Best Lag Window for Spectrum Estimation of Law Order MA Process

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 $\text{MA}\left(1\right)$ and $\text{MA}\left(2\right)$ at the most values of parameters ${\beta }_i$ and series sizes $n$, except for a special case when $\beta =-1$ and $n\ge 40$ in $\text{MA}\left(1\right)$. In addition, the Hanning–Poisson window appears as the best to estimate the SDF of$\hspace{0.17em}\text{MA}\left(2\right)$ when ${\beta }_1={\beta }_2=-0.5$ and $n\ge 40$.