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

• 作者: Qiang Song
• 来源期刊: 美国运筹学期刊(英文)
• 学科: 医学
• 关键词: SEASONAL Time Series Forecasting SEASONALITY Detection AVERAGE POWER FUNCTION of Noise AVERAGE POWER Spectrum AUTOCORRELATION Functions
• 年，卷（期）: 2011,（4）
• 页码范围: 293-304
• 页数: 12页
• 分类号: R73

摘要

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.