%0 Journal Article %T Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity %A Isao Ishida %A Virmantas Kvedaras %J Econometrics %P 2-54 %D 2015 %I MDPI AG %R 10.3390/econometrics3010002 %X We introduce and investigate some properties of a class of nonlinear time series models based on the moving sample quantiles in the autoregressive data generating process. We derive a test fit to detect this type of nonlinearity. Using the daily realized volatility data of Standard & PoorĄ¯s 500 (S&P 500) and several other indices, we obtained good performance using these models in an out-of-sample forecasting exercise compared with the forecasts obtained based on the usual linear heterogeneous autoregressive and other models of realized volatility. %K forecasting %K moving quantiles %K non-linearity %K realized volatility %K test %U http://www.mdpi.com/2225-1146/3/1/2