Detection of Structural Change in the Long‐run Persistence in a Univariate Time Series*

Abstract

In this paper, we investigate a test for structural change in the long-run persistence in a univariate time series. Our model has a unit root with no structural change under the null hypothesis, while under the alternative it changes from a unit-root process to a stationary one or vice versa. We propose a Lagrange multiplier-type test, a test with the quasi-differencing method, and 'demeaned versions' of these tests. We find that the demeaned versions of these tests have better finite-sample properties, although they are not necessarily superior in asymptotics to the other tests.

On the dynamics of inflation persistence around the world

“…Noriega and Ramos-Francia (2008) also find significant drops in inflation persistence for the US using both monthly and quarterly data for a larger sample. See Levin and Piger (2006) for a recent survey. 33 For instance, Altissimo et.…”

“…The selection of k i max for these two countries was made on the basis of how well the procedure picks the apparent level breaks present in the data, by making changes in persistence and changes in level to coincide. On this point, LKT argue that "In practice it is probably not unreasonable to assume that structural breaks in the deterministic kernel d t occur at the same point(s) in the sample as changes in persistence" (p.20), and discuss some evidence on the occurrence of this coincidence (see Kurozumi (2005) In Table 2, the second column refers to the sample or subsample over which the testing procedure is applied. b k i indicates the estimated value of k i in (2), according to the BIC, while M indicates the estimated value of the test statistic in (3).…”

“…8 Using models with time varying parameters, several authors suggest that inflation persistence has diminished along with its overall level. See Cogley and Sargent (2001), Benati (2002), Levin and Piger (2006), Capistrán and Ramos-Francia (2006), Harvey, et. al.…”

US stock market volatility persistence: evidence before and after the burst of the IT bubble

“…11 Table 7 Estimates of d for the second subsample. AR(1) disturbances Estimates with asterisk mean that volatility is higher in the second subsample Estimates with asterisk mean that volatility is higher in the second subsample 10 A very similar break-date was obtained when using other break-date detection methods based on nonfractional models (Andrews 1993(Andrews , 2003Kurozumi 2005). 11 Confidence intervals for the break-date estimates are not computed.…”

Wald Tests for Detecting Multiple Structural Changes in Persistence

“…When the direction of the change is unknown, they consider the minimal value of the pair of statistics for each case. Kurozumi (2005) suggests an alternative testing procedure based on the Lagrange Multiplier (LM) principle while Leybourne et al (2006) develop tests of the unit root null based on standardized cumulative sums of squared sub-sample residuals that do not spuriously reject when the series is a constant I(0) process.…”