Fractal dimensions of values derived from the processes of ar, ma and arima

Abstract

The concept of fractal dimension, which is a tool of fractal geometry, has become an important statistical tool under investigation. Fractal dimension helps to explain figures with a single number. For the purpose of our study, first of all, a computer program to calculate fractal dimensions was prepared by using the Visual Basic programming language. Later, with the help of Microsoft Excel, samples were derived for the models of Autoregressive model - AR (1), Moving-average model - MA (1) and Autoregressive integrated moving average model - ARIMA (0,1,1). By calculating the fractal dimensions of the samples derived separately for each model, the relationships between the model parameters and the fractal dimensions were investigated. Moreover, whether there was a relationship between the fractal dimension and the arithmetic mean and the standard deviation was examined in this study as well. Furthermore, fractal dimensions, different and similar samples were analysed graphically for similarity.