An I(2) Cointegration Model With Piecewise Linear Trends: Likelihood Analysis And Application

This paper presents likelihood analysis of the I(2) cointegrated vector autoregression with piecewise linear deterministic terms. Limiting behavior of the maximum likelihood estimators are derived, which is used to further derive the limiting distribution of the likelihood ratio statistic for the cointegration ranks, extending the result for I(2) models with a linear trend in Nielsen and Rahbek (2007) and for I(1) models with piecewise linear trends in Johansen, Mosconi, and Nielsen (2000). The provided asymptotic theory extends also the results in Johansen, Juselius, Frydman, and Goldberg (2009) where asymptotic inference is discussed in detail for one of the cointegration parameters. To illustrate, an empirical analysis of US consumption, income and wealth, 1965 - 2008, is performed, emphasizing the importance of a change in nominal price trends after 1980.Cointegration, I(2); piecewise linear trends; likelihood analysis; US consumption

Statistically derived contributions of diverse human influences to twentieth-century temperature changes

The warming of the climate system is unequivocal as evidenced by an increase in global temperatures by 0.8 °C over the past century. However, the attribution of the observed warming to human activities remains less clear, particularly because of the apparent slow-down in warming since the late 1990s. Here we analyse radiative forcing and temperature time series with state-of-the-art statistical methods to address this question without climate model simulations. We show that long-term trends in total radiative forcing and temperatures have largely been determined by atmospheric greenhouse gas concentrations, and modulated by other radiative factors. We identify a pronounced increase in the growth rates of both temperatures and radiative forcing around 1960, which marks the onset of sustained global warming. Our analyses also reveal a contribution of human interventions to two periods when global warming slowed down. Our statistical analysis suggests that the reduction in the emissions of ozone-depleting substances under the Montreal Protocol, as well as a reduction in methane emissions, contributed to the lower rate of warming since the 1990s. Furthermore, we identify a contribution from the two world wars and the Great Depression to the documented cooling in the mid-twentieth century, through lower carbon dioxide emissions. We conclude that reductions in greenhouse gas emissions are effective in slowing the rate of warming in the short term.F.E. acknowledges financial support from the Consejo Nacional de Ciencia y Tecnologia (http://www.conacyt.gob.mx) under grant CONACYT-310026, as well as from PASPA DGAPA of the Universidad Nacional Autonoma de Mexico. (CONACYT-310026 - Consejo Nacional de Ciencia y Tecnologia; PASPA DGAPA of the Universidad Nacional Autonoma de Mexico

Statistical evidence about human influence on the climate system

Working Paper No WP2012-012We use recent methods for the analysis of time series data, in particular related to breaks in trends, to establish that human factors are the main contributors to the secular movements in observed global and hemispheric temperatures series. The most important feature documented is a marked increase in the growth rates of temperatures (purged from the Atlantic Multidecadal Oscillation) and anthropogenic greenhouse gases occurring for all series around 1955, which marks the start of sustained global warming. Also evidence shows that human interventions effectively slowed global warming in two occasions. The Montreal Protocol and the technological change in agricultural production in Asia are major drivers behind the slowdown of the warming since 1994, providing evidence about the effectiveness of reducing emissions of greenhouse gases other than CO2 for mitigating climate change in the shorter term. The largest socioeconomic disruptions, the two World Wars and the Great Crash, are shown to have contributed to the cooling in the mid 20th century. While other radiative factors have modulated their effect, the greenhouse gases defined the secular movement in both the total radiative forcing and the global and hemispheric temperature series. Deviations from this anthropogenic trend are shown to have transitory effects

Modelling autoregressive processes with a shifting mean

This paper contains a nonlinear, nonstationary autoregressive model whose intercept changes deterministically over time. The intercept is a flexible function of time, and its construction bears some resemblance to neural network models. A modelling technique, modified from one for single hidden-layer neural network models, is developed for specification and estimation of the model. Its performance is investigated by simulation and further illustrated by two applications to macroeconomic time series.deterministic shift, nonlinear autoregression, nonstationarity, nonlinear trend, structural change Classification JEL: C22; C52.

Forecasting economic variables with nonlinear models

This article is concerned with forecasting from nonlinear conditional mean models. First, a number of often applied nonlinear conditional mean models are introduced and their main properties discussed. The next section is devoted to techniques of building nonlinear models. Ways of computing multi-step ahead forecasts from nonlinear models are surveyed. Tests of forecast accuracy in the case where the models generating the forecasts are nested are discussed. There is a numerical example, showing that even when a stationary nonlinear process generates the observations, future obervations may in some situations be better forecast by a linear model with a unit root. Finally, some empirical studies that compare forecasts from linear and nonlinear models are discussed.Forecast accuracy; forecast comparison; hidden Markov model; neural network; nonlinear modelling; recursive forecast; smooth transition regression; switching regression;

Change-point Problem and Regression: An Annotated Bibliography

The problems of identifying changes at unknown times and of estimating the location of changes in stochastic processes are referred to as the change-point problem or, in the Eastern literature, as disorder . The change-point problem, first introduced in the quality control context, has since developed into a fundamental problem in the areas of statistical control theory, stationarity of a stochastic process, estimation of the current position of a time series, testing and estimation of change in the patterns of a regression model, and most recently in the comparison and matching of DNA sequences in microarray data analysis. Numerous methodological approaches have been implemented in examining change-point models. Maximum-likelihood estimation, Bayesian estimation, isotonic regression, piecewise regression, quasi-likelihood and non-parametric regression are among the methods which have been applied to resolving challenges in change-point problems. Grid-searching approaches have also been used to examine the change-point problem. Statistical analysis of change-point problems depends on the method of data collection. If the data collection is ongoing until some random time, then the appropriate statistical procedure is called sequential. If, however, a large finite set of data is collected with the purpose of determining if at least one change-point occurred, then this may be referred to as non-sequential. Not surprisingly, both the former and the latter have a rich literature with much of the earlier work focusing on sequential methods inspired by applications in quality control for industrial processes. In the regression literature, the change-point model is also referred to as two- or multiple-phase regression, switching regression, segmented regression, two-stage least squares (Shaban, 1980), or broken-line regression. The area of the change-point problem has been the subject of intensive research in the past half-century. The subject has evolved considerably and found applications in many different areas. It seems rather impossible to summarize all of the research carried out over the past 50 years on the change-point problem. We have therefore confined ourselves to those articles on change-point problems which pertain to regression. The important branch of sequential procedures in change-point problems has been left out entirely. We refer the readers to the seminal review papers by Lai (1995, 2001). The so called structural change models, which occupy a considerable portion of the research in the area of change-point, particularly among econometricians, have not been fully considered. We refer the reader to Perron (2005) for an updated review in this area. Articles on change-point in time series are considered only if the methodologies presented in the paper pertain to regression analysis

Structural Breaks in the Cointegrated Vector Autoregressive Model

We generalize the cointegrated vector autoregressive model of Johansen (1988, 1991) to allow for structural breaks. We derive the likelihood ratio test for structural breaks occurring at fixed points in time, and show that it is asymptotically chi-squared. Moreover, we show how inference can be made when the null hypothesis is presence of structural breaks. The estimation technique derived for this purpose can be applied to several other generalizations of the standard model, beyond the structural breaks treated here. For example, the new technique can be applied to estimate models with heteroskedasticity. We apply our generalized model to US term structure data, accounting for structural breaks that coincide with the changes in the Fed's policy in September 1979 and October 1982. Contrary to previous findings we cannot reject the long-run implications of the expectations hypothesis.