9. Modeling: Exponential Smoothing (Holt Winters) - eliasmelul/CrimeInvestigation GitHub Wiki

Figure 17. Holt Winter Actual (black) and Fitted (red) timeseries

As we can observe, the exponential smoothing model fits the values pretty accurately. It follows the yearly seasonality, and overestimates the effect of the 7-day seasonality. However, the volatility of the fitted values about the seasonality moving average seems to be decreasing towards the dates closer to the present.

Figure 18. Holt Winters Forecast of 365 days (blue and gray for actual values and the 95% confidence intervals around those values respectively) NB: Glitch in HW model shifted time-values (x-axis) by 182 days

Holt Winters Model accuracy:

 ME          RMSE         MAE           MPE        MAPE         MASE          ACF1
 -1.028769   31.54892     21.82376     -1.224957   8.383455     0.7280578     0.08765785

This forecasting model allows for better predictions than the Linear Regression models, but, less intuitive ones. This model has a mean absolute percentage error (MAPE) of 8.38. It also has a root mean square error (RMSE) of 31.54 - the standard deviation of the residuals.