Some aspects of wavelet anal ysis in time series

Abstract

The first paper describes an alternative approach for testing the existence of trend among time series. The test method has been constructed using wavelet analysis which have the ability to decompose a time series into low frequencies (trend) and high frequencies (noise) components. Under the normality assumption the test is distributed as F. However, the distribution of the test is unknown under other conditions, like non-normality. To investigate the properties of the test statistic under wide conditions, empirical critical values for the test have been generated using Monte Carlo simulations. The results are then compared with those results obtained by applying the OLS method for testing the trend. A number of cases have been studied regarding the size of the test, where the number of observations, long memory parameter, different types of wavelets and the distribution of the errors have been varied. For each case 10,000 replications have been performed and four different nominal sizes have been studied. For the power calculations the strength of the trend parameter has been varied. In this study, we find that using the tabulated critical values from the F distributions, the test tends to overreject under the null hypothesis, while when using generated critical values, the test performs satisfactorily. The Harr wavelet has shown to exhibit the highest power among the other wavelet's types, but the power is still lower than the OLS under some conditions. The methodology here has been applied to real temperature data in Sweden for the period 1850-1999. The results indicate a significant increasing trend which agrees with the "Global warming" hypothesis during the last 100 years. The second paper, Uointly written with Ghazi Shukur), presents an illustration of the use of wavelet analysis and the importance of time scale decomposition in determining the causality relation between two important macro variables. The relation between government spending and revenue has been studied using three methods, the conventional test, a bootstrap simulation approach and a multivariate Rao's F-test. These test methods have shown different results when using quarterly and monthly data. The wavelet decomposition of the time series into different time scales of variation helped in determining the causality direction between these two macro variables