Large-scale forecasting of large fluctuations using wavelet coherence and multifractal behavior and developing wavelet coherence for multiple time series

Shocks, jumps, booms, and busts are typical large fluctuation markers that appear in crisis. Identifying financial crises and estimating leading indicators with strong relations during crisis periods have an essential role in the literature. This thesis examines the dynamic co-movements of leading indicators' multifractal features to identify financial crises due to large fluctuations. The detected dynamic relationships predict leading indicators with scale-by-scale analysis and make large-scale predictions better than challenger models. As a natural result of these studies, the n-dimensional wavelet coherence method is examined, and the vectorwavelet package is transferred to the R program. This thesis consists of three independent parts, and the contents of the studies are summarized below. In the first part, stock returns' co-movements with other leading indicators in crisis periods are analyzed with multiple and quadruple wavelet coherence using interest rate, exchange rate, and trade balance differences. The scale-by-scale wavelet transformation was used to predict large-scale relationships, and stock return estimation was performed. In the second part, the multifractal characteristics of sectoral default probabilities of the real sector in Turkey and Turkey sovereign CDS rates were examined by detrended fluctuation analysis. Significant dynamic connections between the Hölder exponents of the default rates and CDS during financial crisis periods have been examined. During the periods of financial crises, among the Hölder exponents, severely correlated large scales show multifractal features. Scale-by-scale wavelet transform has been used to predict large-scale relationships, and hence vector fractionally autoregressive integrated moving average forecasting provides better results than scalar models. The final part of the thesis introduces a new wavelet methodology to handle multivariate time series dynamic co-movements by extending multiple quadruple wavelet coherence methodologies. The primary motivation of our works is to measure wavelet coherence analytically for the specific dimension.