Auto-correlograms

The latter equation is easier for repetitive computations because the term at the bottom needs to be calculated only once, and such shortcuts were helpful prior to the computer age. However, using modem packages, it is not difficult to use the first equation, which will be employed in this text. It is important, though, always to understand and check different methods. In most cases there is little difference between the two calculations. 

it is possible to have both negative and positive lags, but for an auto-correlogram, ri = r-i, and sometimes only one half of the correlogram is displayed  

the closer the correlation coefficient is to 1, the more similar are the two series if a high correlation is observed for a large lag, this indicates cyclicity  

as the lag increases, the number of datapoints used to calculate the correlation coefficient decreases, and so r/ becomes less informative and more dependent on noise. Large values of l are not advisable a good compromise is to calculate the correlogram for values of l up to 7/2, or half the points in the original series. 

An auto-correlogram emphasizes only cyclical features. Sometimes there are 11011-cyclical trends superimposed over the time series. Such situations regularly occur in economics. Consider trying to determine the factors relating to expenditure in a seaside 

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The most basic calculation is that of an auto-correlogram. Consider die information depicted in Figure 3.13, which represents a process changing with time. It appears that there is some cyclicity but this is buried within the noise. The data are presented in... 

To include information about process dynamics, lagged variables can be included in X. The (auto)correlograms of all x variables should be developed to determine first how many lagged values are relevant for each variable. Then the data matrix should be augmented accordingly and used to determine the principal components that will be used in the regression step. 

In the step of identifying, we generally determine the order and estimate the parameters by the Box-Jenkins method. That is to say, we could obtain the results through the analysis of the auto-correlogram and partial-autocor-relogram. And the length of season could also be learned from the background of practical applications. 

Figure 8 Two-dimensional sketch illustrating the MIF filtering step in ALMOND. MIFs for the N1 probe (hydrogen bond donor, green) and the O probe (hydrogen bond acceptor, red), top, are processed at the same energy level, e.g., —2 kcal/mol, to yield a few hundred representative nodes, bottom. The grey lines illustrate distances used in the auto- (Nl-Nl) and cross- (Nl-O) correlograms by the MACC-2 encoding algorithm. (See color plate at end of chapter.)...

Figure 9 Auto- and cross-correlogram profile obtained for the furoyl-piperidinyl-methyl-indol sketched in Fig. 8, using a hydrogen bond donor (Nl) and hydrogen bond acceptor (O) probe. The 0-0 autocorrelogram is on the left, the Nl-Nl autocorrelogram in the middle, and the Nl-O cross-correlogram on the right.

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