The Multi-Scale Maximum Likelihood Estimation of Long Memory Processes

In various physical science and social economic phenomena, the long memory processes are widely found and studied in scientific work on phenomena ranging from the microscopic to the cosmic. Utilizing the decorrelation property of wavelet to long memory processes, we improve on the traditional maximum likelihood estimation and present the multi-scale maximum likelihood estimation (MSMLE) which based on discrete wavelet transform and discrete wavelet packet transform respectively. Simulation results show that under certain precision demand, this improved approximate algorithm decreases the burden of computations greatly and can be used as an alternative of parameter estimation