Heteroscedastic modelling via the autoregressive conditional variance subspace

The paper deals with nonparametric estimation of the conditional variance of a time series based on a nonlinear autoregressive model in the squared innovation time series, which does not require specification of a model. We introduce a notion called the autoregressive central variance subspace (ACVS) to obtain the information included in the conditional variance of time series data. We use the squared time series to identify the ACVS by a nonparametric kernel method. In addition, we simultaneously estimate the unknown dimension and lag of the ACVS by a modified information criterion. Finally, we investigate the performance of all the estimators including the ACVS through simulations and a real analysis, which suggests implementing a new dimension reduction approach to modelling time series data that exhibits volatility. (C) 2014 Statistical Society of Canada