an:05259637
Zbl 1260.91184
Lee, Jin
Fractionally integrated long horizon regressions
EN
Stud. Nonlinear Dyn. Econom. 11, No. 1, Article 6, 20 p. (2007).
00217761
2007
j
91B82
Summary: We consider long horizon regression models where the disturbance and the predictor are possibly fractionally integrated. Asymptotic distributions of the OLS estimator and of the test statistic are given. It is found that the t-statistic diverges at the rate of square root of \(T\), where \(T\) is the sample size. Thus, it is desirable to use the scaled test statistic, as it converges to a well-defined limit, which depends on the memory parameters through the functionals on the fractional Wiener processes. Simulation studies present some empirical distributions of the scaled test statistic according to different values of the memory parameters. The proposed model with fractional processes is empirically more tractable than the model with local to unity processes, since memory parameters are consistently estimable unlike localizing parameters in the latter model.