The LM type linearity test for STAR nonlinearities is severely distorted when the process is governed by conditional heteroskedasticity. In order to correct the test we propose a parametric bootstrap. It is shown, by means of Monte Carlo methods, that the bootstrap test is almost exact.

This paper examines the predictability memory of fractionally integrated ARMA processes. Very long memory is found for positively fractionally integrated processes with large positive AR parameters. However, negative AR parameters absorb, to a great extent, the memory generated by a positive...

Since the true nature of a time series process is often unknown it is important to understand the effects of model choice. This paper examines how the choice between modelling stationary time series as ARMA or ARFIMA processes affects the accuracy of forecasts. This is done, for first-order...

This paper demonstrates that long memory leads to spurious rejection of the linearity hypothesis, when a STAR specification constitutes the alternative.

Asymptotic tests for fractional integration are usually badly sized in small samples, even for normally distributed processes. Furthermore, tests that are well-sized under normality may be severely distorted by non-normalities and ARCH errors. This paper demonstrates how the bootstrap can be...

Asymptotic tests for fractional integration, such as the Geweke-Porter-Hudak test, the modified rescaled range test and Lagrange multiplier type tests, exhibit size-distortions in small-samples. This paper investigates a parametric bootstrap testing procedure, for size-correction, by means of a...