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...

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...

his paper deal with aggregation of AR(1) micro variables driven by a common and idiosyncratic shock with random coefficients. We provide a rigorous analysis, based on results on sums of r.v.'s with a possibly finite first moment, of the aggregate variance and spectral density, as the number of...

Sufficient conditions for strict stationarity of ARCH(8) are established, without imposing covariance stationarity and for any specification of the conditional second moment coefficients. GARCH(p,q) as well as the case of hyperbolically decaying coefficients are included, such as the...

We study the impact of large cross-sections of contemporaneous aggregation of GARCH processes and of dynamic GARCH factor models. The results crucially depend on the shape of the cross-sectional distribution of the GARCH coefficients and on the cross-sectional dependence properties of the...

We attempt to present Denis Sargan's work in some kind of historical perspective, in two ways. First, we discuss some previous members of the Tooke Chair of Economic Science and Statistics, which was founded in 1859 and which Sargan held. Second, we discuss one of his artices 'Asymptotic Theory...

Asymptotic inference on nonstationary fractional time series models, including cointegrated ones, is proceeding along two routes, determined by alternative definitions of nonstationary processes. We derive bounds for the mean squared error of the difference between (possibly tapered) discrete...

Fractional cointegration is viewed from a semiparametric viewpoint as a narrow-band phenomenon at frequency zero. We study a narrow-band frequency domain least squares estimate of the cointegrating vector, and related semiparametric methods of inference for testing the memory of observables and...