Traces of the Multifractal Nature of the Financial Crises in Turkey: Co-Movement of the Hölder Exponents and Large-Scale Forecast

Abstract

This paper investigates the multifractal behavior of the probability of default (PD) of real sector firms and Turkey sovereign credit default swap (CDS). Moreover, we emphasize the co-movements of Hölder exponents during the financial crisis periods. For this reason, first, it is necessary to figure out the default probabilities of real sector firms. The default probability is evaluated weekly by the methodology of Moody’s Analytics, which is a commonly used approach, in which the market value of a firm is a call option written on its total assets. Multifractal detrended fluctuation analysis (MF-DFA), multifractal detrended cross-correlation analysis (MF-DCCA) and multifractal detrended moving average cross-correlation analysis (MF-X-DMA) techniques are applied to identify the multifractal behavior of the large-scale fluctuations of PDs and CDSs. In this way, we can evaluate the local Hurst exponents. Besides, the oscillation method is employed to estimate the pointwise and local Hölder exponents. In the period between January 2001 and March 2018, the structure of dynamic co-movements of Hölder exponents is determined by applying wavelet coherency methodology and the relations in crisis period are revealed. The selected period covers the crises with structural differences: Turkey banking crisis, the US sub-prime mortgage crisis and the European sovereign debt crisis that occurred in 2001, 2008 and 2009, respectively. Besides, during the periods of financial crises, among the local Hölder exponents, severely correlated large scales show multifractal features, and hence vector fractionally autoregressive integrated moving average (VFARIMA) forecasting provides better results than scalar models.