Nonlinearity, Nonstationarity, and Spurious Forecasts

44 Pages Posted: 17 Apr 2021

See all articles by Vadim Marmer

Vadim Marmer

University of British Columbia (UBC) - Vancouver School of Economics

Date Written: January 1, 2008

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

Suggested Citation

Marmer, Vadim, Nonlinearity, Nonstationarity, and Spurious Forecasts (January 1, 2008). Journal of Econometrics, Vol. 142, No. 1, 2008, Available at SSRN: https://ssrn.com/abstract=3824487

Vadim Marmer (Contact Author)

University of British Columbia (UBC) - Vancouver School of Economics ( email )

6000 Iona Dr
Vancouver, BC V6T 1L4
Canada

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