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Efficient Bayesian inference for natural time series using ARFIMA processes

Graves, T., Gramacy, R. B., Franzke, C. L. E. and Watkins, Nicholas W. (2015) Efficient Bayesian inference for natural time series using ARFIMA processes. Nonlinear Processes in Geophysics, 22 (6). pp. 679-700. ISSN 1607-7946

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Identification Number: 10.5194/npg-22-679-2015

Abstract

Many geophysical quantities, such as atmospheric temperature, water levels in rivers, and wind speeds, have shown evidence of long memory (LM). LM implies that these quantities experience non-trivial temporal memory, which potentially not only enhances their predictability, but also hampers the detection of externally forced trends. Thus, it is important to reliably identify whether or not a system exhibits LM. In this paper we present a modern and systematic approach to the inference of LM. We use the flexible autoregressive fractional integrated moving average (ARFIMA) model, which is widely used in time series analysis, and of increasing interest in climate science. Unlike most previous work on the inference of LM, which is frequentist in nature, we provide a systematic treatment of Bayesian inference. In particular, we provide a new approximate likelihood for efficient parameter inference, and show how nuisance parameters (e.g., short-memory effects) can be integrated over in order to focus on long-memory parameters and hypothesis testing more directly. We illustrate our new methodology on the Nile water level data and the central England temperature (CET) time series, with favorable comparison to the standard estimators. For CET we also extend our method to seasonal long memory.

Item Type: Article
Official URL: http://www.nonlinear-processes-in-geophysics.net/i...
Additional Information: © 2015 The Authors © CC BY 3.0
Divisions: Centre for Analysis of Time Series
Subjects: Q Science > QC Physics
Q Science > QE Geology
Sets: Research centres and groups > Centre for the Analysis of Time Series (CATS)
Date Deposited: 03 Dec 2015 15:35
Last Modified: 20 Mar 2019 02:45
Projects: 229754, N62909-15-1-N143, EXC177
Funders: Norwegian Research Council, ONR NICOP, German Research Council
URI: http://eprints.lse.ac.uk/id/eprint/64592

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