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We propose new real-time monitoring procedures for the emergence of end-of-sample predictive regimes using sequential implementations of standard (heteroskedasticity-robust) regression t-statistics for predictability applied over relatively short time periods. The procedures we develop can also be used for detecting historical regimes of temporary predictability. Our proposed methods are robust to both the degree of persistence and endogeneity of the regressors in the predictive regression and to certain forms of heteroskedasticity in the shocks. We discuss how the monitoring procedures can be designed such that their false positive rate can be set by the practitioner at the start of the monitoring period using detection rules based on information obtained from the data in a training period. We use these new monitoring procedures to investigate the presence of regime changes in the predictability of the U.S. equity premium at the one-month horizon by traditional macroeconomic and financial variables, and by binary technical analysis indicators. Our results suggest that the one-month ahead equity premium has temporarily been predictable, displaying so-called 'pockets of predictability', and that these episodes of predictability could have been detected in real-time by practitioners using our proposed methodology.

Identifying the start and end dates of explosive bubble regimes has become a prominent issue in the econometric literature. Recent research has demonstrated the advantage of a model-based minimum sum of squared residuals estimator, combined with Bayesian Information Criterion model selection, over recursive unit root testing methods in providing accurate date estimates for a single explosive regime. However, in the context of multiple bubbles, a large number of models are possible, making such a model-based method unappealing. In this paper, we propose a two-step procedure for dating multiple explosive regimes. First, recursive unit root tests are used to identify a ‘date window’ in which an explosive episode starts and ends. Second, a model-based BIC approach is used to precisely estimate the regime change points within each date window. In addition, our method allows us to distinguish between different types of explosive episode, such as whether or not each explosive regime crashes before reverting back to a unit root process, and date any crash regimes. Monte Carlo simulations highlight the effectiveness of our procedure when compared to existing methods of dating. The value of the new methodology is also demonstrated through an empirical application to housing markets.

This article considers the problem of testing for an explosive bubble in financial data in the presence of time-varying volatility. We propose a sign-based variant of the Phillips, Shi, and Yu (2015, International Economic Review 56, 1043–1077) test. Unlike the original test, the sign-based test does not require bootstrap-type methods to control size in the presence of time-varying volatility. Under a locally explosive alternative, the sign-based test delivers higher power than the original test for many time-varying volatility and bubble specifications. However, since the original test can still outperform the sign-based one for some specifications, we also propose a union of rejections procedure that combines the original and sign-based tests, employing a wild bootstrap to control size. This is shown to capture most of the power available from the better performing of the two tests. We also show how a sign-based statistic can be used to date the bubble start and end points. An empirical illustration using Bitcoin price data is provided.

We generalize the Homm and Breitung (2012) CUSUM-based procedure for the real-time detection of explosive autoregressive episodes in financial price data to allow for time-varying volatility. Such behavior can heavily inflate the false positive rate (FPR) of the CUSUM-based procedure to spuriously signal the presence of an explosive episode. Our modified procedure involves replacing the standard variance estimate in the CUSUM statistics with a nonparametric kernel-based spot variance estimate. We show that the sequence of modified CUSUM statistics has a joint limiting null distribution which is invariant to any time-varying volatility present in the innovations and that this delivers a real-time monitoring procedure whose theoretical FPR is controlled. Simulations show that the modification is effective in controlling the empirical FPR of the procedure, yet sacrifices only a small amount of power to detect explosive episodes, relative to the standard procedure, when the shocks are homoskedastic. An empirical illustration using Bitcoin price data is provided.

We propose new methods for the real-time detection of explosive bubbles in financial time series. Most extant methods are constructed for a fixed sample of data and, as such, are only appropriate when applied as one-shot tests. Sequential application of these, declaring the presence of a bubble as soon as one of these statistics exceeds the one-shot critical value, would yield a detection procedure with an unknown false positive rate likely to be far in excess of the nominal level. Our approach sequentially applies the one-shot tests of Astill et al. (2017), comparing sub-sample statistics calculated in real time during the monitoring period with corresponding sub-sample statistics obtained from a prior training period. We propose two procedures: one based on comparing the real time monitoring period statistics with the maximum statistic over the training period, and another which compares the number of consecutive exceedances of a threshold value in the monitoring and training periods, the threshold value obtained from the training period. Both allow the practitioner to determine the false positive rate for any given monitoring horizon, or to ensure this rate does not exceed a specified level by setting a maximum monitoring horizon. Monte Carlo simulations suggest that the finite sample false positive rates lie close to their theoretical counterparts, even in the presence of time-varying volatility and serial correlation in the shocks. The procedures are shown to perform well in the presence of a bubble in the monitoring period, offering the possibility of rapid detection of an emerging bubble in a real time setting. An empirical application to monthly stock market index data is considered.

