Hockey Memorabilia

Hockey Fans

Introduction
Preliminary Analysis
Regression Models
Exponential Smoothing
ARIMA Models
General Discussion
Conclusion
Appendix A
Appendix B
Appendix C
Appendix D
References Principles of Statistics
Amazon.com

Exponential Smoothing

Regular moving average forecasts use the mean of the past k observations as the forecast. This implies equal weight (1/k) to all k data points. With the data we have, it is reasonable to assume that the most recent observations are probably the best approximations for forecasts. The NHL has changed tremendously over the past 83 years and its actions in the recent past have a much larger impact on its present and future state than the going further back in time. Exponential smoothing methods provide a weight scheme that incorporates decreasing weights as observations grow older. Simple exponential smoothing assumes that there are no trend or seasonal aspects in the data and that the level of the series changes slowly over time.

Simple Exponential Smoothing

Since the alpha value that minimizes SSE is 1.0 (Appendix C-1), we see that the simple exponential smoothing is just the Naive forecast. This assumes that the forecast for the next time period will be equal to the previous observed value. The graph below shows this result. As we can see the graph shows that there is no smoothing in the forecast, and shows that exponential smoothing is equivalent to using the last observation as a forecast. Holt's Method

Double exponential smoothing allows forecasting data with trends. Since our data could possibly contain an underlying trend component, we conduct an analysis using Holt's Method. The results from this analysis can be viewed in Appendix C-2. We notice that the Sum of Squared Errors is minimized when alpha is 1.00 and gamma is 0.00. This is a similar result to the one we saw in the single exponential method. Here we get the same result as a Naive Forecast Method 1. The graph shows that the line (blue) representing the fitted games per game using Holt's method and the line (red) representing the fitted games per game using simple exponential smoothing, are identical. It shows us that the forecast for the next time period is the observed value of the previous time period. Thus, we conclude that there is no identifiable trend in the data. 