Models based on factors such as size, value, or momentum are ubiquitous in asset pricing. Therefore, portfolio allocation and risk management require estimates of the volatility of these factors. While realized volatility has become a standard tool for liquid individual assets, this measure is...

Researchers and practitioners employ a variety of time-series processes to forecast betas, using either short-memory models or implicitly imposing infinite memory. We find that both approaches are inadequate: beta factors show consistent long-memory properties. For the vast majority of stocks,...

Researchers and practitioners employ a variety of time-series processes to forecast betas, using either short-memory models or implicitly imposing infinite memory. We find that both approaches are inadequate: beta factors show consistent long-memory properties. For the vast majority of stocks,...

This paper derives the memory of the product series xtyt, where xt and yt are stationary long memory time series of orders dx and dy, respectively. Special attention is paid to the case of squared series and products of series driven by a common stochastic factor. It is found that the memory of...

We propose an automatic model order selection procedure for k-factor GARMA processes. The procedure is based on sequential tests of the maximum of the periodogram and semiparametric estimators of the model parameters. As a byproduct, we introduce a generalized version of Walker's large sample...

The focus of the volatility literature on forecasting and the predominance of the conceptually simpler HAR model over long memory stochastic volatility models has led to the fact that the actual degree of memory estimates has rarely been considered. Estimates in the literature range roughly...