We establish sufficient conditions on durations that arestationary with finite variance and memory parameter $d \in[0,1/2)$ to ensure that the corresponding counting process $N(t)$satisfies $Var N(t) \sim C t^{2d+1}$ ($Cgt;0$) as $t\rightarrow \infty$, with the same memory parameter $d...

We establish sufficient conditions on durations that are stationary with finite variance and memory parameter d 2 [0; 1=2) to ensure that the corresponding counting process N(t) satisfies VarN(t) raquo; Ct2d+1 (C gt; 0) as t ! 1, with the same memory parameter d 2 [0; 1=2) that was assumed for the...

We study the effects of trade duration properties on dependence in counts (number of trans-actions) and thus on dependence in volatility of returns. A return model is established to link counts and volatility. We present theorems as well as a conjecture relating properties of durations to long...

We consider semiparametric estimation of the memory parameter in a long memorystochastic volatility model. We study the estimator based on a log periodogramregression as originally proposed by Geweke and Porter-Hudak (1983,Journal of Time Series Analysis 4, 221 238). Expressions for the...

We consider semiparametric estimation of the memory parameter in a long memorystochastic volatility model. We study the estimator based on a log periodogramregression as originally proposed by Geweke and Porter-Hudak (1983,Journal of Time Series Analysis 4, 221Atilde; Acirc;cent;Atilde; Acirc; Atilde;...

We consider the problem of selecting the number of frequencies, m, in a log-periodogram regression estimator of the memory parameter d of a Gaussian long-memory time series. It is known that under certain conditions the optimal m, minimizing the mean squared error of the corresponding estimator...