Nonlinearity in US macroeconomic time series

Abstract

In this study, we evaluate the linearity of 170 major monthly US macroeconomic time series spanning the years 1959–2002. Employing the linearity test recently proposed by Harvey et al. (2008), which is applicable when the order of integration is uncertain, we determined that more than half of the macroeconomic time series were nonlinear. In particular, approximately 75% of the time series in nominal prices, wages and money category were determined to be nonlinear, whereas the least abundant evidence, corresponding to approximately 43% of the series, was detected in the category of construction, inventories and order.

Acknowledgements

This work was supported by Research Program 2010 of Kookmin University in Korea.

Notes

¹Many other linearity tests have been developed in the literature. The tests generally assume that the variables under examination are either stationary I(0) or nonstationary I(1). Because of space considerations, we do not present here the number of other available linearity tests; see Yoon (2009) for some references.

²To implement the W _λ linearity test, I use the GAUSS program, which is available at http://www.bepress.com/snde/vol12/iss3/art2/.

³For the full sample period, the number of observations is 528. The least number of available observations is 412. Additionally, only seven time series, six interest rates and S&P's composite common stock/price-earning ratio [fspxe] are explicitly denoted as not seasonally adjusted; see the appendix in Marcellino et al. (2006). Note that the DRI BASIC mnemonic is provided in square brackets throughout this study.

⁴Industrial production index – total index [ips10] is also found to be nonlinear at a significance level of 10%.

⁵naics stands for the North American Industry Classification System, which replaced the Standard Industrial Classification from January 2003.

⁶They are ips18, gmcnq, msnq and rtnrq, respectively. The exceptions are industrial production and capacity utilization of nondurable manufacturing, ipd versus ipn and utl13 versus utl25. Personal consumption expenditure on new cars [gmcanq] is also nonlinear.

⁷Lundbergh et al. (2003) instead employ ‘Employment: ratio; help-wanted ads: no. unemployed clf’ [lhelx] and estimate their time-varying STAR model. By way of contrast, we find here that the time series lhelx is linear by the Wλ test.