We study the asymptotic behaviour of frequency domain maximum likelihood estimators of mis-specified models of long memory Gaussian series. We show that even if the long memory structure of the time series is correctly specified, mis-specification of the short memory dynamics may result in...

We make three contributions to using the variance ratio statistic at large horizons. Allowing for general heteroscedasticity in the data, we obtain the asymptotic distribution of the statistic when the horizon k is increasing with the sample size n but at a slower rate so that k/n¨0. The test...

We consider a common components model for multivariate fractional cointegration, in which the s=1 components have different memory parameters. The cointegrating rank is allowed to exceed 1. The true cointegrating vectors can be decomposed into orthogonal fractional cointegrating subspaces such...

We study the effects of trade duration properties on dependence in counts (number of transactions) 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 study the modeling of large data sets of high frequency returns using a long memory stochastic volatility (LMSV) model. Issues pertaining to estimation and forecasting of large datasets using the LMSV model are studied in detail. Furthermore, a new method of de-seasonalizing the volatility in...

We establish sufficient conditions on durations that are stationary with finite variance and memory parameter $d \in [0,1/2)$ to ensure that the corresponding counting process $N(t)$ satisfies $\textmd{Var} \, N(t) \sim C t^{2d+1}$ ($C0$) as $t \rightarrow \infty$, with the same memory parameter...

We establish sufficient conditions on durations that are stationary with finite variance and memory parameter <inline-graphic>null</inline-graphic> to ensure that the corresponding counting process <italic>N</italic>(<italic>t</italic>) satisfies Var <italic>N</italic>(<italic>t</italic>) ~ <italic>Ct</italic>² (<italic>C</italic> 0) as <italic>t</italic> → ∞, with the same memory parameter <inline-graphic>null</inline-graphic> that was assumed for the durations. Thus,...

It is generally accepted that many time series of practical interest exhibit strong dependence, i.e., long memory. For such series, the sample autocorrelations decay slowly and log-log periodogram plots indicate a straight-line relationship. This necessitates a class of models for describing...