SOME LIMIT THEORY FOR AUTOCOVARIANCES WHOSE ORDER DEPENDS ON SAMPLE SIZE

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TESTING FOR LONG MEMORY (2007, methodology): “(iv) xt is a p-dimensional vector of deterministic regressors satisfying the conditions in equations (15) and (16) of Harris, McCabe and Leybourne (2003) , (v) P∞ j=1 lnj · ¯ ¯γj ¯ ¯ < ∞,”
A Powerful Test for Linearity When the Order of Integration is Unknown (2007, methodology): “For the latter, in the rst step we employed the stationarity test of Harris et al. (2003), given by (16) above, which has the attractive property of being asymptotically standard normally distributed under the null of linear or nonlinear stationarity (H0;0 or H1;0); see the proof of Lemma 1 (a) in…”