A test for the presence of a stationary first-order autoregressive process embedded in white noise is constructed so as to be relatively powerful when the autoregressive parameter is close to one. This is done by setting up the autoregression in such a way that it reduces to a constant, instead...

Nonlinear functions of multivariate financial time series can exhibit longmemory and fractional cointegration. However, tools for analysingthese phenomena have principally been justified under assumptionsthat are invalid in this setting. Determination of asymptotic theoryunder more plausible...

Asset returns have a very complicated dynamic pattern. Yet they display regularity across different assets and periods. We consider a new family of volatility models which account for such patterns, focussing in particular on the long memory nature of asset returns volatility. We propose an...

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 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...

A valid asymptotic expansion for the covariance of functions of multivariate normal vectors is applied to approximate autovariances of time series generated by nonlinear transformation of Gaussian latent variates, and nonlinear functions of these, with special reference to long memory stochastic...

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