Bayesian Inference for ARFIMA Models

Durham, Garland; Geweke, John; Porter‐Hudak, Susan; Sowell, Fallaw

doi:10.1111/jtsa.12443

Cited by 11 publications

(4 citation statements)

References 37 publications

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“…Secondly Holan and McElroy (2012) adopted a structural approach to seasonal adjustment. Durham et al (2019) presented the SABL algorithm (sequentially adaptive Bayesian learning) applied to the estimation of ARFIMA models where the posterior density of the parameters is highly non-Gaussian, but where the number of parameters is relatively small. This algorithm differs from the more standard Hastings algorithms in that the updating of the Markov chain is done via a series of individual Bayesian estimation steps, rather than updating the Hamiltonian as in Metropolis-Hastings, Betancourt et al (2014).…”

Section: Bayesian Methodsmentioning

confidence: 99%

Estimation methods for stationary Gegenbauer processes

2022

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This paper reviews alternative methods for estimation for stationary Gegenbauer processes specifically, as distinct from the more general long memory models. A short set of Monte Carlo simulations is used to compare the accuracy of these methods. The conclusion found is that a Bayesian technique results in the highest accuracy. The paper is completed with an examination of the SILSO Sunspot Number series as collated by the Royal Observatory of Belgium.

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Section: Bayesian Methodsmentioning

confidence: 99%

Estimation methods for stationary Gegenbauer processes

2022

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“…Autoregressive fractionally integrated moving average (ARFIMA) models: Bayesian modelling of ARFIMA models using non-informative priors has been done by Pai and Ravishanker (1996), while Durham et al (2019) propose solutions for large time series.…”

Section: Bayesian Forecasting Modelsmentioning

confidence: 99%

A review of predictive uncertainty estimation with machine learning

Tyralis,

Papacharalampous

2024

Artif Intell Rev

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Predictions and forecasts of machine learning models should take the form of probability distributions, aiming to increase the quantity of information communicated to end users. Although applications of probabilistic prediction and forecasting with machine learning models in academia and industry are becoming more frequent, related concepts and methods have not been formalized and structured under a holistic view of the entire field. Here, we review the topic of predictive uncertainty estimation with machine learning algorithms, as well as the related metrics (consistent scoring functions and proper scoring rules) for assessing probabilistic predictions. The review covers a time period spanning from the introduction of early statistical (linear regression and time series models, based on Bayesian statistics or quantile regression) to recent machine learning algorithms (including generalized additive models for location, scale and shape, random forests, boosting and deep learning algorithms) that are more flexible by nature. The review of the progress in the field, expedites our understanding on how to develop new algorithms tailored to users’ needs, since the latest advancements are based on some fundamental concepts applied to more complex algorithms. We conclude by classifying the material and discussing challenges that are becoming a hot topic of research.

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“…, θj+q obtained by expanding out (1 − B) j θ (B). under the stationary constrained ARFIMA(p, d − m d + j, j + q) model given by (4), constraining d to the range [−0.5 + m d − j, 0.5 + m d − j) using the methods described in Sowell (1992), Doornik andOoms (2003), andDurham et al (2019).…”

Section: Relating Non-stationary To Stationary Problems Given Dmentioning

confidence: 99%

Likelihood Inference for Possibly Non-Stationary Processes via Adaptive Overdifferencing

Griffin¹,

Samorodnitsky²,

Matteson³

2020

Preprint

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We make a simple observation that facilitates valid likelihood-based inference for the parameters of the popular ARFIMA or FARIMA model without requiring stationarity by allowing the upper bound d for the memory parameter d to exceed 0.5. We observe that estimating the parameters of a single non-stationary ARFIMA model is equivalent to estimating the parameters of a sequence of stationary ARFIMA models. This enables improved inference because many standard methods perform poorly when estimates are close to the boundary of the parameter space. It also allows us to leverage the wealth of likelihood approximations that have been introduced for estimating the parameters of a stationary process. We explore how estimation of the memory parameter d depends on the upper bound d and introduce adaptive procedures for choosing d. Via simulations, we examine the performance of our adaptive procedures for estimating the memory parameter when the true value is as large as 2.5. Our adaptive procedures estimate the memory parameter well, can be used to obtain confidence intervals for the memory parameter that achieve nominal coverage rates, and perform favorably relative to existing alternatives.

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Bayesian Inference for ARFIMA Models

Cited by 11 publications

References 37 publications

Estimation methods for stationary Gegenbauer processes

Estimation methods for stationary Gegenbauer processes

A review of predictive uncertainty estimation with machine learning

Likelihood Inference for Possibly Non-Stationary Processes via Adaptive Overdifferencing

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