We introduce a nonlinear model of stochastic volatility within the class of ?product type? models. It allows different degrees of dependence for the ?raw? series and for the ?squared? series, for instance implying weak dependence in the former and long memory in the latter. We discuss its main...

Econometric interest in the possibility of long memory has developed as a flexible alternative to, or compromise between, the usual short memory or unit root prescriptions, for example in the context of modelling cointegrating or other relationships and in describing the dependence structure of...

We discuss models that impart a form of long memory in raw time series xt or instantaneous functions thereof, in particular . on the basis of a linear or nonlinear model. The capacity of linear models for xt to imply long-memory in nonlinear functions of xt is discussed. Empirical observation...

Much time series data are recorded on economic and financial variables. Statistical modelling of such data is now very well developed, and has applications in forecasting. We review a variety of statistical models from the viewpoint of 'memory', or strength of dependence across time, which is a...

Employing recent results of Robinson (2005) we consider the asymptotic properties ofconditional-sum-of-squares (CSS) estimates of parametric models for stationary timeseries with long memory. CSS estimation has been considered as a rival to Gaussianmaximum likelihood and Whittle estimation of...

For linear processes, semiparametric estimation of the memory parameter, based on the log-periodogramand local Whittle estimators, has been exhaustively examined and their properties are well established.However, except for some specific cases, little is known about the estimation of the memory...

The aggregation procedure when a sample of length N is divided into blocks of length m = o(N), m ? ? and observations in each block are replaced by their sample mean, is widely used in statistical inference. Taqqu, Teverovsky and Willinger (1995), Teverovsky and Taqqu (1997) introduced an...

There has recently been great interest in time series with long memory, namely series whose dependence decays slowly in the sense that autocovariances are not summable and the spectral density is unbounded. This concept has been extended to SCLM (Seasonal/Cyclical Long Memory) where the...

For linear processes, semiparametric estimation of the memory parameter, based on the log-periodogramand local Whittle estimators, has been exhaustively examined and their properties are well established.However, except for some specific cases, little is known about the estimation of the memory...

Moving from univariate to bivariate jointly dependent long memory time series introduces a phase parameter (?), at the frequency of principal interest, zero; for shortmemory series ? = 0 automatically. The latter case has also been stressed under longmemory, along with the 'fractional...