Development of new forecasting strategies using wavelet transform (wt), multiple wavelet coherence (mwc) and multi-fractal de-trended fluctuation analysis (mfdfa)

Modeling and forecasting has increasingly become very important in analysis of trends in financial markets, particularly in high frequency trades. It is difficult to predict the price return, i.e. profit or loss, due to many unknown variables including social and political unrest, catastrophic events, etc. Hence these time series have different characteristics of movement, so called fluctuations. Wavelet analysis, multiple wavelet coherence analysis and especially scale by scale wavelet transform are powerful tools to investigate the series possessing different frequency levels. Multi fractal de-trended fluctuation analysis also reveals the different frequency levels of characteristics. It is realized that there is no generalized forecasting strategy available using these methods together. Therefore, a new strategy will be proposed through application on real life data sets to detect highly correlated time series and forecast using vector autoregressive moving average and vector autoregressive fractionally integrated moving average methods in order to compare with real data and quantify the efficiency of forecasting. The thesis is composed of four independent sections. The first section covers a forecasting method using three dimensional multiple wavelet coherence and scale by scale wavelet transformation of precious metals. The second section covers the similar method with western and eastern markets but employs a four dimensional multiple wavelet coherence. The third section covers three dimensional multiple wavelet coherence and its multifractal de-trended fluctuation analysis at the specific scale. The third section utilizes two dimensional wavelet coherence and multifractal de-trended fluctuation analysis of the raw data for a specific determined scale.