Inference related to common breaks in a multivariate system with joined segmented trends with applications to global and hemispheric temperatures

What transpires from recent research is that temperatures and radiative forcing seem to be characterized by a linear trend with two changes in the rate of growth. The first occurs in the early 60s and indicates a very large increase in the rate of growth of both temperature and radiative forcing series. This was termed as the “onset of sustained global warming”. The second is related to the more recent so-called hiatus period, which suggests that temperatures and total radiative forcing have increased less rapidly since the mid-90s compared to the larger rate of increase from 1960 to 1990. There are two issues that remain unresolved. The first is whether the breaks in the slope of the trend functions of temperatures and radiative forcing are common. This is important because common breaks coupled with the basic science of climate change would strongly suggest a causal effect from anthropogenic factors to temperatures. The second issue relates to establishing formally via a proper testing procedure that takes into account the noise in the series, whether there was indeed a ‘hiatus period’ for temperatures since the mid 90s. This is important because such a test would counter the widely held view that the hiatus is the product of natural internal variability. Our paper provides tests related to both issues. The results show that the breaks in temperatures and radiative forcing are common and that the hiatus is characterized by a significant decrease in their rate of growth. The statistical results are of independent interest and applicable more generally.Accepted manuscrip

Quasi-likelihood ratio tests for cointegration, cobreaking, and cotrending

We consider a set of variables with two types of non-stationary features, stochastic trends and broken linear trends. We develop tests that can determine whether there is a linear combination of these variables under which the non-stationary features can be canceled out. The first test can determine whether stochastic trends can be eliminated and thus whether cointegration holds, regardless of whether structural breaks in linear trends are eliminated. The second test can determine whether both stochastic trends and breaks in linear trends are simultaneously removed and thus whether cointegration and cobreaking simultaneously hold. The third test can determine whether not only breaks in linear trends but also linear trends themselves are eliminated along with stochastic trends and thus whether both cointegration and cotrending hold

Anthropogenic influence in observed regional warming trends and the implied social time of emergence

The attribution of climate change allows for the evaluation of the contribution of human drivers to observed warming. At the global and hemispheric scales, many physical and observation-based methods have shown a dominant anthropogenic signal, in contrast, regional attribution of climate change relies on physically based numerical climate models. Here we show, using state-of-the-art statistical tests, the existence of a common nonlinear trend in observed regional air surface temperatures largely imparted by anthropogenic forcing. All regions, continents and countries considered have experienced warming during the past century due to increasing anthropogenic radiative forcing. The results show that we now experience mean temperatures that would have been considered extreme values during the mid-20th century. The adaptation window has been getting shorter and is projected to markedly decrease in the next few decades. Our findings provide independent empirical evidence about the anthropogenic influence on the observed warming trend in different regions of the world.Accepted manuscript and Published version

Estimating a common deterministic time trend break in large panels with cross sectional dependence

This paper develops an estimation procedure for a common deterministic time trend break in large panels. The dependent variable in each equation consists of a deterministic trend and an error term. The deterministic trend is subject to a change in the intercept, slope or both, and the break date is common for all equations. The estimation method is simply minimizing the sum of squared residuals for all possible break dates. Both serial and cross sectional correlations are important factors that decide the rate of convergence and the limiting distribution of the break date estimate. The rate of convergence is faster when the errors are stationary than when they have a unit root. When there is no cross sectional dependence among the errors, the rate of convergence depends on the number of equations and thus is faster than the univariate case. When the errors have a common factor structure with factor loadings correlated with the intercept and slope change parameters, the rate of convergence does not depend on the number of equations and thus reduces to the univariate case. The limiting distribution of the break date estimate is also provided. Some Monte Carlo experiments are performed to assess the adequacy of the asymptotic results. A brief empirical example using the US GDP price index is offered.Structural break Deterministic trend Panel data

IMPROVED AND EXTENDED END-OF-SAMPLE INSTABILITY TESTS USING A FEASIBLE QUASI-GENERALIZED LEAST SQUARES PROCEDURE

This paper extends the Andrews (2002, Econometrica 71, 1661–1694) and Andrews and Kim (2006, Journal of Business & Economic Statistics 24, 379–394) ordinary least squares–based end-of-sample instability tests for linear regression models. The author proposes to quasi-difference the data first using a consistent estimate of the sum of the autoregressive coefficients of the error process and then test for the end-of-sample instability. For the cointegration model, the feasible quasi-generalized least squares (FQGLS) version of the Andrews and Kim (2006) P test is considered and is shown, by simulations, to be more robust to serial correlation in the error process and to have power no less than Andrews and Kim’s original test. For the linear time trend model, the FQGLS version of the Andrews (2002) S test is considered with the error process allowed to be nonstationary up to one unit root, and the new test is shown to be robust to potentially nonstationary serial correlation. A simulation study also shows that the finite-sample properties of the proposed test can be further improved when the Andrews (1993, Econometrica 61,139–165) or Andrews and Chen (1994, Journal of Business & Economic Statistics 12, 187–204) median unbiased estimate of the sum of the autoregressive coefficients is used.

Time Instability of the U.S. Monetary System: Multiple Break Tests and Reduced Rank TVP VAR

February 2013Earlier attempts to find evidence of time varying coefficients in the U.S. monetary vector autoregression have been only partially successful. Structural break tests applied to typical data sets often fail to reject the null hypothesis of no break. Bayesian inferences using time varying parameter vector autoregressions provide posterior median values that capture some important movements over time, but the associated confidence intervals are often very wide and make the entire results less conclusive. We apply recently developed multiple structural break tests and find statistically significant evidence of time varying coefficients. We also develop a reduced rank time varying parameter vector autoregression with multivariate stochastic volatility. Our model has a smaller number of free parameters thereby yielding tighter confidence intervals than previously employed unrestricted time varying parameter models.グローバルCOEプログラム = Global COE Program21 p

Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses

Perron [Perron, P., 1989. The great crash, the oil price shock and the unit root hypothesis. Econometrica 57, 1361-1401] introduced a variety of unit root tests that are valid when a break in the trend function of a time series is present. The motivation was to devise testing procedures that were invariant to the magnitude of the shift in level and/or slope. In particular, if a change is present it is allowed under both the null and alternative hypotheses. This analysis was carried under the assumption of a known break date. The subsequent literature aimed to devise testing procedures valid in the case of an unknown break date. However, in doing so, most of the literature and, in particular the commonly used test of Zivot and Andrews [Zivot, E., Andrews, D.W.K., 1992. Further evidence on the great crash, the oil price shock and the unit root hypothesis. Journal of Business and Economic Statistics 10, 251-270], assumed that if a break occurs, it does so only under the alternative hypothesis of stationarity. This is undesirable since (a) it imposes an asymmetric treatment when allowing for a break, so that the test may reject when the noise is integrated but the trend is changing; (b) if a break is present, this information is not exploited to improve the power of the test. In this paper, we propose a testing procedure that addresses both issues. It allows a break under both the null and alternative hypotheses and, when a break is present, the limit distribution of the test is the same as in the case of a known break date, thereby allowing increased power while maintaining the correct size. Simulation experiments confirm that our procedure offers an improvement over commonly used methods in small samples.Structural change Pre-test Trend function Integrated processes Hypothesis testing