Tahminleme yöntemlerinin dalgacık analizi ve çoklu fraktal eğilimden arındırılmış dalgalanma analizi kullanılarak geliştirilmesi

This thesis comprehensively explores the multifractal structure characterizing precious metal prices and their dynamic relationships. Utilizing advanced techniques such as Vector Fractionally Integrated Autoregressive Moving Average (V-FARIMA) modeling and Multifractal Cross-Correlation Detrended Moving Average Analysis (MF-X-DMA), the research delivers critical insights into forecasting accuracy and risk-return tradeoff in commodities investments. The initial portion of the research hones in on the multifractal structure inherent in precious metal prices, with a particular emphasis on periods of financial instability. The insights gathered in this phase contribute significantly to constructing precise predictions for commodity price variations, empowering investors to make knowledgeable decisions, manage risks effectively, and protect their investments even in a turbulent market. The study then investigates the dynamic relationship between the return rates of gold and platinum, discovering substantial connections across varying frequencies and time frames. This finding supports the concept of co-movement behavior in commodities markets, further influencing risk management, portfolio diversification techniques, and the formation of effective trading strategies. A notable discovery in this research is the consistent comovement over long periods of time as indicated by the constancy in Hölder exponents at lower frequencies. This result not only validates the proposed forecasting approach but also opens potential avenues for future investigations in the field. The first section presents the effectiveness of the V-FARIMA model, emphasizing its superiority in forecasting the Hölder exponents of multifractal precious metal time series. The V-FARIMA model shows promise in spotting underlying trends and patterns in data, increasing our comprehension of price movements in precious metal markets, leading to improved investment decisions. Subsequently, the study employs the MF-X-DMA for multifractal time series with significant coherence, confirming the presence of multifractal cross-correlation between gold and platinum at all scales. In spite of lower correlations, the two commodities still display long-term power-law cross-correlation, a finding of immense value for diversified investment portfolios. The study finishes with a notable affirmation of the MF-X-DMA approach's superiority to the MF-DFA technique in reliably detecting long-term memory in co-movement time series. The combination of continuous wavelet transform (CWT) and MF-X-DMA methodologies provides new insights into the true dynamics of the gold and platinum markets, helping to shape future investment strategies and risk management procedures.