Further in the article there is a description of the test of hypothesis with zero correlation coefficient between the bit autocorrelation function
of the binary sequence analysed and standard bit autocorrelation functions
of binary sequences stored in the database, which correspond to particular radio transmission systems.
The stationarity or non-stationarity of a stochastic process can also be determined by inspection of the sample autocorrelation function
(ACF) (see TABLE 3 below), since the theoretical ACF of a stationary process tends to either die down quickly towards zero with increasing lag k or to cut off after a particular lag k=q (i.
13) that the random process is stationary at any point in space, but the magnitude of the autocorrelation function
depends on coordinate through the local depth h(x).
The stationary phase technique allows that using a predefined shape of the signal PSD function (thus, a desired response of the compression filter and implicitly, a low level of the sidelobes assigned to the signal autocorrelation function
will be assured.
The sample autocorrelation functions
are analyzed in order to examine the reasons for the lack of independence.
A rather natural extension of the normative procedure, based on the autocorrelation function
, might rely on the correlation matrix (6).
Sequences with zero or low autocorrelation function
have been widely used in Statistics and in particular in the theory of optimal experimental designs.
0464 Figure 2: Autocorrelation Function
(ACF) and Partial Autocorrelation Function
Table 2 shows the sample autocorrelation function
(ACF) and partial autocorrelation function
(PACF) for daily returns and squared daily returns of Wheat series.
Although the combined power spectral density (PSD) and autocorrelation function
(ACF) approach provides a complete description of error sources, the results are still difficult to interpret.
Also financial series often show long memory wherein hyperbolic decay rates of the autocorrelation function
of the log price, at odds with the efficient market hypothesis, were first observed by Greene and Fielitz (1977) and Taylor (1986).
We can express the relationship between the autocorrelation function
Kx([tau]) of stationary stochastic process and its power spectral density Sx([omega]) (Levin, 1960) based on the Wiener-Khinchin relations.