Spurious Trend and Cycle in the State Space Decomposition of a Time Series with a Unit Root

22 Pages Posted: 4 Jul 2004 Last revised: 5 Sep 2010

Date Written: November 1987

Abstract

Recent research has proposed the state space (88) framework for decomposition of GNP and other economic time series into trend and cycle components, using the Kalman filter. This paper reviews the empirical evidence and suggests that the resulting decomposition may be spurious, just as detrending by linear regression is known to generate spurious trends and cycles in nonstationary time series. A Monte Carlo experiment confirms that when data is generated by a random walk, the 88 model tends to indicate (incorrectly) that the series consists of cyclical variations around a smooth trend. The improvement in fit over the true model will typically appear to be statistically significant. These results suggest that caution should be exercised in drawing inferences about the nature of economic processes from the 88 decomposition.

Suggested Citation

Nelson, Charles R., Spurious Trend and Cycle in the State Space Decomposition of a Time Series with a Unit Root (November 1987). NBER Working Paper No. t0063, Available at SSRN: https://ssrn.com/abstract=282675

Charles R. Nelson (Contact Author)

Dept of Economics ( email )

Box 353330
Seattle, WA 98195-3330
United States

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