Analytic expressions for predictive distributions in mixture autoregressive models

Boshnakov, Georgi N.

doi:10.1016/j.spl.2009.04.009

Cited by 10 publications

(13 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that parameter estimation for the MBL K ( p ,0, q , q ) model would be easily performed through the EM algorithm and since this model has a covariance ARMA structure, order selection may be performed using classical criteria such as the AIC and BIC (see Psaradakis and Spagnolo, 2006 for the Markov mixture AR case). Finally, along the lines of Boshnakov (2009) which has derived the conditional characteristic functions for MAR models, multistep ahead predictions for the MBL model may be obtained while deriving its conditional characteristic function for long horizons.…”

Section: Discussionmentioning

confidence: 99%

On an independent and identically distributed mixture bilinear time-series model

Aknouche

Rabehi

2010

Journal of Time Series Analysis

View full text Add to dashboard Cite

A class of nonlinear time-series models in which the underlying process follows a finite mixture of bilinear representations is proposed. The mixture feature appears in the conditional distribution of the process which is given as a finite mixture of distributions evaluated at the normed innovations of diagonal bilinear specifications. This class is aimed at capturing special characteristics exhibited by many observed time series such as tail heaviness, multimodality, asymmetry and change in regime. Some probabilistic properties of the proposed model, namely strict and second-order stationarity, geometric ergodicity, covariance structure, existence of higher order moments, tail behaviour and invertibility, are first studied. Parameter estimation is then performed through the EM algorithm, performance of which is shown via simulation experiments. Applications to some real-time-series data are proposed and through which it is shown how neglecting the mixture framework in a bilinear representation results in a loss in adequacy. Copyright Copyright 2010 Blackwell Publishing Ltd

show abstract

Section: Discussionmentioning

confidence: 99%

On an independent and identically distributed mixture bilinear time-series model

Aknouche

Rabehi

2010

Journal of Time Series Analysis

View full text Add to dashboard Cite

show abstract

“…( 1). The h-steps ahead predictive distributions of y t+h at time t can be obtained by simulation (Wong and Li 2000) or, in the case of Gaussian and α-stable components, analytically (Boshnakov 2009).…”

Section: The Mixture Autoregressive Modelmentioning

confidence: 99%

“…Think for example of the point prediction for a symmetric bimodal density: a point prediction would fall exactly between the two modes, in a point of lower density, and would therefore be misleading. In addition, when the predictive distribution is available, prediction intervals can easily be obtained by extracting the quantiles of interest (Boshnakov 2009;Lawless and Fredette 2005).…”

Section: Bayesian Density Forecasts With Mixture Autoregressive Modelsmentioning

confidence: 99%

“…Wong and Li (2000) and Boshnakov (2009) respectively introduced a simulation based and an analytical method for for density forecasts assuming a MAR model. The first method relies on Monte Carlo simulations, while the second derives exact h-step ahead predictive distributions of a given observation.…”

Section: Bayesian Density Forecasts With Mixture Autoregressive Modelsmentioning

confidence: 99%

“…Thus, detection of label switching has the sole purpose of providing identifiability and interpretation of the model. We estimate the 1-step and 2-step predictive distributions of the IBM data at t = 258 using the analytical method by Boshnakov (2009), and compare them to the ones obtained by EM algorithm (see Fig. 13).…”

Section: Bayesian Density Forecasts With Mixture Autoregressive Modelsmentioning

confidence: 99%

See 2 more Smart Citations

Bayesian analysis of mixture autoregressive models covering the complete parameter space

Ravagli

Boshnakov

2021

Comput Stat

Self Cite

View full text Add to dashboard Cite

Mixture autoregressive (MAR) models provide a flexible way to model time series with predictive distributions which depend on the recent history of the process and are able to accommodate asymmetry and multimodality. Bayesian inference for such models offers the additional advantage of incorporating the uncertainty in the estimated models into the predictions. We introduce a new way of sampling from the posterior distribution of the parameters of MAR models which allows for covering the complete parameter space of the models, unlike previous approaches. We also propose a relabelling algorithm to deal a posteriori with label switching. We apply our new method to simulated and real datasets, discuss the accuracy and performance of our new method, as well as its advantages over previous studies. The idea of density forecasting using MCMC output is also introduced.

show abstract

Linear Time Series Models with Non-Gaussian Innovations

Balakrishna

2021

Non-Gaussian Autoregressive-Type Time Series

View full text Add to dashboard Cite

Analytic expressions for predictive distributions in mixture autoregressive models

Cited by 10 publications

References 3 publications

On an independent and identically distributed mixture bilinear time-series model

On an independent and identically distributed mixture bilinear time-series model

Bayesian analysis of mixture autoregressive models covering the complete parameter space

Linear Time Series Models with Non-Gaussian Innovations

Contact Info

Product

Resources

About