On recursive estimation for time varying autoregressive processes

By Eric Moulines, Pierre Priouret, Franccois Roueff. 2005

73 citations recorded by the source corpus.

This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong to appropriate smoothness classes. An adequate normalization for the correction term used in the recursive estimation procedure allows for very mild assumptions on the innovations distributions. The rate of convergence of the pointwise estimates is shown to be minimax in β-Lipschitz classes for 0 < β ≤ 1. For 1 < β ≤ 2, this property no longer holds. This can be seen by using an asymptotic expansion of the estimation error. A bias reduction method is then proposed for recovering the minimax rate.

Subfields: Control and Systems Engineering, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/756d912ef7922d428ae6d6d72509b6ea12ac7af7

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In Control and Systems Engineering

In Finance

In Statistics and Probability

Citations in the corpus

Nonparametric regression for locally stationary time series (2012, background): “[19]) or they heavily draw on the independence of the random matrices involved (see, e.”
On some nonstationary, nonlinear random processes and their stationary approximations (2006, unknown): “Since λ([A0(i)]n) ≤ 1 − δ for i = 1, . . . ,M and by using Moulines et al. (2005), Lemma 12, there exists a K independent of A0(r) and m such that ‖[A0(r)]mn ‖spec ≤ K(1 − δ/2)m.”
Locally stationary long memory estimation (2009, result): “Such results are somewhat similar to that for estimating the time varying parameter of a locally stationary short memory process, see [21], or, in a more general fashion, Example 3.”
Inference of time-varying regression models (2012, background): “Other contributions on parameter estimation can be found in [12, 13, 24, 37] among others.”
Bridging the gap between constant step size stochastic gradient descent and Markov chains (2017, methodology): “To the authors knowledge, the use of the Richardson-Romberg method for stochastic approximation has only been considered in [41] to recover the minimax rate for recursive estimation of time varying autoregressive process.”