This paper considers the short- and long-memory linear processes with GARCH (1,1) noises. The functional limit distributions of the partial sum and the sample autocovariances are derived when the tail index α is in (0,2), equal to 2, and in (2,∞), respectively. The partial sum weakly...

We prove the uniqueness of linear i.i.d. representations of heavy-tailed processes whose distribution belongs to the domain of attraction of an $\alpha$-stable law, with $\alpha2$. This shows the possibility to identify nonparametrically both the sequence of two-sided moving average coefficients...

We establish asymptotic normality of weighted sums of stationary linear processes with general triangular array weights and when the innovations in the linear process are martingale differences. The results are obtained under minimal conditions on the weights and as long as the process of...

This paper proposes two simple and new specification tests based on the use of an orthogonal series for a considerable class of cointegrated time series models with endogeneity and nonsta-tionarity. The paper then establishes an asymptotic theory for each of the proposed tests. The first test is...

In this paper, we estimate the Shannon entropy S(f)=-E[log(f(x))] of a one-sided linear process with probability density function f(x). We employ the integral estimator Sn(f), which utilizes the standard kernel density estimator fn(x) of f(x). We show that Sn(f) converges to S(f) almost surely...

This paper develops a new test for a unit root in autoregressive models with serially correlated errors. The test is based on the ``empirical'' Cressie-Read statistic and uses a sieve approximation to eliminate the bias in the asymptotic distribution of the test due to presence of serial...