We consider tests for structural change, based on the SupF and Cramer-von-Mises type statistics of Andrews (1993) and Nyblom (1989), respectively, in the slope and/or intercept parameters of a predictive regression model where the predictors display strong persistence. The SupF type tests are motivated by alternatives where the parameters display a small number of breaks at deterministic points in the sample, while the Cramer-von-Mises alternative is one where the coefficients are random and slowly evolve through time. In order to allow for an unknown degree of persistence in the predictors, and for both conditional and unconditional heteroskedasticity in the data, we implement the tests using a fixed regressor wild bootstrap procedure. The asymptotic validity of the bootstrap tests is established by showing that the asymptotic distributions of the bootstrap parameter constancy statistics, conditional on the data, coincide with those of the asymptotic null distributions of the corresponding statistics computed on the original data, conditional on the predictors. Monte Carlo simulations suggest that the bootstrap parameter stability tests work well in finite samples, with the tests based on the Cramer-von-Mises type principle seemingly the most useful in practice. An empirical application to U.S. stock returns data demonstrates the practical usefulness of these methods.

In this paper, we show that when computing standard Diebold-Mariano-type tests for equal forecast accuracy and forecast encompassing, the long-run variance can frequently be negative when dealing with multi-step-ahead predictions in small, but empirically relevant, sample sizes. We subsequently consider a number of alternative approaches to dealing with this problem, including direct inference in the problem cases and use of long-run variance estimators that guarantee positivity. The finite sample size and power of the different approaches are evaluated using extensive Monte Carlo simulation exercises. Overall, for multi-step-ahead forecasts, we find that the recently proposed Coroneo and Iacone (2016) test, which is based on a weighted periodogram long-run variance estimator, offers the best finite sample size and power performance.

SUMMARY: In the large community-based SCOOP trial, systematic fracture risk screening using FRAX(®) led to greater use of AOM and greater adherence, in women at high fracture risk, compared with usual care. PURPOSE: In the SCreening of Older wOmen for Prevention of fracture’ (SCOOP) trial we investigated the effect of the screening intervention on subsequent long-term self-reported adherence to antiosteoporosis medications(AOM). METHODS: SCOOP was a primary care-based UK multi-centre trial of screening for fracture risk. 12,483 women (70-85years) were randomised to either usual NHS care, or assessment using the FRAX(®) tool +/- dual-energy X-ray absorptiometry(DXA), with medication recommended for those found to be at high risk of hip fracture. Self-reported AOM use was obtained by postal questionnaires at 6, 12, 24, 36, 48 and 60 months. Analysis was limited to those who initiated AOM during follow-up. Logistic regression was used to explore baseline determinants of adherence(good>=80%; poor

Harvey and Leybourne (2015) construct confidence sets for the timing of a break in level and/or trend, based on inverting sequences of test statistics for a break at all possible dates. These are valid, in the sense of yielding correct asymptotic coverage, for I(0) or I(1) errors. In constructing the tests, location-dependent weights are chosen for values of the break magnitude parameter such that each test conveniently has the same limit null distribution. By not imposing such a scheme, we show that it is generally possible to significantly shorten the length of the confidence sets, whilst maintaining accurate coverage properties.

This paper considers the problem of testing for an explosive bubble in financial data in the presence of time-varying volatility. We propose a weighted least squares-based variant of the Phillips, Wu and Yu (2011) test for explosive autoregressive behaviour. We find that such an approach has appealing asymptotic power properties, with the potential to deliver substantially greater power than the established OLS-based approach for many volatility and bubble settings. Given that the OLS-based test can outperform the weighted least squares-based test for other volatility and bubble specifications, we also suggested a union of rejections procedure that succeeds in capturing the better power available from the two constituent tests for a given alternative. Our approach involves a nonparametric kernel-based volatility function estimator for computation of the weighted least squares-based statistic, together with the use of a wild bootstrap procedure applied jointly to both individual tests, delivering a powerful testing procedure that is asymptotically size-robust to a wide range of time-varying volatility specifications.

