Forecast density combinations of dynamic models and data driven portfolio strategies

Baştürk, Nalan; Borowska, Agnieszka; Grassi, Stefano; Hoogerheide, Lennart F.; Dijk, Herman K. van

doi:10.1016/j.jeconom.2018.11.011

Cited by 18 publications

(10 citation statements)

References 60 publications

(43 reference statements)

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“…Whilst antecedents of these new principles are found in the 'probably approximately correct' (PAC)-Bayes approach to prediction in the machine learning literature (see Guedj, 2019, for a review), it is in the statistics and econometrics literature that this 'loss-based prediction' has come to more formal maturity, including in terms of its theoretical validation. This includes Bayesian work on weighted combinations of predictions, such as, for example, Billio et al (2013), Casarin et al (2015), Pettenuzzo and Ravazzolo (2016), Bassetti et al (2018), Bas ¸türk et al (2019), McAlinn and West (2019) and McAlinn et al (2020), where weights are updated via various predictive criteria, and the true model is not assumed to be one of the constituent models -i.e. an M-open state of the world (Bernardo and Smith, 1994) is implicitly adopted.…”

Section: Introductionmentioning

confidence: 99%

Loss-Based Variational Bayes Prediction

Frazier¹,

Loaiza-Maya²,

Martin³

et al. 2021

Preprint

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We propose a new method for Bayesian prediction that caters for models with a large number of parameters and is robust to model misspecification. Given a class of high-dimensional (but parametric) predictive models, this new approach constructs a posterior predictive using a variational approximation to a loss-based, or Gibbs, posterior that is directly focused on predictive accuracy. The theoretical behavior of the new prediction approach is analyzed and a form of optimality demonstrated. Applications to both simulated and empirical data using high-dimensional Bayesian neural network and autoregressive mixture models demonstrate that the approach provides more accurate results than various alternatives, including misspecified likelihood-based predictions.

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Section: Introductionmentioning

confidence: 99%

Loss-Based Variational Bayes Prediction

Frazier¹,

Loaiza-Maya²,

Martin³

et al. 2021

Preprint

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“…To further exploit the power of our quasi-Bayesian framework, in future research we intend to employ the PCP in the context of forecast combination via Model Averaging using partially censored predictive likelihoods, or in a (quasi-)Bayesian framework with time-varying weights for pairs of models and estimation methods (and possibly investment strategies), extending Bastürk et al (2019). Also extensions of the classical approach of Opschoor et al (2016) based on so-called pooling are relevant in this regard.…”

Section: Discussionmentioning

confidence: 99%

Partially censored posterior for robust and efficient risk evaluation

Borowska

Hoogerheide

Koopman

et al. 2020

Journal of Econometrics

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A novel approach to inference for a specific region of the predictive distribution is introduced. An important domain of application is accurate prediction of financial risk measures, where the area of interest is the left tail of the predictive density of logreturns. Our proposed approach originates from the Bayesian approach to parameter estimation and time series forecasting, however it is robust in the sense that it provides a more accurate estimation of the predictive density in the region of interest in case of misspecification. The first main contribution of the paper is the novel concept of the Partially Censored Posterior (PCP), where the set of model parameters is partitioned into two subsets: for the first subset of parameters we consider the standard marginal posterior, for the second subset of parameters (that are particularly related to the region of interest) we consider the conditional censored posterior. The censoring means that observations outside the region of interest are censored: for those observations only the probability of being outside the region of interest matters. This quasi-Bayesian approach yields more precise parameter estimation than a fully censored posterior for all parameters, and has more focus on the region of interest than a standard Bayesian approach. The second main contribution is that we introduce two novel methods for computationally efficient simulation: Conditional MitISEM, a Markov chain Monte Carlo method to simulate model parameters from the Partially Censored Posterior, and PCP-QERMit, an Importance Sampling method that is introduced to further decrease the numerical standard errors of the Value-at-Risk and Expected Shortfall estimators. The third main contribution is that we consider the effect of using a timevarying boundary of the region of interest, which may provide more information about the left tail of the distribution of the standardized innovations. Extensive simulation and empirical studies show the ability of the introduced method to outperform standard approaches.

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“…The Bayesian literature, having access as it does to posterior simulation schemes, has entertained more sophisticated (including time-varying) weighting schemes, in which predictive performance-quantified by a range of different problem-specific loss measures-influences the posterior up-dates of the weights. Key work here, including some also driven by the criterion of calibration, includes Billio et al (2013), Casarin, Grassi, et al (2015, Casarin, Leisen, et al (2015), Casarin et al (2016), Pettenuzzo and Ravazzolo (2016), Aastveit et al (2018), Bassetti et al (2018), Baştürk et al (2019) and Casarin et al (2019). 13 In principle, any of the above combination schemes could be used to construct the predictive class P t , with the chosen measure of predictive accuracy used to define the update in (2).…”

Section: A Comment On the Role Of Predictive Combinationsmentioning

confidence: 99%

“…Whilst an established literature on estimating mixtures of predictives exists (see Aastveit et al, 2019, for an extensive review)—including work that invokes Bayesian principles (e.g. Billio et al, 2013, Casarin, Leisen, et al, 2015, Pettenuzzo & Ravazzolo, 2016, Bassetti et al, 2018, and Baştürk et al, 2019, amongst others)—our paper provides an alternative way of updating predictive combinations via non‐likelihood‐based Bayesian principles. We comment further on the connection of our work with the literature on predictive combinations, plus provide detailed referencing to this literature, in Section 4.2.…”

Section: Introductionmentioning

confidence: 99%

Focused Bayesian prediction

Loaiza-Maya

Martin

Frazier

2021

J of Applied Econometrics

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We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After observing data, we update the prior to a posterior over these models, via a criterion that captures a user-specified measure of predictive accuracy. Under regularity, this update yields posterior concentration onto the element of the predictive class that maximizes the expectation of the accuracy measure. In a series of simulation experiments and empirical examples, we find notable gains in predictive accuracy relative to conventional likelihood-based prediction.

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Forecast density combinations of dynamic models and data driven portfolio strategies

Cited by 18 publications

References 60 publications

Loss-Based Variational Bayes Prediction

Loss-Based Variational Bayes Prediction

Partially censored posterior for robust and efficient risk evaluation

Focused Bayesian prediction

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