MGARCH models: Trade-off between feasibility and flexibility

Almeida, Daniel de; Hotta, Luiz Koodi; Ruiz, Esther

doi:10.1016/j.ijforecast.2017.08.003

Cited by 38 publications

(26 citation statements)

References 127 publications

(124 reference statements)

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“…This is not too surprising, as BEKK and DCC have been shown to perform similarly well in simulation studies and empirical comparisons regarding forecasting conditions and in prediction of variance, covariances, and correlations (e.g. Caporin & McAleer, 2008;de Almeida et al, 2018;Huang, Su, & Li, 2010) Data Requirements. The results of the pdBEKK and, to some degree the DCC model, yielded parameter estimates with very large CrI's suggesting low precision and high uncertainty surrounding some of the MGARCH parameters.…”

Section: Dcc-mgarchmentioning

confidence: 72%

A new frontier for studying within-person variability: Bayesian multivariate generalized autoregressive conditional heteroskedasticity models.

Rast¹,

Martin²,

Liu³

et al. 2022

Psychological Methods

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Research on individual variation has received increased attention. The bulk of the models discussed in psychological research so far, focus mainly on the temporal development of the mean structure. We expand the view on within-person residual variability and present a new model parameterization derived from classic multivariate GARCH models used to predict and forecast volatility in financial time-series. We propose a new pdBEKK and a modified DCC model that accommodate external time-varying predictors for the within-person variance. The main goal of this work is to evaluate the potential usefulness of MGARCH models for research in within-person variability. MGARCH models partition the within-person variance into, at least, three components: An overall constant and unconditional baseline variance, a process that introduces variance conditional on previous innovations, or random shocks, and a process that governs the carry-over effects of previous conditional variance, similar to an AR model. These models allow for variance spill-over effects from one time-series to another. We illustrate the pdBEKK-and the DCC-MGARCH on two individuals who have rated their daily positive and negative affect over 100 consecutive days. The full models comprised a multivariate ARMA(1,1) model for the means and included physical activity as moderator of the overall baseline variance. Overall, the pdBEKK seems to result in a more straight forward psychological interpretation, but the DCC is generally easier to estimate and can accommodate more simultaneous time-series. Both models require rather large amounts of datapoints to detect non-zero parameters. We provide an R-package bmgarch that facilitates the estimation of these types of models.

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Section: Dcc-mgarchmentioning

confidence: 72%

A new frontier for studying within-person variability: Bayesian multivariate generalized autoregressive conditional heteroskedasticity models.

Rast¹,

Martin²,

Liu³

et al. 2022

Psychological Methods

View full text Add to dashboard Cite

show abstract

“…The latter point refers to the "curse of dimensionality" (Bellman, 1961;Caporin & McAleer, 2012), of the BEKK which can only model a limited number of time-series. de Almeida et al (2018), for example, were only able to estimate BEKK models with less than five simultaneous time-series while the DCC parameterization was able to accommodate up to 10. Our R-package bmgarch performed similarly; in a small simulation we were able to estimate up to seven time-series with the pdBEKK parameterization before all starting values were rejected and sampling was aborted.…”

Section: Discussionmentioning

confidence: 99%

“…The results of the pdBEKK and, to some degree the DCC model, yielded parameter estimates with very large CrI's suggesting low precision and high uncertainty surrounding some of the MGARCH parameters. MGARCH models have been thoroughly investigated in simulation studies and real applications throughout the last two decades with the general consent that these models are robust in terms of prediction and forecasting (e.g Boussama, Fuchs, & Stelzer, 2011;de Almeida et al, 2018;Rossi & Spazzini, 2010). In the context of our work, however, it remains unclear what the data requirements are when these models are used on behavioral data.…”

Section: Dcc-mgarchmentioning

confidence: 99%

A New Frontier for Studying Within-Person Variability: Bayesian Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models

Rast¹,

Martin²,

Liu³

et al. 2020

Preprint

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Research on individual variation has received increased attention. The bulk of the models discussed in psychological research so far, focus mainly on the temporal development of the mean structure. We expand the view on the within-person residual variability and present a new model parameterization derived from classic multivariate GARCH models used to predict and forecast volatility in financial time-series. We propose a new pdBEKK and a modified DCC model that accommodate external time-varying predictors for the within-person variance. This main goal of this work is to evaluate the potential usefulness of MGARCH models for research in within-person variability. MGARCH models partition the within-person variance into, at least, three components: An overall constant and unconditional baseline variance, a process that introduces variance conditional on previous innovations, or random shocks, and a process that governs the carry-over effects of previous conditional variance, similar to an AR model. Moreover, these models allow for variance spill-over effects from one time-series to another. We illustrate the pdBEKK-and the DCC-MGARCH on two individuals who have rated their daily positive and negative affect over 100 consecutive days. The full models comprised a multivariate ARMA(1,1) model for the means and included physical activity as moderator of the overall baseline variance.Overall, the pdBEKK seems to result in a more straight forward psychological interpretation, but the DCC is generally easier to estimate and can accommodate more simultaneous time-series. Both models require rather large amounts of datapoints to detect non-zero parameters. Potentials and limitations are discussed. We provide an R-package bmgarch that facilitates the estimation of these types of models.

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“…GARCH models can be readily extended to multivariate models (MGARCH; Engle & Kroner, 1995) and since their introduction a number of different parameterizations have been presented (for an overview see eg. Bauwens, Laurent, & Rombouts, 2006; de Almeida, Hotta, & Ruiz, 2018).…”

Section: Multivariate Garch Models Formentioning

confidence: 99%

Bayesian Multivariate GARCH Models for Within-Person Variance Forecasting

Rast¹,

Martin²,

Rodriguez³

2020

Preprint

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We present a multivariate GARCH (MGARCH) model to forecast model averaged (co-)variances, correlations, and means in behavioral data for single individuals. We consider four MGARCH model parameterizations; three classic models (CCC, DCC, andBEKK) as well as a recently introduced model (pdBEKK) optimized for behavioral research. To obtain the averaged forecasts across the four models, we will first need to compute the model weights, obtained from a model stacking method. To do so, we need to approximate the expected log predictive density via a fully Bayesian leave-future-out cross validation technique. This approach has not been described so far in the literature. We provide an illustrative implementation using real data on two individuals from the longitudinal Intelligent Systems for Assessing Aging Change (ISAAC) study covering up to 4 years of daily measurements on individual computer use and walking speed. The individual participants show distinct patterns in the model weights, suggesting that individuals differ in the parameterizations that best capture their behavior. We generate weighted forecasts for up to 5 consecutive two-week periods for both individuals. These foreceast are compared to forecasts from the single best model. The resulting predictions are shown to be superior or at least equivalent to the forecasts from the single best model. We close with a discussion on limitations and an outlook. We provide an R package

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MGARCH models: Trade-off between feasibility and flexibility

Cited by 38 publications

References 127 publications

A new frontier for studying within-person variability: Bayesian multivariate generalized autoregressive conditional heteroskedasticity models.

A new frontier for studying within-person variability: Bayesian multivariate generalized autoregressive conditional heteroskedasticity models.

A New Frontier for Studying Within-Person Variability: Bayesian Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models

Bayesian Multivariate GARCH Models for Within-Person Variance Forecasting

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