Trends and cycles as unobserved components in macroeconomic time series: A Bayesian perspective

Bayesian techniques are employed to analyze an unobserved components model that measures the persistence of time series innovations. The model combines a stochastic trend (random walk with drift) and a cyclical component (an autoregressive integrated moving averae-ARIMA-process). To analyze persistence, we conduct posterior inference over the trend component innovation variance: zero variance implies that innovations have transitory effects, while nonzero variance implies that the effects are permanent. We also conduct posterior inference over AR and MA roots: unit AR roots imply that innovations have permanent effects, while unit MA roots for differenced data imply that the effects are transitory. We apply our techniques to four of the Nelson-Plosser (1982) series studied by Harvey (1985): real GNP, industrial production, stock prices, and the CPI. For the CPI, innovations appear to have permanent effects; for the remaining series, they do not.