Auto cross-covariance

ACC transforms = Auto-Cross-Covariance transforms —> autocorrelation descriptors... 

Sjdstrdm, M., Rarmar, S. and Wieslander, A. (1995) Polypeptide sequence property relationships in Escherichia coli based on auto cross covariances. Chemom. Intell. Lab. Syst., 29, 295-305. 

Then, for each peptide sequence, auto- and cross-covariances with lags k= 1, 2,. .., K, are calculated as... 

Nystrom, A., Andersson, P.M. and Lundstedt, T. (2000) Multivariate data analysis of topographically modified a-melanotropin analogues using auto and cross auto covariances (ACC). Quant. Struct. -Act. Relat., 19, 264—269. 

While the estimates of the autocorrelation coefficients for the Cg time series (lower rows in 1 to ordy change slightly, the estimates the autocorrelation coefficients for the Benzene time series (upper rows in to 3) are clearly affected since three parameters are dropped from the model. The remaining coefficients are affected, too. In particular, the lagged cross-correlations to the Cg time series change from 1.67 to 2.51 and from -2.91 to -2.67 (right upper entries in 1 and This confirms the serious effect of even unobtrusive outliers in multivariate times series analysis. By incorporating the outliers effects, the model s AIC decreases from -4.22 to -4.72. Similarly, SIC decreases from -4.05 to -4.17. The analyses of residuals. show a similar pattern as for the initial model and reveal no serious hints for cross- or auto-correlation. i Now, the multivariate Jarque-Bera test does not reject the hypothesis of multivariate normally distributed variables (at a 5% level). The residuals empirical covariance matrix is finally estimated as... 

Autocorrelation Coefficient n The auto covariance normalized by the product of the standard deviations of the two sections from the single random variable sequence used to calculate the autocovariance. In other words the autocorrelation coefficient is the cross-correlation coefficient of two sub-sequences of the same random variable. It is probably the most commonly used measure of the correlation between two sections of a single random variable sequence. It is often simply but incorrectly referred to as the autocorrelation, which is the un-normalized expectation value of the product of the two sequence sections. The autocorrelation coefficient of the two subsequences of random variable, X, is often denoted by Pxx(ii>T) where i is the starting index of the second section, and T is the length of the sections. The precise mathematical definition of autocorrelation coefficient of two random variable sequence sections is given by ... 

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