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

We propose to use a variant of the local polynomial Whittle estimator to estimate the memory parameter in volatility for long-memory stochastic volatility models with potential nonstationarity in the volatility process. We show that the estimator is asymptotically normal and capable of obtaining...