Keywords: linear models, optimal design, orthogonal designs, discrete Fourier transform, power spectral density, construction 1 Introduction Sequences with zero or low autocorrelation function have been widely used in Statistics and in particular in the theory of optimal experimental designs.

The random force [xi] (t) is Gaussian and fully characterized by its autocorrelation function satisfying the fluctuation-dissipation relation <[xi](t)[xi](t')> = [k.

Therefore, we have evaluated the autocorrelation function (ACF) and partial autocorrelation function (PACF) of the OLS regression residuals using SAS procedure PROC ARIMA (see SAS/ETS User's Guide, 1993).

The aperiodic autocorrelation function (ACF) of sequence S of length N is given as, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] .

Therefore, I evaluated the autocorrelation function (ACF) and partial autocorrelation function (PACF) of the OLS regression residuals using SAS procedure PROC ARIMA (see SAS/ETS User's Guide, 1993).

autocorrelation function and partial autocorrelation function of residuals) and the pseudo-[R.

In this meaning we can talk about the stability or instability of the stochastic process and to evaluate it by calculating autocorrelation functions (ACF) for certain time intervals (e.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1) The autocorrelation function of an ergodic process in the limited interval n=[0, N-1], k=[0, N-1] is calculated as a finite sum, (Marie, 2002) eq.