reduces to Yt = + Yt-1 + et where the fitted values are = 760.6366 and = 16.8146. The P-value for the equation is less than the signifiance level of 0.05 such that the model is considered as statistically significant. Appendix A provides the summary of other values of the regression equation for RGRT. The plot for the estimated values of the trend component is reflected in Figure 3.
In order to allocate for the seasonality of RGRT, the average index per quarter is calculated. The index is computed as the predicted y-values using the regression equation divided by the actual y-values from the dataset (Rowbotham, Gall