Average Power Function of Noise and Its Applications in Seasonal Time Series Modeling and Forecasting

Qiang Song

doi:10.4236/ajor.2011.14034

Abstract

This paper presents a new method of detecting multi-periodicities in a seasonal time series. Conventional methods such as the average power spectrum or the autocorrelation function plot have been used in detecting multiple periodicities. However, there are numerous cases where those methods either fail, or lead to incorrectly detected periods. This, in turn in applications, produces improper models and results in larger forecasting errors. There is a strong need for a new approach to detecting multi-periodicities. This paper tends to fill this gap by proposing a new method which relies on a mathematical instrument, called the Average Power Function of Noise (APFN) of a time series. APFN has a prominent property that it has a strict local minimum at each period of the time series. This characteristic helps one in detecting periods in time series. Unlike the power spectrum method where it is assumed that the time series is composed of sinusoidal functions of different frequencies, in APFN it is assumed that the time series is periodic, the unique and a much weaker assumption. Therefore, this new instrument is expected to be more powerful in multi-periodicity detection than both the autocorrelation function plot and the average power spectrum. Properties of APFN and applications of the new method in periodicity detection and in forecasting are presented.

Highlights

Modeling and forecasting seasonal time series with multiple periodicities has regained attentions from researchers [1,2,3,4,5,6,7,8]
This paper presents a new method of detecting multi-periodicities in a seasonal time series
This paper tends to fill this gap by proposing a new method which relies on a mathematical instrument, called the Average Power Function of Noise (APFN) of a time series

Summary

Introduction

Modeling and forecasting seasonal time series with multiple periodicities has regained attentions from researchers [1,2,3,4,5,6,7,8]. In the literature of modeling and forecasting seasonal time series with multiperiodicities, the lengths of periods are determined by human beings, based on either their experience or their specific domain knowledge of the time series under study. When the plurality of time series to work with is small, it may not be a significant problem for human beings to determine the length of each period. It will become a forbidding task if the number of time series is in the range of tens of thousands, not to mention the possibility that the periodicities may change over time. One has to resort to automated algorithms to detect the periodicities in a time series

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