Testing for a unit root in a process exhibiting a structural break in the presence of GARCH errors

This paper considers the effect of GARCH errors on the tests proposed byPerron (1997) for a unit root in the presence of a structural break. We assessthe impact of degeneracy and integratedness of the conditional varianceindividually and find that, apart from in the limit, the testing procedure isinsensitive to the degree of degeneracy but does exhibit an increasingover-sizing as the process becomes more integrated. When we consider the GARCHspecifications that we are likely to encounter in empirical research, we findthat the Perron tests are reasonably robust to the presence of GARCH and donot suffer from severe over-or under-rejection of a correct null hypothesis.

Linear vs. log-linear unit-root specification: an application of mis-specification encompassing

The objective of this paper is to apply the mis-specification (M-S) encompassing perspective to the problem of choosing between linear and log-linear unit-root models. A simple M-S encompassing test, based on an auxiliary regression stemming from the conditional second moment, is proposed and its empirical size and power are investigated using Monte Carlo simulations. It is shown that by focusing on the conditional process the sampling distributions of the relevant statistics are well behaved under both the null and alternative hypotheses. The proposed M-S encompassing test is illustrated using US total disposable income quarterly data.

Reviewing the sustainability/stationarity of current account imbalances with tests for bounded integration

We investigate for 26 OECD economies whether their current account imbalances to GDP are driven by stochastic trends. Regarding bounded stationarity as the more natural counterpart of sustainability, results from Phillips–Perron tests for unit root and bounded unit root processes are contrasted. While the former hint at stationarity of current account imbalances for 12 economies, the latter indicate bounded stationarity for only six economies. Through panel-based test statistics, current account imbalances are diagnosed as bounded non-stationary. Thus, (spurious) rejections of the unit root hypothesis might be due to the existence of bounds reflecting hidden policy controls or financial crises.

Testing for unit roots in bounded time series

Many key economic and financial series are bounded either by construction or through policy controls. Conventional unit root tests are potentially unreliable in the presence of bounds, since they tend to over-reject the null hypothesis of a unit root, even asymptotically. So far, very little work has been undertaken to develop unit root tests which can be applied to bounded time series. In this paper we address this gap in the literature by proposing unit root tests which are valid in the presence of bounds. We present new augmented Dickey–Fuller type tests as well as new versions of the modified ‘M’ tests developed by Ng and Perron [Ng, S., Perron, P., 2001. LAG length selection and the construction of unit root tests with good size and power. Econometrica 69, 1519–1554] and demonstrate how these tests, combined with a simulation-based method to retrieve the relevant critical values, make it possible to control size asymptotically. A Monte Carlo study suggests that the proposed tests perform well in finite samples. Moreover, the tests outperform the Phillips–Perron type tests originally proposed in Cavaliere [Cavaliere, G., 2005. Limited time series with a unit root. Econometric Theory 21, 907–945]. An illustrative application to U.S. interest rate data is provided

Testing for non-stationarity and cointegration allowing for the possibility of a structural break: an application to EuroSterling interest rates

In this paper we examine the order of integration of EuroSterling interest rates by employing techniques that can allow for a structural break under the null and/or alternative hypothesis of the unit-root tests. In light of these results, we investigate the cointegrating relationship implied by the single, linear expectations hypothesis of the term structure of interest rates employing two techniques, one of which allows for the possibility of a break in the mean of the cointegrating relationship. The aim of the paper is to investigate whether or not the interest rate series can be viewed as I(1) processes and furthermore, to consider whether there has been a structural break in the series. We also determine whether, if we allow for a break in the cointegration analysis, the results are consistent with those obtained when a break is not allowed for. The main results reported in this paper support the conjecture that the ‘short’ Euro-currency rates are characterised as I(1) series that exhibit a structural break on or near Black Wednesday, 16 September 1992, whereas the ‘long’ rates are I(1) series that do not support the presence of a structural break. The evidence from the cointegration analysis suggests that tests of the expectations hypothesis based on data sets that include the ERM crisis period, or a period that includes a structural break, might be problematic if the structural break is not explicitly taken into account in the testing framework.

Bayesian model averaging and identification of structural breaks in time series

Bayesian Model Averaging (BMA) is used for testing for multiple break points in univariate series using conjugate normal-gamma priors. This approach can test for the number of structural breaks and produce posterior probabilities for a break at each point in time. Results are averaged over specifications including: stationary; stationary around trend and unit root models, each containing different types and number of breaks and different lag lengths. The procedures are used to test for structural breaks on 14 annual macroeconomic series and 11 natural resource price series. The results indicate that there are structural breaks in all of the natural resource series and most of the macroeconomic series. Many of the series had multiple breaks. Our findings regarding the existence of unit roots, having allowed for structural breaks in the data, are largely consistent with previous work.

