This paper proposes bootstrap assisted specification tests for the autoregressive fractionally integrated moving average model based on the Bartlett <italic>T</italic>-process with estimated parameters whose limiting distribution under the null depends on the estimated model and the estimation method employed....

In a multiple time series regression model the residuals are heteroskedastic and serially correlated of unknown form. GLS estimates of the regression coefficients using kernel regression and spectral methods are shown to be adaptive, in the sense of having the same asymptotic distribution, to...