In order for predictive regression tests to deliver asymptotically valid inference, account has to be taken of the degree of persistence of the predictors under test. There is also a maintained assumption that any predictability in the variable of interest is purely attributable to the predictors under test. Violation of this assumption by the omission of relevant persistent predictors renders the predictive regression invalid with the result that both the finite sample and asymptotic size of the predictability tests can be significantly infated, with the potential therefore to spuriously indicate predictability. In response we propose a predictive regression invalidity test based on a stationarity testing approach. To allow for an unknown degree of persistence in the putative predictors, and for heteroskedasticity in the data, we implement our proposed test using a fixed regressor wild bootstrap procedure. We demonstrate the asymptotic validity of the proposed bootstrap test. This entails demonstrating that the asymptotic distribution of the bootstrap statistic, conditional on the data, is the same (to first-order) as the asymptotic null distribution of the statistic computed on the original data, conditional on the predictor. This corrects a long-standing error in the bootstrap literature whereby it is incorrectly argued that for strongly persistent regressors the validity of the fixed regressor bootstrap obtains through equivalence to an unconditional limit distribution. Our bootstrap results are therefore of interest in their own right and are likely to have important applications beyond the present context. An illustration is given by re-examining the results relating to U.S. stock returns data in Campbell and Yogo (2006).

SUMMARY 1 Competitive interactions are assumed to play a role in governing species distributions but are difficult to infer using observational data. In addition, morphological identification may overlook species, obscuring patterns of competitive exclusion. To address these limitations, we showcase a molecular (DNA barcoding) approach to species-unit delineation and sample stream insect communities at small spatial scales where environmental filtering and dispersal limitations are minimised. 2 Rocks from riffles were sampled for stream insects, in particular caddisfly (Trichoptera), beetle (Coleoptera) and blackfly (Simuliidae) larvae from filterer and grazer guilds at White Clay Creek, Pennsylvania, U.S.A. (20 June, 2013). Additive partitioning of species diversity was used to establish at which spatial scale(s) variation in the distribution of species occurs; this informed us of the spatial scale at which to conduct checkerboard analyses, which tested for signatures of species segregations (e.g. competitive exclusion). 3 Only a small portion of the total species diversity occurred at the smallest spatial level (mean = 30% on individual rocks). Distributional variation in species was greatest at the kilometre scale (where beta-diversity was 37% and 41% for filterers and grazers respectively). At the scale of White Clay Creek sampled (c. 3 km extent), species of filterers showed a strong tendency to segregate on individual rocks, while grazers showed random structure approaching aggregation. 4 This study demonstrates a potential approach to assessing the role of competition in structuring communities using observational data and highlights the importance of accurate species units for analysis (e.g. DNA barcoding). Using a combination of analyses, we were able to link patterns of segregation to competitive interactions among stream insect species in a filterer guild, while determining these interactions were not important in a grazer guild.

In this paper we examine the local power of unit root tests against globally stationary exponential smooth transition autoregressive [ESTAR] alternatives under two sources of uncertainty: the degree of nonlinearity in the ESTAR model, and the presence of a linear deterministic trend. First, we show that the KSS test (Kapetanios, G., Y. Shin, and A. Snell. 2003. “Testing for a Unit Root in the Nonlinear STAR Framework.” Journal of Econometrics 112: 359–379) for nonlinear stationarity has local asymptotic power gains over standard Dickey-Fuller [DF] tests for certain degrees of nonlinearity in the ESTAR model, but that for other degrees of nonlinearity, the linear DF test has superior power. Second, we derive limiting distributions of demeaned, and demeaned and detrended KSS and DF tests under a local ESTAR alternative when a local trend is present in the DGP. We show that the power of the demeaned tests outperforms that of the detrended tests when no trend is present in the DGP, but deteriorates as the magnitude of the trend increases. We propose a union of rejections testing procedure that combines all four individual tests and show that this captures most of the power available from the individual tests across different degrees of nonlinearity and trend magnitudes. We also show that incorporating a trend detection procedure into this union testing strategy can result in higher power when a large trend is present in the DGP.

