Time series analysis by fuzzy linear regression

Abstract

Fuzzy set theory constitutes the theoretical background for abstractly formalizing the vague phenomenon of complex systems. Vague data are defined herein as specialized fuzzy sets, i.e., fuzzy numbers, and a fuzzy linear regression model is described as a fuzzy function with such numbers as vague parameters. We applied a generic algorithm to identify the associated coefficients of the model, and provide both analytically and graphically, a linear approximation of the vague function, together with description of its potential application. We also provide an example of the fuzzy linear regression model being employed in a time series with economic indicators, namely the evolution of the unemployment, agricultural production, and construction between 2009 and 2011 in the Czech Republic. We selected this period since it represents the period when the financial and economic crisis started, and a certain degree of uncertainty existed in the evolution of economic indicators. Results take the form of fuzzy regression models in relation to variables of the time-specific series. For the period 2009-2011, analysis confirmed assumptions held by the authors on the seasonal behaviour of such variables and connections between them. In 2010, the system behaved in a fuzzier manner; hence, relationships between variables were vaguer than otherwise, brought about by factors such as difference in the elasticity of demand, state interventions, globalization, and transnational impacts.