Expected Idiosyncratic Volatility

We use 92,632,873 daily returns for 33,010 US firms to establish the best forecasting model for realized idiosyncratic variances. Comparing forecasts from 10 different models, we find that the most popular models, the martingale and GARCH type models, perform worst. Using the root-mean-squared-error (RMSE) to judge model performance, ARMA(1,1) models perform the best for about 40% of the firms in both in-sample and out-of-sample tests. The ARMA(1,1) model delivers an average RMSE that is statistically significantly lower than all alternative models, and also performs well when not the very best. Its forecasts reverse large, unexpected shocks to realized variances. When using this model, or any model except the martingale model, to revisit the relation between idiosyncratic risk and returns, we fail to find a significant relation