NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

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

Charles R. Nelson

NBER Technical Working Paper No. 63
Issued in November 1987
NBER Program(s):   ME

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.

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Document Object Identifier (DOI): 10.3386/t0063

Published: Journal of Economic Dynamics and Control, vol. 12,no.2/3, June/September 1988, pp475-488.

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