In order to describe the comovements in both conditional mean and conditional variance of high dimensional nonstationary time series by dimension reduction, we introduce the conditional heteroscedasticity with factor structure to the error correction model. The new model is called the error correction volatility factor model. Some specification and estimation approaches are developed. In particular, the determination of the number of factors is discussed. Our setting is general in the sense that we impose neither i.i.d assumption on idiosyncratic components in the factor structure nor independence between factors and idiosyncratic errors. We illustrate the proposed approach with a Monte Carlo simulation and a real data example.
- dimension reduction
- error correction-volatility factor model
- penalized goodness-of-fit criteria
- model selection