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...

We consider semiparametric estimation of the memory parameter in a model that includes as special cases both long-memory stochastic volatility and fractionally integrated exponential GARCH (FIEGARCH) models. Under our general model the logarithms of the squared returns can be decomposed into the...

We consider semiparametric fractional exponential (FEXP) estimators of the memory parameter d for a potentially non-stationary linear long-memory time series with additive polynomial trend. We use differencing to annihilate the polynomial trend, followed by tapering to handle the potential...

This paper deals with a general class of observation-driven time series models with a special focus on time series of counts. We provide conditions under which there exist strict-sense stationary and ergodic versions of such processes. The consistency of the maximum likelihood estimators is then...

This paper discusses quantitative bounds on the convergence rates of Markov chains, under conditions implying polynomial convergence rates. This paper extends an earlier work by Roberts and Tweedie (Stochastic Process. Appl. 80(2) (1999) 211), which provides quantitative bounds for the total...