Although it is clear that the volatility of asset returns is serially correlated, there is no general agreement as to the most appropriate parametric model for characterizing this temporal dependence. In this paper, we propose a simple way of modeling financial market volatility using high-frequency data. The method avoids using a tight parametric model by instead simply fitting a long autoregression to log-squared, squared, or absolute high-frequency returns. This can either be estimated by the usual time domain method, or alternatively the autoregressive coefficients can be backed out from the smoothed periodogram estimate of the spectrum of log-squared, squared, or absolute returns. We show how this approach can be used to construct volatility forecasts, which compare favorably with some leading alternatives in an out-of-sample forecasting exercise.

We consider forecasting with uncertainty about the choice of predictor variables. The researcher wants to select a model, estimate the parameters, and use this for forecasting. We investigate the dis-tributional properties of a number of different schemes for model choice and parameter estimation: in-sample model selection using the Akaike information criterion, out-of-sample model selection, and splitting the data into subsamples for model selection and parameter estimation. Using a weak-predictor local asymptotic scheme, we provide a representation result that facilitates comparison of the distributional properties of the procedures and their associated forecast risks. We develop a sim-ulation procedure that improves the accuracy of the out-of-sample and split-sample methods uni-formly over the local parameter space. We also examine how bootstrap aggregation (bagging) affects the local asymptotic risk of the estimators and their associated forecasts. Numerically, we find that for many values of the local parameter, the out-of-sample and split-sample schemes perform poorly if implemented in the conventional way. But they perform well, if implemented in conjunction with our risk-reduction method or bagging.

Long-term nominal interest rates are surprisingly sensitive to high-frequency (daily or monthly) movements in short-term rates. Since 2000, this high-frequency sensitivity has grown even stronger in U.S. data. By contrast, the association between low-frequency changes (at 6- or 12-month horizons) in long- and short-term rates, which was also strong before 2000, has weakened substantially. This puzzling post-2000 pattern arises because increases in short rates temporarily raise the term premium component of long-term yields, leading long rates to temporarily overreact to changes in short rates. The frequency-dependent excess sensitivity of long-term rates that we observe in recent years is best understood using a model in which (i) declines in short rates trigger “rate-amplifying” shifts in investor demand for long-term bonds, and (ii) the arbitrage response to these demand shifts is both limited and slow. We study, theoretically and empirically, how such rate-amplifying demand can be traced to mortgage-refinancing activity, investors who extrapolate recent changes in short rates, and investors who “reach for yield” when short rates fall. We discuss the implications of our findings for the validity of event study methodologies and the transmission of monetary policy.