We propose a mechanism for shock amplification that potentially can account for fat tails in the distribution of the growth rate of national output. We argue that extreme macroeconomic events, such as the Great Depression and the Great Recession, were preceded by significant turmoil in the banking system. We have developed a model of bank network formation and presented numerical simulations that show that, for the benchmark case, aggregate credit follows a random walk. When we introduce fire sales the model does not only produce larger variations in the growth of aggregate credit but also shows that there is an asymmetry between booms and busts that is also consistent with empirical evidence.

We develop a test for the presence of nonlinear deterministic components in a univariate time series, approximated using a Fourier series expansion, designed to be asymptotically robust to the order of integration of the process and to any weak dependence present. Our approach is motivated by the Wald-based testing procedure of Harvey, Leybourne and Xiao (2010) [Journal of Time Series Analysis, vol. 31, p.379-391], but uses a function of an auxiliary unit root statistic to select between the asymptotic I(0) and I(1) critical values, rather than modifying the Wald test statistic as in Harvey et al.. We show that our proposed test has uniformly greater local asymptotic power than the test of Harvey et al. when the shocks are I(1), identical local asymptotic power when the shocks are I(0), and also improved .nite sample properties. We also consider the issue of determining the number of Fourier frequencies used to specify any nonlinear deterministic components, evaluating the performance of algorithmic- and information criterion-based model selection procedures.

In a recent paper, Harvey et al. (2013) [HLT] propose a new unit root test that allows for the possibility of multiple breaks in trend. Their proposed test is based on the infimum of the sequence (across all candidate break points) of local GLS detrended augmented Dickey-Fuller-type statistics. HLT show that the power of their unit root test is robust to the magnitude of any trend breaks. In contrast, HLT show that the power of the only alternative available procedure of Carrion-i-Silvestre et al. (2009), which employs a pre-test-based approach, can be very low indeed (even zero) for the magnitudes of trend breaks typically observed in practice. Both HLT and Carrion-i-Silvestre et al. (2009) base their approaches on the assumption of homoskedastic shocks. In this paper we analyse the impact of non-stationary volatility (for example single and multiple abrupt variance breaks, smooth transition variance breaks, and trending variances) on the tests proposed in HLT. We show that the limiting null distribution of the HLT unit root test statistic is not pivotal under non- stationary volatility. A solution to the problem, which does not require the practitioner to specify a parametric model for volatility, is provided using the wild bootstrap and is shown to perform well in practice. A number of dfferent possible implementations of the bootstrap algorithm are discussed.

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 efficient and generally offer superior power to OLS-based approaches; however, the power gains are much more modest than in the lower-tail testing context. We also find that asymptotically non-negligible initial conditions do not affect the power ranking in the same way as they do for lower-tail tests, with the QD-based tests retaining a power advantage in such cases.

Trend breaks appear to be prevalent in macroeconomic time series, and unit root tests therefore need to make allowance for these if they are to avoid the serious effects that unmodelled trend breaks have on power. Carrion-i-Silvestre et al. (2009) propose a pre-test-based approach which delivers near asymptotically efficient unit root inference both when breaks do not occur and where multiple breaks occur, provided the break magnitudes are fixed. Unfortunately, however, the fixed magnitude trend break asymptotic theory does not predict well the finite sample power functions of these tests, and power can be very low for the magnitudes of trend breaks typically observed in practice. In response to this problem we propose a unit root test that allows for multiple breaks in trend, obtained by taking the infimum of the sequence (across all candidate break points in a trimmed range) of local GLS detrended augmented Dickey–Fuller-type statistics. We show that this procedure has power that is robust to the magnitude of any trend breaks, thereby retaining good finite sample power in the presence of plausibly-sized breaks. We also demonstrate that, unlike the OLS detrended infimum tests of Zivot and Andrews (1992), these tests display no tendency to spuriously reject in the limit when fixed magnitude trend breaks occur under the unit root null.

In this paper we propose a new procedure for detecting additive outliers in a univariate time series based on a bootstrap implementation of the test of Perron and Rodriguez (2003, Journal of Time Series Analysis 24, 193-220). This procedure is used to test the null hypothesis that a time series is uncontaminated by additive outliers against the alternative that one or more additive outliers are present. We demonstrate that the existing tests of, inter alia, Vogelsang (1999, Journal of Time Series Analysis 20, 237–52) Perron and Rodriguez (2003) and Burridge and Taylor (2006, Journal of Time Series Analysis 27, 685–701) are unable to strike a balance between size and power when the order of integration of a time series is unknown and the time series is driven by innovations drawn from an unknown distribution. We show that the proposed bootstrap testing procedure is able to control size to such an extent that its size properties are comparable with the robust test of Burridge and Taylor (2006) when the distribution of the innovations is not assumed known, whilst maintaining power in the Gaussian environment close to that of the test of Perron and Rodriguez (2003).

