Monotonicity restrictions used in a system of early warnings applied to monthly economic data

Abstract

When making political decisions, the ability to make correct predictions about the behaviour of the business cycle in the future is important. The ability to forecast business cycles determines the success of, for example, governmental programmes. By business cycles we generally refer to the fluctuations over time in the total economy. A variety of techniques for predicting the business cycles have been proposed. Some of the proposed techniques aim to predict the values of the business cycle. These techniques often prove to give very bad fits near turning points. Other forecasting methods are designed to predict the time of the turning points in the cycle. Many of the turning point prediction methods are based on discovery of turning points in a leading indicator. A leading indicator represents activity, which lead business cycle turning points, thus having its turning points before the general business cycle. It is often the case that the times of the turning points of the business cycle and a lagged leading index coincide remarkably well, even though the actual values of the two time series do not.

In report I a method is proposed that uses the theory of statistical surveillance and monotonicity conditions to decide if a leading indicator, X, has reached a turning point. The proposed alarm function is based on the maximum likelihood ratio. The time series X is modelled as consisting of two components, namely trend cycle and error, where the cycles in the first component are not periodic. Non-parametric regression is used to estimate the trend cycle. The only information used is the fact that the trend cycle is monotonically increasing up to a peak and thereafter monotonically decreasing. A simulation study is made in order to illustrate the proposed method. The median run length to the first false alarm and the expected delay time were considered to be relevant measures of the performance of the proposed method. The results from the simulation study indicate that when there is no turning point, the average time to the first false alarm is five years, whereas when there is a turning point the average time to the alarm is 3 months.

A possible complication in the monitoring of a leading indicator X is the fact that the observations on X will be made monthly and thus they are likely to exhibit seasonal variation. The proposed method is not designed to deal with seasonality, and therefore the observations must be adjusted for seasonality, prior to surveillance. This possible complication is considered to be solved in report I, but it is treated in report II. The seasonal variation should be eliminated only in order that the turning points should be identified. Since the proposed method of surveillance uses robust regression under monotonicity restrictions the seasonal adjustment method must not change the monotonicity. Moving average techniques, used for seasonal adjustment, are investigated as to their monotonicity preserving properties. The results from this study indicate that when there is no turning point the moving average estimator does preserve the monotonicity. If there, however, is a turning point the moving average estimator does not preserve the time of the turning point, except for some special cases.