Statistica Sinica 25 (2015), 1025-1044
Abstract: Consistently determining the number of factors plays an important role in factor modelling for volatility of multivariate time series. In this paper, the modelling is extended to handle the nonstationary time series scenario with conditional heteroscedasticity. Then a ridge-type ratio estimate and a BIC-type estimate are proposed and proved to be consistent. Their finite sample performance is examined through simulations and the analysis of two data sets. An observation from the numerical studies is, that unlike the cases with stationary and homoscedastic sequences in the literature, the dimensionality blessing no longer holds for the ratio-based estimates, but still does for the BIC-type estimate.
Key words and phrases: BIC-type criterion, dimension reduction, eigenanalysis, factor modelling, multivariate volatility, nonstationarity, ratio estimate.