Seasonalized Time Series Regression Forecasting Details

1. Determine the order of seasonality (m) via inspection of the data, and via inspection of the time series plot. In the case of this problem, it is four.

2. For each unique season, compute a seasonal index (SI), by dividing the average demand for each unique season by the average demand for all periods. In the case of this problem, the four seasonal indices are 0.8228, 1.1089, 1.2581 and .8103.

3. The actual demand is then deseasonalized by dividing the actual demand by its seasonal index.

4. The above step filters out seasonality and isolates the trend. In this case, it is noticed that the trend is nonlinear.

5. Given the nonlinear trend, a quadratic model is chosen to describe the change in deseasonalized demand over time. “i” is used to note the period, while “Y_i” is used to describe deseasonalized demand for period i. As such, the following model is used for estimation of the deseasonalized, nonlinear trend: Y_i = a + bi + ci². Regression is used to find parameter values for a, b and c. The parameter values are then used to “fit” the trend for the given data set. For this problem, a = 995.56, b = 0.9768 and c = 0.3698.

6. Now that the trend component has been captured, it can be combined with the seasonal component to “fit” the estimated time series. Multiplying the trend component computed directly above by the seasonal index for the appropriate period accomplishes this.

7. “Fits” have been computed. Forecasts are made by extending the “fits” into the future.