Montag, 30. Mai 2016, 16:45 - 18:15 iCal

ISOR Colloquium

"Limit theory for functionals of linear processes at the boundary of non-stationarity (joint work with I. Kasparis)"

Speaker: James Duffy (Univ. Oxford)

Lecture Hall 12 OMP1 (2nd Floor)
Oskar-Morgenstern-Platz 1, 1090 Vienna


We develop limit theory for standardised sums of non-linear transformations of (arrays of) linear processes that lie at the 'boundary' demarcating stationarity from non-stationarity. This includes, as leading examples, autoregressive processes with roots drifting slowly towards unity ('moderate deviations from unity' in the terminology of Phillips & Magdalinos, 2007, JoE), and fractionally integrated processes with d = 0.5.

On the one hand, these processes are sufficiently dependent to be non-stationary, and thus resist the application of limit theorems appropriate to stationary linear processes. On the other hand, their dependence is also sufficiently weak to prevent the appeal to convergence results that rely on the finite-dimensional convergence of standardised processes to tight limits (e.g. Pötscher, 2004, ET).

The present work aims to fill this significant lacuna in the existing theory. As discussed in Duffy (2015), one application of these results is to proving the uniform validity of standard testing procedures in a nonparametric predictive regression, in the sense that the size of these tests controlled, asymptotically, uniformly in the parameter governing the degree of the persistence of the regressor. [I will discuss this in some detail in my presentation.]

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Institut für Statistik und Operations Research


Mag. Vera Lehmwald
Fakultät für Wirtschaftswissenschaften
Institut für Statistik und Operations Research
+43 1 4277 38651