In this note it is shown that the expectation of the usual MLE estimator of the mean-reversion parameter in linear diffusion models does not exist. However, the moment does exist conditionally on the estimator of the autoregressive parameter in the discretized model being positive.

This paper revisits the generalized adaptive expectations (GAE) mechanism presented by Shepherd (2012) [When are adaptive expectations rational? A generalization, Economics Letters, 115, 4–6]. It provides the precise conditions under which GAE hold, and also discusses its implications for the...

The use of recursive demeaning and detrending procedures in unit root tests has been popular in the literature, since they lead to more precise estimation of the persistence parameter and greater power in unit root tests. However, we find that unit root tests using these recursive procedures...

Two alternatives to Enders and Lee’s (2012a,b) Fourier unit root testing strategy, which incorporates pretesting for nonlinearity, are considered. One is based on the union of rejection (UR) approach, and the other is a hybrid strategy that combines the UR approach with the use of extra...

We show that the CUSUM and LM tests for structural change in the volatility process enjoy monotonic power. The framework is general including many recently proposed non-stationary GARCH-type models. The result is in contrast to the well-known issue of non-monotonic power for the CUSUM-based...

This paper investigates the adjustment of the prices of four key petroleum products in the UK following changes in the price of crude oil. We find significant evidence that the pre-tax prices of diesel, kerosene, and gas oil adjust more rapidly in an upward than a downward direction, but that...

We study the leading properties of 30 US high yield spreads for economic growth between 1996 and 2012 and show that they disappeared in the second half of the 2000s. Our empirical findings demonstrate the unreliability of high yield spreads as leading indicators and cast doubts on the existence...

We apply a recent quantile autoregression unit root test to US GDP. The test takes into account that the transmission of a shock might depend on the sign and the size of the shock. We find that positive and negative shocks including large recessionary shocks like the 2008/2009 crisis have...

A CUSUM test is proposed for testing structural breaks in a long-memory heterogeneous autoregressive model. The limiting distribution of the CUSUM test is shown to be a simple function of a standard Brownian bridge, contrasting with the nuisance parameter dependent asymptotics of other CUSUM...

We compare the asymptotic local power of upper-tail unit root tests against an explosive alternative based on ordinary least squares (OLS) and quasi-differenced (QD) demeaning/detrending. We find that under an asymptotically negligible initialisation, the QD-based tests are near asymptotically...