Cointegration of nonstationary time series is considered in a fractional context. Both the observable series and the cointegrating error can be fractional processes. The familiar situation in which the respective integration orders are 1 and 0 is nested, but these values have typically been...

In a number of semiparametric models, smoothing seems necessary in order to obtain estimates of the parametric component which are asymptotically normal and converge at parametric rate. However, smoothing can inflate the error in the normal approximation, so that refined approximations are of...

Asset returns are frequently assumed to be determined by one or more common factors. We consider a bivariate factor model where the unobservable common factor and idiosyncratic errors are stationary and serially uncorrelated but have strong dependence in higher moments. Stochastic volatility...

We derive an optimal kernel K([lambda]) for spectral averaging in the neighbourhood of a spectral peak corresponding to long-range dependence. Unusually, K([lambda]) --> 0 as [lambda] --> 0.

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...

Much time series data are recorded on economic and financial variables. Statistical modeling 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...

We consider a multivariate continuous-time process, generated by a system of linear stochastic differential equations, driven by white noise, and involving coefficients that possibly vary over time. The process is observable only at discrete, but not necessarily equally-spaced, time points...

We show that it is possible to adapt to nonparametric disturbance autocorrelation in time series regression in the presence of long memory in both regressors and disturbances by using a smoothed nonparametric spectrum estimate in frequency-domain generalized least squares. When the collective...

Strong consistency and asymptotic normality of the Gaussian pseudo-maximum likelihood estimate of the parameters in a wide class of ARCH($ \infty $) processes are established. The conditions are shown to hold in case of exponential and hyperbolic decay in the ARCH weights, though in the latter...