Bootstrap union tests for unit roots in the presence of nonstationary volatility

We provide a joint treatment of three major issues that surround testing for a unit root in practice: uncertainty as to whether or not a linear deterministic trend is present in the data, uncertainty as to whether the initial condition of the process is (asymptotically) negligible or not, and the possible presence of nonstationary volatility in the data. Harvey, Leybourne and Taylor (2010, Journal of Econometrics, forthcoming) propose decision rules based on a four-way union of rejections of QD and OLS detrended tests, both with and without allowing for a linear trend, to deal with the first two problems. However, in the presence of nonstationary volatility these test statistics have limit distributions which depend on the form of the volatility process, making tests based on the standard asymptotic critical values invalid. We construct bootstrap versions of the four-way union of rejections test, which, by employing the wild bootstrap, are shown to be asymptotically valid in the presence of nonstationary volatility. These bootstrap union tests therefore allow for a joint treatment of all three of the aforementioned problems.Unit root; local trend; initial condition; asymptotic power; union of rejections decision rule; nonstationary volatility; wild bootstrap

RURAL-TO-URBAN WATER TRANSFERS: MEASURING DIRECT FOREGONE BENEFITS OF IRRIGATION WATER UNDER UNCERTAIN WATER SUPPLIES

Irrigation water from a southeastern Colorado county has been sold to distant municipalities. The county's junior water right delivered limited and uncertain water supplies which were used on relatively poor soils. The ability of water markets to allocate water to the highest-valued use was addressed by assessing the direct foregone benefits of the transfer using deterministic and discrete stochastic sequential (DSSP) programming models. Crop mix predicted by the DSSP followed observed regional patterns. The DSSP was thus used to derive regional water demand from which foregone value was estimated. Direct regional foregone agricultural benefits were relatively low-due to uncertain water supplies and unproductive soils-indicating the market selected a low-valued supply for transfer.Resource /Energy Economics and Policy,

Testing against stochastic trend and seasonality in the presence of unattended breaks and unit roots

This paper considers the problem of testing against stochastic trend and seasonality in the presence of structural breaks and unit roots at frequencies other than those directly under test, which we term unattended breaks and unattended unit roots respectively. We show that under unattended breaks the true size of the Kwiatkowski et. al. (1992) [KPSS] test at frequency zero and the Canova and Hansen (1995) [CH] test at the seasonal frequencies fall well below the nominal level under the null with an associated, often very dramatic, loss of power under the alternative. We demonstrate that a simple modification of the statistics can recover the usual limiting distribution appropriate to the case where there are no breaks, provided unit roots do not exist at any of the unattended frequencies. Where unattended unit roots occur we show that the above statistics converge in probability to zero under the null. However, computing the KPSS and CH statistics after pre-filtering the data is simultaneously efficacious against both unattended breaks and unattended unit roots, in the sense that the statistics retain their usual pivotal limiting null distributions appropriate to the case where neither occurs. The case where breaks may potentially occur at all frequencies is also discussed. The practical relevance of the theoretical contribution of the paper is illustrated through a number of empirical examples.stationarity tests, structural breaks, pre-filtering, unattended unit roots

Testing for a change in persistence in the presence of non-stationary volatility

In this paper we consider tests for the null of (trend-) stationarity against the alternative of a change in persistence at some (known or unknown) point in the observed sample, either from I(0) to I(1) behaviour or vice versa, of, inter alia, Kim (2000). We show that in circumstances where the innovation process displays non-stationary unconditional volatility of a very general form, which includes single and multiple volatility breaks as special cases, the ratio-based statistics used to test for persistence change do not have pivotal limiting null distributions. Numerical evidence suggests that this can cause severe over-sizing in the tests. In practice it may therefore be hard to discriminate between persistence change processes and processes with constant persistence but which display time-varying unconditional volatility. We solve the identified inference problem by proposing wild bootstrap-based implementations of the tests. Monte Carlo evidence suggests that the bootstrap tests perform well in finite samples. An empirical application to a variety of measures of U.S. price inflation data is provided.Persistence change; non-stationary volatility; wild bootstrap

