Time-lagged correlation matrix

The time-lagged correlation matrix, R(t), is converted into a Euclidean distance matrix with the canonical transform [7] ... 

Today, the modern version of time-lag focusing, or delayed extraction,14 16 is used in almost all MALDI-TOF mass spectrometers. It is in fact a special case of the Wiley and McLaren method, in which the initial spatial distribution (usually a very thin sample and matrix mixture dried on a stainless steel plate) is assumed to be zero. Therefore, after the delay time the velocity and spatial distributions are correlated, i.e. ions of highest velocity have moved the greatest distance. This space velocity correlated focusing has been described by Colby and Riley,17 and provides considerably better focusing than can be obtained from two independent and uncorrelated initial distributions in space and velocity/energy that comprise the general Wiley-McLaren case. 

There are two conservation constraints in this system first, the sum of the concentrations of 85 and 87 is constant second, the sum of the concentrations of 83, 84, and 85 is constant. Hence of the 5 response concentrations, only 3 are independent the matrix R made up of the correlations is four-dimensional, three concentration dimensions and the time lag r. 

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... 

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