Bayesian semi-parametric estimation of the long-memory parameter under FEXP-priors

2012/02/22 by Willem Kruijer, Judith Rousseau, Kruijer, Willem +1
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1202.4863

openalex publication_date 2012/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a Gaussian time series with long-memory behavior, we use the FEXP-model for semi-parametric estimation of the long-memory parameter d. The true spectral density f_o is assumed to have long-memory parameter d_o and a FEXP-expansion of Sobolev-regularity \be > 1. We prove that when k follows a Poisson or geometric prior, or a sieve prior increasing at rate n^(1)/(1+2\be), d converges to d_o at a suboptimal rate. When the sieve prior increases at rate n^(1)/(2\be) however, the minimax rate is almost obtained. Our results can be seen as a Bayesian equivalent of the result which Moulines and Soulier obtained for some frequentist estimators.

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