Efficient Bayesian inference for long memory processes

TL;DR

This paper introduces a Bayesian inference method for long memory processes using ARFIMA models, providing an efficient likelihood and improved hypothesis testing for long-term dependence in time series data.

Contribution

It presents a novel approximate likelihood for ARFIMA models and a Bayesian framework that effectively isolates long memory effects from nuisance parameters.

Findings

Favorable comparison with standard estimators on synthetic data

Effective hypothesis testing for long memory parameters

Applicable to both synthetic and observational data

Abstract

In forecasting problems it is important to know whether or not recent events represent a regime change (low long-term predictive potential), or rather a local manifestation of longer term effects (potentially higher predictive potential). Mathematically, a key question is about whether the underlying stochastic process exhibits "memory", and if so whether the memory is "long" in a precise sense. Being able to detect or rule out such effects can have a profound impact on speculative investment (e.g., in financial markets) and inform public policy (e.g., characterising the size and timescales of the earth system's response to the anthropogenic CO2 perturbation). Most previous work on inference of long memory effects is frequentist in nature. Here we provide a systematic treatment of Bayesian inference for long memory processes via the Autoregressive Fractional Integrated Moving Average (ARFIMA) model. 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 than ever before. We illustrate our new methodology on both synthetic and observational data, with favorable comparison to the standard estimators.