The Local Whittle Estimator of Long-Memory Stochastic Volatility

We propose a new semiparametric estimator of the degree of persistencein volatility for long memory stochastic volatility (LMSV) models.The estimator uses the periodogram of the log squared returnsin a local Whittle criterion which explicitly accounts for thenoise term in the LMSV model. Finite-sample and asymptotic standarderrors for the estimator are provided. An extensive simulationstudy reveals that the local Whittle estimator is much lessbiased and that the finite-sample standard errors yield moreaccurate confidence intervals than the widely-used GPH estimator.The estimator is also found to be robust against possible leverageeffects. In an empirical analysis of the daily Deutsche Mark/USDollar exchange rate, the new estimator indicates stronger persistencein volatility than the GPH estimator, provided that a largenumber of frequencies is used.     

Asymptotics for duration-driven long range dependent processes

We consider processes with second order long range dependence resulting from heavy tailed durations. We refer to this phenomenon as duration-driven long range dependence (DDLRD), as opposed to the more widely studied linear long range dependence based on fractional differencing of an i.i.d. process. We consider in detail two specific processes having DDLRD, originally presented in Taqqu and Levy [1986. Using renewal processes to generate long-range dependence and high variability. Dependence in Probability and Statistics. Birkhauser, Boston, pp. 73–89], and Parke [1999. What is fractional integration? Review of Economics and Statistics 81, 632–638]. For these processes, we obtain the limiting distribution of suitably standardized discrete Fourier transforms (DFTs) and sample autocovariances. At low frequencies, the standardized DFTs converge to a stable law, as do the standardized sample autocovariances at fixed lags. Finite collections of standardized sample autocovariances at a fixed set of lags converge to a degenerate distribution. The standardized DFTs at high frequencies converge to a Gaussian law. Our asymptotic results are strikingly similar for the two DDLRD processes studied. We calibrate our asymptotic results with a simulation study which also investigates the properties of the semiparametric log periodogram regression estimator of the memory parameter.     

Multiple-Predictor Regressions: Hypothesis Testing

We propose a new hypothesis-testing method for multipredictorregressions in small samples, where the dependent variable isregressed on lagged variables that are autoregressive. The newtest is based on the augmented regression method (Amihud andHurvich, 2004), which produces reduced-bias coefficients andis easy to implement. The method's usefulness is demonstratedby simulations and by testing a model where stock returns arepredicted by two variables, income-to-consumption and dividendyield.     

Predictive regression with order-p autoregressive predictors

Studies of predictive regressions analyze the case where y_t is predicted by x_t ? 1 with x_t being first-order autoregressive, AR(1). Under some conditions, the OLS-estimated predictive coefficient is known to be biased. We analyze a predictive model where y_t is predicted by x_t ? 1, x_t ? 2,… x_t ? p with x_t being autoregressive of order p, AR(p) with p > 1. We develop a generalized augmented regression method that produces a reduced-bias point estimate of the predictive coefficients and derive an appropriate hypothesis testing procedure. We apply our method to the prediction of quarterly stock returns by dividend yield, which is apparently AR(2). Using our method results in the AR(2) predictor series having insignificant effect, although under OLS, or the commonly assumed AR(1) structure, the predictive model is significant. We also generalize our method to the case of multiple AR(p) predictors.