Academic journal article Atlantic Economic Journal

First-Order Autoregression and the Uncertainty Principle

Academic journal article Atlantic Economic Journal

First-Order Autoregression and the Uncertainty Principle

Article excerpt

In a study of annual U.S. corn prices from 1867 to 1948, George Judge, et al. |Introduction to the Theory and Practice of Econometrics, New York: Wiley, 1982, 690-99~ find that the deviations from the mean price are well represented by the first-order autoregression

|X.sub.t~ |is equal to~ r|X.sub.t - 1~ + |e.sub.t~, (1)

where the autocorrelation parameter r is estimated to be 0.80. In using this result to forecast corn prices, one should consider two facts which conspire to limit the predictive capability of model (1). In the first place, the identity |X.sub.t~ |equivalent to~ |X.sub.t - 1~ + (|X.sub.t~ - |X.sub.t - 1~) (2)

shows that an accurate forecast of |X.sub.t~, requires a knowledge of the previous value |X.sub.t - 1~ and the rate of change |X.sub.t~ - |X.sub.t - 1~. This knowledge may be explicit or implicit, but the identity shows that it is indispensable. In fact, if |X.sub.t - 1~ is subtracted from both sides of (1), the result is an equation in which |X.sub.t - 1~ predicts the rate of change:

|X.sub.t~ - |X.sub.t - 1~ |is equal to~ - (1 - r)|X.sub.t - 1~ + |e.sub.t~. (3) Equation (3) describes a process of extrapolation by dead reckoning: |X.sub.t - 1~ |right arrow~ |X.sub.t~ - |X.sub.t - 1~ |right arrow~ |X.sub.t~ |right arrow~ |X.sub.t + 1~ - |X.sub.t~ |right arrow~ |X.sub.t + 1~, and so on.

In the second place, however, Heisenberg's uncertainty principle guarantees that the previous value and the rate of change cannot both be measured with unlimited accuracy, even in the ideal case where one has exact knowledge of r and Var(|e. …

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