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Parallelization Experience with Four Canonical Econometric Models Using ParMitISEM

Nalan Baştürk, Stefano Grassi, Lennart Hoogerheide, Herman van Dijk

2016
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Econometrics
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... bedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract: This paper presents the parallel computing implementation of the MitISEM algorithm, labeled Parallel MitISEM. The basic MitISEM algorithm provides an automatic and flexible method to approximate a non-elliptical target density using adaptive mixtures of Student-t densities, where only a kernel of the target density is required. The approximation can be used as a candidate density in Importance Sampling or Metropolis Hastings methods for Bayesian inference on model parameters and probabilities. We present and discuss four canonical econometric models using a Graphics Processing Unit and a multi-core Central Processing Unit version of the MitISEM algorithm. The results show that the parallelization of the MitISEM algorithm on Graphics Processing Units and multi-core Central Processing Units is straightforward and fast to program using MATLAB. Moreover the speed performance of the Graphics Processing Unit version is much higher than the Central Processing Unit one. Econometrics 2016, 4, 11 2 of 20 Recently, Hoogerheide et al. [7] proposed the Mixture of Student-t Distributions using Importance Sampling weighted Expectation Maximization (MitISEM) algorithm which is an automatic and flexible method to approximate a target posterior or predictive density which possibly has non-elliptical shapes that are not known a priori. The algorithm provides an approximation to the joint target density that can be used to obtain features of interest. More importantly, in Bayesian inference, this approximation can be used as a candidate or proposal density for the Metropolis Hastings (MH) or Importance Sampling (IS) algorithms, see [8, 9] . 1 Thus, the use of the MitISEM algorithm for Bayesian inference involves two steps. In the first step, the MitISEM approximation to the joint posterior density of model parameters is obtained, that is, a mixture of Student-t candidate densities is fitted to the target using an expectation maximization (EM) algorithm where each step of the optimization procedure is weighted using IS. In the second step, the obtained candidate density is used in IS or the independence chain MH algorithms for Bayesian inference on the model parameters and model probabilities. Several recent papers use and extend the MitISEM algorithm for Bayesian inference. Reference [10] incorporates the MitISEM algorithm to the estimation of non-Gaussian state space models, [11] uses MitISEM for Value-at-Risk estimation, [12,13] estimates non-causal models using MitISEM and [14] uses MitISEM for Bayesian inference of latent variable models. Recently, [15] provided the R package MitISEM, together with routines to use MitISEM and its sequential extension for Bayesian inference of model parameters and model probabilities. Speeding up computations in such econometric models is appealing for several reasons. First, the amount of data used in these models are typically increasing in areas such as finance, macroeconomics and marketing. Second, such increases in data are often accompanied by construction of more complex models as soon as estimation of these models is possible. For some applications, such as in macroeconomics, estimations taking days or weeks are common. Last but not least, decision making based on econometric models often needs to be performed in a timely manner in areas such as financial risk management. These requirements bring out the necessity to perform quick computations of the econometric models. The estimation of those models can be done using parallel MCMC, where a straightforward implementation is to run p independent chains in parallel and to merge the results. This comes with some theoretical constraints as described in [16] [17] [18] [19] . Reference [20] noted that there is a renewed interest in IS, due to the possibility of straightforward parallel implementation. Numerical efficiency in sampling methods is not only related to the efficient sample size or relative numerical efficiency, but also to the possibility to perform the simulation process in a parallel fashion. Unlike alternative methods such as the random walk MH or the Gibbs sampler, IS makes use of independent draws from the candidate density, which can be obtained from multiple-core processors or computer clusters. This, in turn, yields an increase in calculation speed, see, among others, [21] . The basic MitISEM algorithm may also benefit from parallel processing implementations due to its close relation with the IS algorithm. This paper presents the parallel implementation of the MitISEM algorithm, labeled as Parallel MitISEM (ParMitISEM). Such an implementation requires determining at which steps in the MitISEM parallel processing can be implemented, and adjust, consequently, the remaining steps. We gain insight on the computational speed-up in four canonical econometric models using parallel computing possibilities on Graphics Processing Units (GPUs) and multicore Central Processing Unit (CPUs).

doi:10.3390/econometrics4010011
fatcat:4uu6ozzdwzb57pappsmupo3f5y