The paper presents a comparative study on the performance of commonly used estimators of the fractional order of integration when data is contaminated by noise. In particular, measurement errors, additive outliers, temporary change outliers, and structural change outliers are addressed. It...

We consider semiparametric estimation in time series regression in the presence of long range dependence in both the errors and the stochastic regressors. A central limit theorem is established for a class of semiparametric frequency domain weighted least squares estimates, which includes both...

Recent literature shows that embedding fractionally integrated time series models with spectral poles at the long-run and/or seasonal frequencies in autoregressive frameworks leads to estimators and test statistics with non-standard limiting distributions that must be simulated on a case-by-case...

We derive a functional central limit theorem for the empirical spectral measure or discretely averaged (integrated) periodogram of a multivariate long range dependent stochastic process in a degenerating neighborhood of the origin. We show that, under certain restrictions on the memory...

We introduce a multivariate Lagrange Multiplier (LM) test for fractional integration. We derive and analyze the LM statistic and show that it is asymptotically chi-squared distributed under local alternatives, and that, under Gaussianity, the LM test is asymptotically efficient against local...