Nonlinearity, Nonstationarity, and Spurious Forecasts

Abstract

Implications of nonlinearity, nonstationarity and misspecification are considered from a forecasting perspective. Our model allows for small departures from the martingale difference sequence hypothesis by including a nonlinear component, formulated as a general, integrable transformation of the I(1) predictor. We assume that the true generating mechanism is unknown to the econometrician and he is therefore forced to use some approximating functions. It is shown that in this framework the linear regression techniques lead to spurious forecasts. Improvements of the forecast accuracy are possible with properly chosen nonlinear transformations of the predictor. The paper derives the limiting distribution of the forecastsíMSE. In the case of square integrable approximants, it depends on the L2-distance between the nonlinear component and approximating function. Optimal forecasts are available for a given class of approximants.

Keywords: Forecasting, Integrated time series, Misspecified models, Nonlinear transformations, Stock returns

JEL Classification: C22, C53, G14