Complex Variance in Modern Econometrics

Abstract

One of the modern trends in economics is the use of elements of the theory of functions of complex variables. When constructing complex-valued econometric models, researchers come across the fact that in mathematical statistics the section associated with processing a complex random variable is based on the hypothesis on independence of the real and imaginary parts of complex variables. This hypothesis leads to the necessity of calculating the actual characteristics of complex random variables, including variance. As shown in the article, this assumption significantly limits the possibilities of modern econometrics. Therefore, the article substantiates the need to use complex variance in econometrics. The analysis of the properties of complex variance and the meaning of its real and imaginary parts is carried out. It is shown how, using a complex variance, to estimate the confidence limits for a complex random variable. Since the use of complex variance in econometrics and mathematical statistics is proposed for the first time ever, the article discusses the formation of complex-valued correlation and regression analysis, sections of which will be used in econometrics of complex variables.

Keywords

• econometrics
• complex-valued econometric models
• complex variance
• correlation moment
• complex pair correlation coefficient