Robust Inference on Seasonal Unit Roots via a Bootstrap Applied to OECD Macroeconomic Series

Recent experimental results presented in Burridge and Taylor (2001a,b, and 2003) show that, as usually implemented, the Hylleberg et al. (1990) seasonal unit root tests can be rather liberal, with true level often substantially higher than nominal level. This effect is due to the presence of any of three things: data-based lag selection in the implementation of the tests, and either or both periodic heteroscedasticity and serial correlation in the driving shocks. Burridge and Taylor (2003) demonstrate that under experimental conditions a carefully implemented bootstrap substantially corrects test level without loss of power. The present study applies their technique to a large number of publicly available series, and demonstrates conclusively that the bootstrap produces less liberal, and, given the experimental results cited above, more reliable inference. We report results for Sweden, the UK and the US, which are typical of the fifteen countries in our panel. Other results, the GAUSS code, and raw data are all available at: www.staff.city.ac.uk/p.burridge

Some effects of tropical storm Agnes on water quality in the Patuxent River estuary

A post Agnes study emphasizing environmental factors...weekly sampling at eight stations from 28 June to August 30, 1972. Spatial and temporal changes in the distribution of many factors, e.g., salinity, dissolved oxygen (DO), seston, particulate carbon and nitrogen, inorganic and organic fractions of dissolved nitrogen and phosphorus, and chlorophyll a were studied and compared to earlier extensive records. Patterns shown by the present data were compared especially with a local heavy storm that occurred in the Patuxent drainage basin during July 1963. Some interesting correlations were observed in the data. (PDF has 39 pages.

Grassland futures in Great Britain – Productivity assessment and scenarios for land use change opportunities

This is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).To optimise trade-offs provided by future changes in grassland use intensity, spatially and temporally explicit estimates of respective grassland productivities are required at the systems level. Here, we benchmark the potential national availability of grassland biomass, identify optimal strategies for its management, and investigate the relative importance of intensification over reversion (prioritising productivity versus environmental ecosystem services). Process-conservative meta-models for different grasslands were used to calculate the baseline dry matter yields (DMY; 1961–1990) at 1 km2 resolution for the whole UK. The effects of climate change, rising atmospheric [CO2] and technological progress on baseline DMYs were used to estimate future grassland productivities (up to 2050) for low and medium CO2 emission scenarios of UKCP09. UK benchmark productivities of 12.5, 8.7 and 2.8 t/ha on temporary, permanent and rough-grazing grassland, respectively, accounted for productivity gains by 2010. By 2050, productivities under medium emission scenario are predicted to increase to 15.5 and 9.8 t/ha on temporary and permanent grassland, respectively, but not on rough grassland. Based on surveyed grassland distributions for Great Britain in 2010 the annual availability of grassland biomass is likely to rise from 64 to 72 million tonnes by 2050. Assuming optimal N application could close existing productivity gaps of ca. 40% a range of management options could deliver additional 21 ∗ 106 tonnes of biomass available for bioenergy. Scenarios of changes in grassland use intensity demonstrated considerable scope for maintaining or further increasing grassland production and sparing some grassland for the provision of environmental ecosystem services.Peer reviewedFinal Published versio

Some effects of Hurricane Agnes on water quality in the Patuxent River Estuary

A post-Agnes study that emphasized environmental factors was carried out on the Patuxent River estuary with weekly sampling at eight stations from 28 June t o 30 August 1972. Spatial and temporal changes in the distribution of many factors , e.g., salinity , dissolved oxygen, seston, particulate carbon and nitrogen, inorganic and organic fractions of dissolved nitrogen and phosphorus, and chlorophyll a were studied and compared t o extensive earlier records. Patterns shown by the present data were compared especially with a local heavy storm that occurred in the Patuxent drainage basin during July 1969. Estimates were made of the amounts of material contributed via upland drainage. A first approximation indicated that 14.8 x l0 (3) metric tons of seston were contributed t o the head of the estuary between 21 and 24 June. (PDF contains 46 pages