Turning point identification and Bayesian forecasting of a volatile time series

Abstract

Volatile time series are part of the industrial engineering forecasting and planning environment. An example of a volatile time series is the daily closing price of a stock, such as IBM, which is adaptively forecasted in this paper. Volatile series are beset with random shocks, from day-to-day, which may be characterized as 1) no charge in the series, 2) a step change, 3) a ramp change, or 4) a transient change. These random shocks are referred to as states of the time series. Probabilities for the various states are determined (computationally and subjectively) and are combined with the Bayesian results of Kaiman (3, 6) to update adaptively a forecasting equation. The method, therefore, is a multi-state procedure which embeds the Bayesian estimation method of Kalman. To illustrate the technique, a linear forecasting equation is used to predict the daily closing prices of IBM stock for 79 trading days starting on September 8 and extending to December 29, 1987; a period which includes the “crash” of October 19, 1987. In general seasonality may be added, if desired. It is assumed that the reader is familiar with Kalman's results.