Efficiency improvements in inference on stationary and nonstationary fractional time series

By Peter M. Robinson. 2004

47 citations recorded by the source corpus.

We consider a time series model involving a fractional stochastic component, whose integration order can lie in the stationary/invertible or nonstationary regions and be unknown, and an additive deterministic component consisting of a generalized polynomial. The model can thus incorporate competing descriptions of trending behavior. The stationary input to the stochastic component has parametric autocorrelation, but innovation with distribution of unknown form. The model is thus semiparametric, and we develop estimates of the parametric component which are asymptotically normal and achieve an M-estimation efficiency bound, equal to that found in work using an adaptive LAM/LAN approach. A major technical feature which we treat is the effect of truncating the autoregressive representation in order to form innovation proxies. This is relevant also when the innovation density is parameterized, and we provide a result for that case also. Our semiparametric estimates employ nonparametric series estimation, which avoids some complications and conditions in kernel approaches featured in much work on adaptive estimation of time series models; our work thus also contributes to methods and theory for nonfractional time series models, such as autoregressive moving averages. A Monte Carlo study of finite sample performance of the semiparametric estimates is included.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e6efa66438daedde8983428b302624a419c17d17

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Finance

In Statistics and Probability

Citations in the corpus

Asymptotic theory of least squares estimators for nearly unstable processes under strong dependence (2007, methodology): “, Brockwell and Davis [3] for an overview and Robinson [23] for further discussion about Type-I and Type-II fractional integrated noise; note that the parametrization d = H − 1/2 is more commonly used in the econometric literature).”
TESTING FOR WHITE NOISE UNDER UNKNOWN DEPENDENCE AND ITS APPLICATIONS TO DIAGNOSTIC CHECKING FOR TIME SERIES MODELS (2010, background): “…′=1 ∞ ∑ k,k′=0 ψk,tψk′,t ′E(ut ut ′u−ku−k′) = n−2 n ∑ t=1 ∞ ∑ k=0 ψ2k,tσ 4 +n−2 n ∑ t,t ′=1 ∞ ∑ k,k′=0 ψk,tψk′,t ′cum(ut ,ut ′ ,u−k ,u−k′) = O( logn/n2 +n−1)= O(n−1), where we have applied the fact that ∑∞k=0 ψ2k,t = O(t−1) (see Robinson, 2005) and the absolute summability of the fourth cumulants.”
Efficient Wald Tests for Fractional Unit Roots (2007, background): “In this respect, Robinson (2005) provides an approach for handling this issue.”
Gaussian pseudo-maximum likelihood estimation of fractional time series models (2011, unknown): “(5) Adaptive estimates, which have greater efficiency at distributions of unknown, non-Gaussian form, can be obtained by taking one Newton step from our estimates (as in [20]).”
Efficient estimation of the semiparametric spatial autoregressive model (2006, methodology): “: (A.39) It follows from Lemma 10 of Robinson (2005) that a3 = Op n 1 2 h L3=2 2 L 1 2 4 L 2 L !”