Wavelet denoising and detrending analysis of gold prices and usd/try exchange rates

For this thesis, nonlinear dynamics of gold prices and USD/TRY exchange rates between January, 03 2005 and February 18, 2015 have been investigated through wavelet based denoising and detrended methods. Four different types of wavelet family namely, Haar, Daubechies, Meyer and Symlet have been employed within the stationary wavelet transform (SWT) framework. The purpose of this thesis is twofold. Firstly, we compared different wavelet thresholding methods of universal, Stein's unbiased risk estimator (SURE), false discovery rate (FDR) and global cross validation (GCV) thresholding algorithms for both hard and soft thresholding to remove the noise inherent gold price and USD/TRY exchange rate data. According to signal-to-noise (SNR) and peaked signal-to-noise (PSNR) ratio, hard thresholding method provides better performance in extracting noise from the original data. Moreover, SURE method seems to be superior compared to other methods in terms of SNR and PSNR values. Another important empirical finding is that Symlet wavelet with 8 vanishing moments have higher SNR and PSNR values. Secondly, cyclical behaviour of gold price and USD/TRY exchange rate dynamics have been uncovered via wavelet map indexing. The results suggest that SWT based detrending models provide good cyclical components for gold price and USD/TRY exchange rate data.