*J. Japan Statist. Soc.,* Vol. 31 (No. 2), pp. 129-152, 2001

## Examining Similarities Among Phases of Business Cycles —Is the 1990s US Expansion Similar to the 1960s'?—

Masaki Katsuura and Allan P. Layton

**Abstract. **
Statistical similarities among the latest long expansion in the U.S. and some other past expansions, in particular that of the 1960s, are examined. Corresponding to the definition of statistical similarity, a test based on the covariance matrices of business cycle component variables for the different expansions is proposed. Among available tests, the test based on partial common principal component analysis is argued to be most appropriate. The test is applied to the components of both GDP and the coincident composite index. As a result, the 1990s expansion is concluded to be statistically similar to that of the 1960s. Using the same method we also examine the statistical similarities of whole cycles (defined on a peak-to-peak basis).

*Key words and phrases*:
Business Cycle; Statistical Similarity; Covariance Matrix Structure; Composite Index; Partial Common Principal Component Analysis.

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