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BITRE | Report 115Root Mean Square ErrorThe root mean square error (RMSE), MSE .Mean Absolute Percent Error100∑ yn = 1nThe mean absolute percent prediction error (MAPE), ( y − yˆ)The summation ignores observations where yt = 0.Mean Absolute Error1 nThe mean absolute prediction error, ∑ =y t− yˆt 1nR-SquareThe R 2 statistic, R 2 = 1-SSE / SST. If the model fits the series badly, the model errorsum of squares, SSE, may be larger than SST and the R 2 statistic will be negative.Adjusted R-SquareThe adjusted R 2 statistic, 1 - ([(n-1)/(n-k)]) (1- R 2 ).Amemiya’s Adjusted R-SquareAmemiya’s adjusted R 2 , 1 - ([(n+k)/(n-k)]) (1 - R 2 ).Random Walk R-SquareThe random walk R 2 statistic (Harvey’s R 2 statistic using the random walk model forcomparison), 1 - ([(n-1)/n]) SSE / RWSSE, where=nRWSSE ∑ ( − − ) 2=yt 2 tyt−1μ , and 1 nμ = ∑ =( y −−)t ty .2 t 1n − 1Akaike’s Information CriterionAkaike’s information criterion (AIC), n ln( MSE ) + 2 k.Schwarz Bayesian Information CriterionSchwarz Bayesian information criterion (SBC or BIC), n ln( MSE ) + k ln( n ).Amemiya’s Prediction CriterionAmemiya’s prediction criterion, [1/n] SST ([(n+k)/(n-k)])(1- R2) = ([(n+k)/(n-k )]) [1/n]SSE.Maximum ErrorThe largest prediction error.Minimum ErrorThe smallest prediction error.Maximum Percent ErrorThe largest percent prediction error, 100max ( y t− yˆt)/y t).The summation ignores observations where y t= 0.Minimum Percent ErrorThe smallest percent prediction error, 100 min( y t− yˆt)/y t).The summation ignores observations where y t= 0.t.tt/ yt.258