Uncertain vector autoregressive model with imprecise observations
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METHODOLOGIES AND APPLICATION
Uncertain vector autoregressive model with imprecise observations Han Tang1
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Prior uncertain autoregressive (UAR) model research has focused principally on a univariate time series. However, different variables tend to influence each other in reality. In order to fill this gap, this paper explores the interrelationships among different variables and proposes an exposition of uncertain vector autoregressive (UVAR) model. Furthermore, we choose the least squares principle to estimate the unknown parameters in the UVAR model and analyze the residual of disturbance term. Then, we present the point estimation and confidence interval of the variables in the next period. Finally, the empirical results show that essential improvements in forecasting can be obtained by adding relative variables. Keywords Uncertainty theory · Uncertain vector autoregressive model · Principle of least squares · Residual analysis · Confidence interval
1 Introduction The goal of the statistical analysis is to interpret the complex interrelationships among different variables based on the statistical data. Probabilistic statistics provides us with a large number of models for fitting different types of data, yet it should also be noted that one common assumption of those models is that observation data are precise numbers. Nevertheless, the observation data cannot be precisely observed in many cases, for example the data of the carbon emission and the data of the oil reserves. Therefore, relevant domain experts are required to provide empirical data of vague factors. Liu (2010) supported the view that it is persuasive to employ methodologies of uncertainty theory in the analysis related to vague factors. Uncertainty theory was founded by Liu (2007) in 2007 and consummated by Liu (2009) in 2009, and it has become a branch of mathematics to rationally deal with personal belief degrees. So far, uncertainty theory has been widely applied in many fields. Uncertain statistics is an important part of uncertainty theory, and it was firstly studied by Liu (2010) in 2010 to collect and interpret expert’s experimental data. As a funCommunicated by V. Loia.
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Han Tang [email protected] Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
damental concept in uncertainty theory, uncertain variable is usually used to describe the empirical data. Afterward, scholars did qualitative related research. To model the distribution function of uncertain variable, Liu (2010) rendered the linear interpolation method, Chen and Ralescu (2012) produced B-spline method, and Wang et al. (2012) developed Delphi method about how the estimates of multiple experts are combined. In order to estimate unknown parameters in an uncertainty distribution with known functional form, Liu (2010) proposed the principle of least squares, Wang and Peng (2014) suggested the method of moments, and Lio and Liu (2020) presented the maximum likelihood est
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