Stochastic drifts

Stochastic drift

The word stochastic (Gr. στωχος, guess) means random, pertaining to chance. Stochastic models are based on random trials and usually envelope a randomly determined sequence of observations.

Also known as ‘gambler’s ruin,’ random events often look meaningful. Gamblers often infuse streaks of wins with special meaning such as ‘this must be my lucky day.’ However, the laws of probability follow an ironclad logic of their own and in the end, the house is always the winner. The theory of statistics can help us to recognize the random movements of a sealed bottle carrying a castaway’s message to the Four Corners of the Earth from its movement in the Labrador stream.

Stochastic drift transformed into white noise.

For millennia, the ultimate criterion of truth was ‘I saw it.’ With the advent of mediated visual communications and virtual reality, this primary criterion of verity is being eroded. The advent of television in the second half of this century expanded our knowledge and weakened our critical faculties. We are more readily persuaded and our loyalties are more readily swayed. To really benefit from the expanded horizons visual modes of communication offer, we have to sharpen our critical faculties. Practical rules for doing that are often implicit in the quantitative methods of social sciences, offering many tools for detection of stochastic drifts and separation of information from error. These methods help us to sort fact from fiction, propaganda from information, true meaning of communications from their purported meaning. In their entirety they offer powerful tools, indispensable in our times to critical human beings, capable of viewing more sides of the issues than one. This book offers insights on the inner working of these methods, their assumptions and limitations, strengths and weaknesses and suggests how the results of quantitative research in social sciences can expand your horizons and sharpen your vision.

Longitudinal studies of secular events are frequently conceptualized as consisting of a trend component fitted by a polynomial, a cyclical component often fitted by an analysis based on autocorrelations or on a Fourier series, and a random component (stochastic drift) to be removed. In the course of the time series analysis, identification of cyclical and stochastic drift components is often attempted by alternating autocorrelation analysis and differencing of the trend. Autocorrelation analysis helps to identify the correct phase of the fitted model while the successive differencing transforms the stochastic drift component into white noise.

References
Krus, D.J., & Ko, H.O. (1983) Algorithm for autocorrelation analysis of secular trends. Educational and Psychological Measurement, 43, 821-828.
Krus, D. J., & Jacobsen, J. L. (1983) Through a glass, clearly? A computer program for generalized adaptive filtering. Educational and Psychological Measurement, 43, 149-154