An analysis of the time series properties of the UK ex-post real interest rate: fractional integration, breaks or nonlinear

Abstract

In this article we examine the persistent nature of the 3-month UK real interest rate for the period 1957:Q2 to 2008:Q2. We employ unit root and cointegration tests, confidence intervals for the sum of the Autoregressive (AR) coefficient, fractional integration tests, structural break tests and threshold modelling. Evidence from both unit root tests and AR modelling support the view that the real rate is nonstationary. Similarly, and in contrast to previous literature, the fractional integration test supports covariance nonstationarity, although there is evidence of mean reversion. Evidence from structural break tests support stationary behaviour, but only if we allow for three or more breaks, which may not be defendable on economic grounds. Finally, stationary behaviour is supported by a nonlinear exponential smooth transition model, which suggests that the real rate behaves in a random walk fashion when the rate is close to equilibrium but exhibits strong mean reversion when the disequilibrium becomes large.

Notes

¹ That is, .

² The tests in Tables 1, 2 and 3 mirror Tables 2, 3 and 4 of Neely and Rapach (2008). We thank David Rapach for the programs. We extend their econometric tests by including nonlinear testing procedures.

³ Crowder and Hoffman (1996) point out that impulse response analysis show that shocks have very persistent effects on the ex-post real rate, even though US ex-post real rate appears to be I(0).

⁴ Andrews and Chen (1994) point out that the sum of the AR coefficients, ρ, measures the persistence in a series, because it is related to the cumulative impulse response function and the spectrum at zero frequency. More conventional asymptotic or bootstrap confidence intervals do not generate valid confidence intervals for nearly integrated processes (Basawa et al., 1991), however, Hansen (1999) and Romano and Wolf (2001) show that their procedures generate confidence intervals for ρ with correct first-order asymptotic coverage. Mikusheva (2007) show that the Hansen (1999) grid-bootstrap procedure has correct asymptotical coverage, but, the Romano and Wolf (2001) subsampling procedure does not.

⁵ Indeed there exists research demonstrating that evidence of fractional integration long memory may arise due to failure to account for structural breaks as discussed in this section (see for example, Lobato and Savin, 1998; Diebold and Inoue, 2001). Similarly, recent research has shown that fractional integration can be mistaken for non-linear behaviour as discussed in the following section (see for example, Granger and Teräsvirta, 1999; Byers and Peel, 2003). Furthermore, with specific reference to real interest rate data, Venetis et al. (2006) reported fractional integration using monthly real interest rate data over the period 1975 to 1999 for 14 European countries and the US. But note that there is evidence that this property is spurious with results suggesting structural breaks.

⁶ It would be interesting in future research to consider regime-switching models and recently developed structural break tests such as described by Elliott and Muller (2006).

⁷ In contrast to this evidence for breaks in the real rate, the Bai and Perron (1998) methodology fails to discover significant evidence of structural breaks in the mean of per capita consumption growth (we omit complete results for brevity).