Abstract
In this article, we investigate spectrum estimation of law order moving average (MA) process. The main tool is the lag window which is one of the important components of the consistent form to estimate spectral density function (SDF). We show, based on a computer simulation, that the Blackman window is the best lag window to estimate the SDF of MA1 and MA2 at the most values of parameters βi and series sizes n, except for a special case when β=−1 and n≥40 in MA1. In addition, the Hanning–Poisson window appears as the best to estimate the SDF of MA2 when β1=β2=−0.5 and n≥40.
Highlights
A set xt of numerical data made sequentially in time t is called time series [1]. ere are some important processes of a time series: autoregressive, moving average, and autoregressive-moving average processes.Spectral analysis can be defined as a process that assigns power versus frequency
E spectrum estimation methods can be classified into parametric and nonparametric methods [3]. e consistent estimate of spectral density function f(ω) is the most important nonparametric spectral analysis method, which depends on lag window λT(v) and truncation point T [4]
Window functions are used in the estimation of power spectra and bispectra in order to ensure the consistency of the periodogram and the Fourier-type bispectrum estimation methods
Summary
A set xt of numerical data (observations) made sequentially in time t is called time series [1]. ere are some important processes of a time series: autoregressive, moving average, and autoregressive-moving average processes. E object of spectral analysis is to estimate and study the spectrum of the time series processes for the phenomena of physics and engineering [2]. E consistent estimate of spectral density function f(ω) is the most important nonparametric spectral analysis method, which depends on lag window λT(v) and truncation point T [4]. Window functions are used in the estimation of power spectra and bispectra in order to ensure the consistency of the periodogram and the Fourier-type bispectrum estimation methods. E basic concepts given in Sections 2–5 present white noise, moving average process of order q and their properties, spectral density function (SDF) on general and SDF of MA(q), and the consistent estimate of SDF, and some.
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