Smooth Transitions, Neural Networks, and Linear Models - CiteSeerX
Smooth Transitions, Neural Networks, and Linear Models - CiteSeerX
Smooth Transitions, Neural Networks, and Linear Models - CiteSeerX
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AEvaluating ForecastsThe performance measures used in this paper are the following.1. Normalized root mean squared error (nRMSE):ÒÊÅË´µ ÚÙÙØ½Ì Ø ¼ ¿È Ì ØØ ¼ ¾ Ø·Ø (20) ݾwhere Ý ¾ is the estimated in-sample unconditional variance of the series.2. Mean Absolute Error (MAE):Å´µ Ì ½Ì Ø Ø·Ø (21)¼ ¿ØØ ¼3. Median Absolute Deviation (MAD):Å´µ median´ Ø·Ø median´ Ø·Ø µµ (22)The MAD is as a measure that is robust to outliers.4. The proportion of times the sign of excess returns is correctly forecasted (SIGN):ËÁÆ´µ Ì½Æ Ø (23)Ì Ø ¼ ¿ØØ ¼whereÆ Ø ½ if Ý Ø· Ý Ø·Ø ¼;¼otherwise.BForecasting with Nonlinear <strong>Models</strong>Multi-step forecasting with nonlinear models is more challenging than forecasting with linear models.See, for example, Granger <strong>and</strong> Teräsvirta (1993, Section 8.1) for a general discussion.19
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