We consider unit root testing allowing for a break in trend when partial information is available regarding the location of the break date. This takes the form of knowledge of a relatively narrow window of data within which the break takes place, should it occur at all. For such circumstances, we suggest employing a union of rejections strategy, which combines a unit root test that allows for a trend break somewhere within the window with a unit root test that makes no allowance for a trend break. Asymptotic and finite sample evidence shows that our suggested strategy works well, provided that, when a break does occur, the partial information is correct. An empirical application to UK interest rate data containing the 1973 ‘oil shock’ is also considered.

A significant proportion of the trade basket of many developing countries is comprised of primary commodities. This implies relative price movements in commodities may have important consequences for economic growth and poverty reduction. Taking a long-run perspective, we examine the historical relation between a new aggregate index of commodity prices, economic activity and interest rates. Initial empirical tests show that commodity prices present a downward trend with breaks over the entire industrial age, providing clear support for the Prebisch-Singer hypothesis. It would also appear that this trend has declined at a faster rate since the 1870s. Conversely, several GDP series such as World, Chile, China, UK and US, trend upwards with breaks. Such trending behaviour in both commodity prices and economic activity suggests a latent common factor like technological innovation. To assess the relationships between economic series, we apply a stationary VAR (Vector Autoregression) to model movements around trends. Strikingly, there is evidence that commodity prices Granger cause income and interest rates, whilst interest rates Granger cause commodity prices. From these results and the related impulse response function analysis, the historical perspective provides some useful information for contemporary policy makers. For example, loose monetary policy has tended to support higher commodity prices. More-over, commodity price movements have an asymmetric country effect on economic activity; periods of falling commodity prices will support GDP growth for com-modity importers like the US but depress growth for commodity exporters such as Chile.

We examine the behaviour of OLS-demeaned/detrended and GLS-demeaned/detrended unit root tests that employ stationary covariates, as proposed by Hansen (1995, “Rethinking the Univariate Approach to Unit Root Testing.” Econometric Theory 11:1148–71) and Elliott and Jansson (2003, “Testing for Unit Roots with Stationary Covariates.” Journal of Econometrics 115:75–89), respectively, in situations where the magnitude of the initial condition of the time series under consideration may be non-negligible. We show that the asymptotic power of such tests is very sensitive to the initial condition; OLS- and GLS-based tests achieve relatively high power for large and small magnitudes of the initial condition, respectively. Combining information from both types of test via a simple union of rejections strategy is shown to effectively capture the higher power available across all initial condition magnitudes.

In this paper we consider testing for a unit root in the possible presence of a trend break at an unknown time. Zivot and Andrews (1992) [Journal of Business and Economic Statistics 10, 251–270] proposed using the infimum of t -ratio Dickey–Fuller statistics across all candidate break points in a trimmed range, however this procedure can have an asymptotic size of one when a break occurs under the unit root null. We show that if the same approach is used, but instead with coefficient Dickey–Fuller statistics in an additive outlier framework, the test is asymptotically conservative when a break is present under the null, provided the degree of trimming is appropriately controlled. The test is also shown to have superior local asymptotic power to the t -ratio version.

In practice a degree of uncertainty will always exist concerning what specification to adopt for the deterministic trend function when running unit root tests. While most macroeconomic time series appear to display an underlying trend, it is often far from clear whether this component is best modelled as a simple linear trend (so that long-run growth rates are constant) or by a more complicated non-linear trend function which may, for instance, allow the deterministic trend component to evolve gradually over time. In this paper we consider the effects on unit root testing of allowing for a local quadratic trend, a simple yet very flexible example of the latter. Where a local quadratic trend is present but not modelled we show that the quasi-differenced detrended Dickey-Fuller-type test of Elliott et al. (1996) has both size and power which tend to zero asymptotically. An extension of the Elliott et al. (1996) approach to allow for a quadratic trend resolves this problem but is shown to result in large power losses relative to the standard detrended test when no quadratic trend is present. We consequently propose a simple and practical approach to dealing with this form of uncertainty based on a union of rejections-based decision rule whereby the unit root null is rejected whenever either of the detrended or quadratic detrended unit root tests rejects. A modification of this basic strategy is also suggested which further improves on the properties of the procedure. An application to relative primary commodity price data highlights the empirical relevance of the methods outlined in this paper. A by-product of our analysis is the development of a test for the presence of a quadratic trend which is robust to whether or not the data admit a unit root.

