Maximum likelihood estimation for α-stable autoregressive processes

By B. Andrews, Matt Calder, Richard A. Davis. 2009

86 citations recorded by the source corpus.

We consider maximum likelihood estimation for both causal and noncausal autoregressive time series processes with non-Gaussian α-stable noise. A nondegenerate limiting distribution is given for maximum likelihood estimators of the parameters of the autoregressive model equation and the parameters of the stable noise distribution. The estimators for the autoregressive parameters are n 1 /α -consistent and converge in distribution to the maximizer of a random function. The form of this limiting distribution is intractable, but the shape of the distribution for these estimators can be examined using the bootstrap procedure. The bootstrap is asymptotically valid under general conditions. The estimators for the parameters of the stable noise distribution have the traditional n 1/2 rate of convergence and are asymptotically normal. The behavior of the estimators for finite samples is studied via simulation, and we use maximum likelihood estimation to fit a noncausal autoregressive model to the natural logarithms of volumes of Wal-Mart stock traded daily on the New York Stock Exchange.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b3adfaeb4d74ad9acc98cf243e49545fd899f48b

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Citations in the corpus

Local explosion modelling by non‐causal process (2017, unknown): “For α-stable causal and non-causal AR processes, the asymptotic distribution of the maximum likelihood estimator was established by Andrews et al. (2009) (see also Lanne and Saikkonen (2011)).”
Filtering, Prediction and Simulation Methods for Noncausal Processes (2016, methodology): “As the limiting distribution of the AML estimators of and 8 is intractable because of Cauchy errors (Andrews et al., 2009, Th. 3.2), the standard errors are computed by bootstrap (Davis and Wu, 1997; Andrews et al., 2009, Th. 3.4).”
Noncausal Autoregressions for Economic Time Series (2010, unknown): “This generalization has been considered by Andrews et al. (2006) in a related context and, following the arguments used in their paper, it can also be straightforwardly handled in our case. Thus, we shall assume that the density function f (x;λ) satisfies the regularity conditions of Andrews et al. ”
Approximate self-weighted LAD estimation of discretely observed ergodic Ornstein-Uhlenbeck processes (2010, unknown): “Throughout this paper we assume that: Θ is a bounded convex domain such that its closure Θ − ⊂ (0 , ∞ ) × R ; (2)”
MIXED CAUSAL-NONCAUSAL AR PROCESSES AND THE MODELLING OF EXPLOSIVE BUBBLES (2017, background): “Replacing α-stable laws by their domain of attraction alleviates the risk of misspecification.10 8 See Andrews et al. (2009) for asymptotic properties of the ML estimator of both causal and noncausal AR processes with non-Gaussian α-stable distribution.”