DETECTION OF TURNING POINTS IN A TIME SERIES
- 1 October 1971
- journal article
- Published by Wiley in Decision Sciences
- Vol. 2 (4) , 383-403
- https://doi.org/10.1111/j.1540-5915.1971.tb00891.x
Abstract
Consider a time series for which, over a finite interval, there is a model that provides an adequate forecast of the series. Without loss of genality one can take the series over this period of time to have meanOand variance s̀2. At some time the underlying process changes to some other model. The previous model no longer produces errors with mean zero. It is assumed, however, that the variance remains s̀2. The problem considered here is to detect the change in the process as quickly as possible after it happens. The technique is a computationally feasible extension of Wald's [14] sequential analysis, to develop a parabolic mask centered over the most recent cumulative sum (“cusum”) of the forecast errors. Detection occurs when any previous point in the series of cusums lies outside the parabola. The technique is illustrated by an APL program applied to the logarithms of weekly changes in closing prices for IBM common stock on the New York Stock Exchange over the period 1968–1970.Keywords
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