72 Forecasting Sales from Discrete Wavelet Transformed Compressed Interest Rates

This paper provides a comparative analysis of the effectiveness of the Discrete Wavelet Transform (DWT) in forecasting sales from compressed interest rates. Using a least mean square (LMS) prediction algorithm, we study the performance of forecasting sales from DWT compressed interest rates for each of the first ten wavelets from the class of Daubechies' orthogonal wavelets at different compression ratios. For each of the wavelets, we perform a multi-level DWT on the uncompressed interest rate data. Next, for each level, we forecast sales from an approximation of the interest rate sequence derive from scaling coefficients at that level. A LMS linear prediction algorithm is then applied to each of the approximations to get their respective sales forecast. Finally, at each of the levels, we compare the performance using the root mean square error, correlation coefficient and compression ratio. These results were also compared to the forecast from the uncompressed interest rates. Our results show that at Level 1, with compression ratios in the range 50% through 52%, there were only modest variations. However, at Level 4, with compression ratios in the range 91% through 94%, there were more significant variations with db8 yielding the best performance; even when compared to the forecast obtained from the uncompressed interest rates.