Abstract
The multivariate estimation problems arise if the observations are available for several related variables of interest. The multivariate time series may be found in many fields of application such as economics, meteorology and utilities. The current study has three main objectives. The first one is to develop an approximate convenient Bayesian methodology to estimate the parameters of multivariate moving average processes. The second objective is to investigate the numerical efficiency of the proposed technique in solving the estimation problems by conducting a wide simulation study. The last objective is to study the sensitivity of the numerical efficiency with respect to the parameters values and time series length. The results show that the proposed technique succeeded in estimating the parameters of the multivariate moving average processes. The results are not sensitive to the changes in parameter values or in time series length.
Highlights
The multivariate time series may be found in many fields of application such as economics, business, meteorology, hydrology and utilities
The Bayesian and non–Bayesian approaches of univariate and multivariate time series are based on a class of parametric models such as moving average (MA) models
The main objective of this study is to develop an approximate convenient Bayesian methodology to estimate the parameters of multivariate moving average, denoted by VMAk(q), processes
Summary
The multivariate (vector) time series may be found in many fields of application such as economics, business, meteorology, hydrology and utilities. [25] proposed three different methods to compute the exact likelihood function of vector moving average processes It seems that the non–Bayesian literature on the estimation problems of multivariate processes traditionally focused on maximum likelihood methods because of their desirable properties. [30] developed an efficient numerical expression for the likelihood function of stationary and partially non–stationary autoregressive moving average processes Another development was done by [31] who proposed a new procedure for the exact maximum likelihood estimation of mixed VARMA models. The main objective of this study is to develop an approximate convenient Bayesian methodology to estimate the parameters of multivariate moving average, denoted by VMAk(q), processes.
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