Suppose that the real-valued RVs X 0 , X 1 and X 2 have zero means and a covariance matrix given by Is it possible for these RVs to be part of a stationary process   Show that the autocorrelation...

Suppose that the real-valued RVs X₀, X₁
and X₂
have zero means and a covariance matrix given by

Is it possible for these RVs to be part of a stationary process

Show that the autocorrelation width for the PDF gσ(·) of Equation (55b) is

The autocorrelation width is thus proportional to the standard deviation σ, which again is intuitively reasonable. By comparison, using Equations (58b) and (60b), the equivalent width and the variance width are
 All three widths are depicted in Figure 73 for the case σ = 1.

We will use the autocorrelation width throughout Chapters 6, 7 and 8 as a unified way of defining the bandwidth for nonparametric estimators of the spectral density function.