We consider different methods for combining probability forecasts. In empirical exercises, the data generating process of the forecasts and the event being forecast is not known, and therefore the optimal form of combination will also be unknown. We consider the properties of various combination schemes for a number of plausible data generating processes, and indicate which types of combinations are likely to be useful. We also show that whether forecast encompassing is found to hold between two rival sets of forecasts or not may depend on the type of combination adopted. The relative performances of the different combination methods are illustrated, with an application to predicting recession probabilities using leading indicators.

We analyze the impact of nonstationary volatility on the break fraction estimator and associated trend break unit root tests of Harris, Harvey, Leybourne, and Taylor (2009) (HHLT). We show that although HHLT’s break fraction estimator retains the same large-sample properties as demonstrated by HHLT for homoskedastic shocks, the limiting null distributions of unit root statistics based around this estimator are not pivotal under nonstationary volatility. A solution to the identified inference problem, which does not require the practitioner to specify a parametric model for volatility, is provided using the wild bootstrap and is shown to perform well in practice.

The InterPulse technique is an advanced gas tungsten constricted arc welding (GTCAW) method for controlled heat input welding of titanium alloys. Microstructural and microtextural analysis has been used to show that the technique has the potential to produce high integrity welds in Cp-Ti and Ti–6Al–4V while welding outside of a vacuum chamber and without a trailing gas shield. The arc waveform control provided by the technique is shown to have the potential to tailor weld macrostructures, microstructures and microtextures. At the cooling rates associated with the technique, α-variants sharing a common ( 1 1 2 ¯ 0 ) pole are found to cluster together into groups within prior β grains, leading to large areas where all variants are separated by a misorientation of 60°. Characterisation of these microtextures may provide new insight into microtexture–properties relations and the mechanisms of microtextural evolution.

In this paper we propose tests for the null hypothesis that a time series process displays a constant level against the alternative that it displays (possibly) multiple changes in level. Our proposed tests are based on functions of appropriately standardized sequences of the differences between sub-sample mean estimates from the series under investigation. The tests we propose differ notably from extant tests for level breaks in the literature in that they are designed to be robust as to whether the process admits an autoregressive unit root (the data are I ( 1 ) ) or stable autoregressive roots (the data are I ( 0 ) ). We derive the asymptotic null distributions of our proposed tests, along with representations for their asymptotic local power functions against Pitman drift alternatives under both I ( 0 ) and I ( 1 ) environments. Associated estimators of the level break fractions are also discussed. We initially outline our procedure through the case of non-trending series, but our analysis is subsequently extended to allow for series which display an underlying linear trend, in addition to possible level breaks. Monte Carlo simulation results are presented which suggest that the proposed tests perform well in small samples, showing good size control under the null, regardless of the order of integration of the data, and displaying very decent power when level breaks occur.

We consider testing for the presence of nonlinearities in the deterministic component of a time series, approximating the potential nonlinear behaviour using a Fourier function expansion. In contrast to procedures that are currently available, we develop tests that are robust to the order of integration, in the sense that they are asymptotically correctly sized regardless of whether the stochastic component of the series is stationary or contains a unit root. The tests we propose take the form of Wald statistics based on cumulated series, together with a correction factor to line up the asymptotic critical values across the I(0) and I(1) environments. The local asymptotic power and finite sample properties of the tests are evaluated using various different correction factors. We envisage that the testing procedure we recommend should be very useful to applied researchers wishing to draw robust inference regarding the presence of nonlinear deterministic components in a series.

We employ a unique data set and new time-series techniques to reexamine the existence of trends in relative primary commodity prices. The data set comprises 25 commodities and provides a new historical perspective, spanning the seventeenth to the twenty-first centuries. New tests for the trend function, robust to the order of integration of the series, are applied to the data. Results show that eleven price series present a significant and downward trend over all or some fraction of the sample period. In the very long run, a secular, deteriorating trend is a relevant phenomenon for a significant proportion of primary commodities. © 2010 The President and Fellows of Harvard College and the Massachusetts Institute of Technology.