M-Stationary (Multiplicative Stationary) Processes: A Revisit

• Activity Number: 360
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Md Jobayer Hossain*+ and Wayne A. Woodward and Henry L. Gray
• Companies: Nemours and Southern Methodist University and Southern Methodist University
• Keywords: M-stationary ; elongating ; compacting ; time varying ; periodic

Abstract

M-stationary processes, introduced by Gray and Zhang, were a breakthrough in the analysis of non-stationary time series whose pseudo periodic behavior lengthens approximately linearly with time. They used a time deformation technique for the analysis of continuous M-stationary processes with a time index (t) restricted to (0,Inf). Gray, Vijverberg and Woodward extended these results to discrete processes. Later all these results were generalized by the introduction of G(Lambda) processes. Euler processes and Harmonic in Log Space processes are examples of M-stationary processes. These methods outperformed the conventional methods. In the current research, we extend the definition of M-stationary processes on t with the ranges (-Inf,0) and (0,Inf) for analyzing non-stationary processes with periodic behavior that compresses or lengthens with time. We refer to M-stationary processes as Left M-stationary and Right M-stationary when t is restricted to (-Inf,0) and (0,Inf) respectively. The new M-stationary processes produced superior results compared to conventional approaches for analyzing time series with an approximate linear compacting or elongating pseudo periodic behavior.