Prediction Of Turning Points Research Articles

Econometric modeling of urban and other substate areas: An analysis of alternative methodologies

Questions raised by J.R. Meyer and J.W. Millimar on the appropriate level of sophistication in regional econometric models are addressed by comparing the modeling methodologies for each of six diverse substate areas. The methodologies range from aggregated recursive structures driven by an ARIMA time-series model of export-base employment to highly detailed simultaneous equation models. It is found that recursive model accuracy is relatively insensitive to forecast accuracy of the model-driving variable and simultaneous models are more accurate than recursive ones, but relative accuracies of aggregated and detailed simultaneous models are less clear. Population and personal income estimates are improved by disaggregation, but with respect to employment, there is a trade-off in model structure between average employment prediction accuracy over a number of time periods and turning point prediction accuracy.

Predicting the Turning Points of a Time Series

Students of economic time series recognize the notion of a -a point in time when a series which had been increasing reverses and, for a time, decreases.' An example of a turning point is given in figure 1 where the time series of quarterly, seasonally adjusted real GNP is shown. The time points 1957:3 and 1973:4 can be considered turning points since they each mark the beginning of a downturn. For economists, turning points have long been an object of study and comment (Zarnowitz 1972). Turning points have received relatively less attention from statisticians. Thus, the term is not found in the indexes of Wiener (1949), Yaglom (1962), Whittle (1963), Box and Jenkins (1970), Hannan (1970), Anderson (1971), Brillinger (1975), or Fuller (1976). More to the point (though more subjectively), the concept of a turning point is absent as well. In Section II of this paper I discuss the relationship between the theory of minimum mean square error linear prediction and the turning point prediction problem. I show why the linear prediction theory does not give a solution to the Linear least-squares prediction methods are not directly applicable to the prediction of time series points. In this paper the linear least-squares technique is extended to allow computation of the distribution of the turning points of a time series, conditional on past observations. The method is illustrated using quarterly seasonally adjusted GNP.

On the Appraisal of Cyclical Turning-Point Predictors

IN ORDER to review past economic forecasts and to investigate methods of improving economic predictions in the future, economists require criteria for appraising the predictive accuracy of their forecasts. For quantitative predictions of national product and its components, such criteria have been advanced and discussed. Forecast errors are naturally measurable as dollar deviations between predicted and actual magnitudes. The errors in a number of different forecasts can therefore be readily compared. In addition, naive models which imply persistence of either the rate of change or the level of national product have been accepted as benchmarks for comparison with economists' predictions. There has been little discussion, however, of criteria for appraising the accuracy of cyclical turning-point forecasts, which project reversals in the direction of change of economic activity. This paper advances a method for evaluating turningpoint predictions and illustrates the operation of the proposed system on historical data collected by the National Bureau of Economic Research. The assumptions underlying the scoring system and the characteristics of the method are discussed below. Few claims are made for the system; it is far from ideal. It is offered with the conviction that some objective standard of appraisal is required for turning-point forecasts and that the specification of one possible system may evoke fruitful discussion of the problem. If existing methods of forecasting are to be evaluated and if new methods are to be sought, it must be possible to recognize a good forecast and to distinguish degrees of accuracy. Even if a particular forecasting tool or method is used in combination with other evidence and judgment, it is desirable to determine the predictive contribution of that element of the forecast. It may well be that informed judgment can produce successful forecasting. Still, it is reasonable to inquire whether a particular tool is an aid or a hindrance to the exercise of good judgment. The possibility of employing a method subjectively does not prevent the objective appraisal of that method. Only if predictive techniques can be evaluated objectively can the accuracy of economic forecasting be viewed as a test of methods rather than of men. In principle, the value of a prediction should be gauged in terms of the uses for which the forecast is desired. In order to obtain guidance for their actions, decision-makers can exercise a choice among * This paper was written as part of the project in Research on Short-Term Economic Forecasting conducted at the Cowles Foundation for Research in Economics at Yale University and financed by the Rockefeller Foundation. I am indebted to Mrs. Wilma W. Heston for her valuable assistance in processing the data presented below. Dr. Geoffrey Moore, of the National Bureau of Economic Research, kindly provided me with data and also offered helpful criticisms. The F. W. Dodge Corporation authorized the release of its data on construction contracts. I am also grateful to Harry Eisenpress, William Fellner, Todd May, Richard Porter, Robert Summers, and James Tobin for their constructive suggestions.