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Technique for determining the correlation coefficient for non-stationary time series. (Russian. English summary) Zbl 1299.62081

In the reviewed article the authors solve the following problem. The sample correlation coefficient between two data sets is stabilized to its general value with increase in the sample size only for wide-sense stationary processes, the mean and variance of which do not depend on time. For non-stationary processes the volatility of correlation is observed as a function of time for a sample of certain size and, also, its volatility at the same moment of time for samples of different sizes. The question is how to determine the value of correlation and its reliability for non-stationary series. The necessary condition for correct determining the non-stationary correlation is to find the optimal length of the sample on which to calculate the sample moments of distribution. It is required to find the length of the sample at which a certain correlation value between two series represents the most reliability. A non-stationary sample correlation coefficient is the usual sample correlation coefficient which depends on the sample length and the current time, from which back in time the sample is measured. For each interval whose width determines the accuracy of the correlation coefficient, one can find the length of the sample in which the fraction of correlations that fall into this interval is the largest. This fraction represents a level of confidence of the correlation connection. That interval, for which this fraction is the largest, is taken as the interval that contains the correlation coefficient.
A technique for determining the correlation coefficient is proposed. Two criteria, joint optimization of which allows one to find the greatest size of sample and the confidence interval most likely containing the correlation coefficient are introduced.
This technique is assumed to be used to determine the correlation matrix for multifactorial problems of ecological and epidemiological monitoring and forecasting.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62H20 Measures of association (correlation, canonical correlation, etc.)
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