Adventitious root formation in anacardium occidentale L. in response to phytohormones and removal of roots

Despite advances in tissue culture techniques, propagation by leafy, softwood cuttings is the preferred, practical system for vegetative reproduction of many tree and shrub species. Species are frequently defined as 'difficult'- or 'easy-to-root' when propagated by conventional cuttings. Speed of rooting is often linked with ease of propagation, and slow-to-root species may be 'difficult' precisely because tissues deteriorate prior to the formation of adventitious roots. Even when roots form, limited development of these may impair the establishment of a cutting. In this study we used softwood cuttings of cashew (Anacardium occidentale), a species considered as 'difficult-to-root'. We aimed to test the hypothesis that speed, and extent of early rooting, is critical in determining success with this species; and that the potential to form adventitious roots will decrease with time in the propagation environment. Using two genotypes, initial rooting rates were examined in the presence or absence of exogenous auxin. In cuttings that formed adventitious roots, either entire roots or root tips were removed, to determine if further root formation/development was feasible. To investigate if subsequent root responses were linked to phytohormone action, a number of cuttings were also treated with either exogenous auxin (indole-3-butyric acid-IBA) or cytokinin (zeatin). Despite the reputation of Anacardium as being 'difficult-to-root', we found high rooting rates in two genotypes (AC 10 and CCP 1001). Removing adventitious roots from cuttings and returning them to the propagation environment, resulted in subsequent re-rooting. Indeed, individual cuttings could develop new adventitious roots on four to five separate occasions over a 9 week period. Data showed that rooting potential increased, not decreased with time in the propagation environment and that cutting viability was unaffected. Root expression was faster (8-15 days) after the removal of previous roots compared to when the cuttings were first stuck (21 days). Exposing cuttings to IBA at the time of preparation, improved initial rooting in AC 10, but not in CCP 1001. Application of IBA once roots had formed had little effect on subsequent development, but zeatin reduced root length and promoted root number and dry matter accumulation. These results challenge our hypothesis, and indicate that rooting potential remains high in Anacardium. The precise mechanisms that regulate the number of adventitious roots expressed, remain to be determined. Nevertheless, results indicate that rooting potential can be high in 'difficult-to-root' species, and suggest that providing supportive environments is the key to expressing this potential. (c) 2006 Elsevier B.V. All rights reserved.

Root distributions of Australian herbaceous perennial legumes in response to phosphorus placement

Many Australian plant species have specific root adaptations for growth in phosphorus-impoverished soils, and are often sensitive to high external P concentrations. The growth responses of native Australian legumes in agricultural soils with elevated P availability in the surface horizons are unknown. The aim of these experiments was to test the hypothesis that increased P concentration in surface soil would reduce root proliferation at depth in native legumes. The effect of P placement on root distribution was assessed for two Australian legumes, Kennedia prorepens F. Muell. and Lotus australis Andrews, and the exotic Medicago sativa L. Three treatments were established in a low-P loam soil: amendment of 0.15 g mono-calcium phosphate in either (i) the top 50 mm (120 µg P g–1) or (ii) the top 500 mm (12 µg P g–1) of soil, and an unamended control. In the unamended soil M. sativa was shallow rooted, with 58% of the root length of in the top 50 mm. K. prorepens and L. australis had a more even distribution down the pot length, with only 4 and 22% of their roots in the 0–50 mm pot section, respectively. When exposed to amendment of P in the top 50 mm, root length in the top 50 mm increased 4-fold for K. prorepens and 10-fold for M. sativa, although the pattern of root distribution did not change for M. sativa. L. australis was relatively unresponsive to P additions and had an even distribution of roots down the pot. Shoot P concentrations differed according to species but not treatment (K. prorepens 2.1 mg g–1, L. australis 2.4 mg g–1, M. sativa 3.2 mg g–1). Total shoot P content was higher for K. prorepens than for the other species in all treatments. In a second experiment, mono-ester phosphatases were analysed from 1-mm slices of soil collected directly adjacent to the rhizosphere. All species exuded phosphatases into the rhizosphere, but addition of P to soil reduced phosphatase activity only for K. prorepens. Overall, high P concentration in the surface soil altered root distribution, but did not reduce root proliferation at depth. Furthermore, the Australian herbaceous perennial legumes had root distributions that enhanced P acquisition from low-P soils.

Host and habitat filtering in seedling root-associated fungal communities: taxonomic and functional diversity are altered in ‘novel’ soils

Climatic and land use changes have significant consequences for the distribution of tree species, both through natural dispersal processes and following management prescriptions. Responses to these changes will be expressed most strongly in seedlings near current species range boundaries. In northern temperate forest ecosystems, where changes are already being observed, ectomycorrhizal fungi contribute significantly to successful tree establishment. We hypothesised that communities of fungal symbionts might therefore play a role in facilitating, or limiting, host seedling range expansion. To test this hypothesis, ectomycorrhizal communities of interior Douglas-fir and interior lodgepole pine seedlings were analysed in a common greenhouse environment following growth in five soils collected along an ecosystem gradient. Currently, Douglas-fir’s natural distribution encompasses three of the five soils, whereas lodgepole pine’s extends much further north. Host filtering was evident amongst the 29 fungal species encountered: 7 were shared, 9 exclusive to Douglas-fir and 13 exclusive to lodgepole pine. Seedlings of both host species formed symbioses with each soil fungal community, thus Douglas-fir did so even where those soils came from outside its current distribution. However, these latter communities displayed significant taxonomic and functional differences to those found within the host distribution, indicative of habitat filtering. In contrast, lodgepole pine fungal communities displayed high functional similarity across the soil gradient. Taxonomic and/or functional shifts in Douglas-fir fungal communities may prove ecologically significant during the predicted northward migration of this species; especially in combination with changes in climate and management operations, such as seed transfer across geographical regions for forestry purposes.