Exact rational expectations,cointegration, and reduced rank regression

We interpret the linear relations from exact rational expectations models as restrictions on the parameters of the statistical model called the cointegrated vector autoregressive model for non-stationary variables. We then show how reduced rank regression [Anderson, T.W., 1951. Estimating linear restrictions on regression coefficients for multivariate normal distributions. Ann. Math. Statist. 22, 327–351] plays an important role in the calculation of maximum likelihood estimators of the restricted parameters.     

SUBSAMPLING THE JOHANSEN TEST WITH STABLE INNOVATIONS

By taking into account the thick-tail property of the errors, cointegration analysis in vector error-correction models with infinite-variance stable errors is a natural generalization of cointegration analysis in error-correction models with normally distributed errors. We study the Johansen test for cointegrated systems under symmetric stable innovations with discrete spectral measures. The results show that the distributions of the Johansen test statistics under these innovations involve nuisance parameters. To overcome the problem of nuisance parameters, we implement a nonparametric subsampling procedure. We document some subsampling simulation results and demonstrate in an empirical example how the test can be used in practice.     

Testing for spurious and cointegrated regressions: A wavelet approach

This paper proposes a wavelet-based approach to analyze spurious and cointegrated regressions in time series. The approach is based on the properties of the wavelet covariance and correlation in Monte Carlo studies of spurious and cointegrated regression. In the case of the spurious regression, the null hypotheses of zero wavelet covariance and correlation for these series across the scales fail to be rejected. Conversely, these null hypotheses across the scales are rejected for the cointegrated bivariate time series. These nonresidual-based tests are then applied to analyze if any relationship exists between the extraterrestrial phenomenon of sunspots and the earthly economic time series of oil prices. Conventional residual-based tests appear sensitive to the specification in both the cointegrating regression and the lag order in the augmented Dickey–Fuller tests on the residuals. In contrast, the wavelet tests, with their bootstrap t-statistics and confidence intervals, detect the spuriousness of this relationship.     

Estimation of cointegrated models with exogenous variables

We consider a cointegrated vector autoregressive process of integrated order 1, where the process consists of endogenous variables and exogenous variables. Johansen [Cointegration in partial systems and the efficiency of single-equation analysis. J Econometrics. 1992;52:389–402], Harbo et al. [Asymptotic inference on cointegrating rank in partial systems. J Amer Statist Assoc. 1998;16:388–399], and Pesaran et al. [Structural analysis of vector error correction models with exogenous I(1) variables. J Econometrics. 2000;97:293–343] considered inference of such processes assuming that the non-stationary exogenous variables are not cointegrated, and thus they are weakly exogenous. We consider the case where exogenous variables are cointegrated. Parameterization and estimation of the model is considered, and the asymptotic properties of the estimators are presented. The method in this paper is also applicable for the models considered in Mosconi and Giannini [Non-causality in cointegrated systems: representation estimation and testing. Oxford Bull Econ Stat. 1992;54:399–417], Pradel and Rault [Exogeneity in vector error correction models with purely exogenous long-run paths. Oxford Bull Econ Stat. 2003;65:629–653], and Hunter [Cointegrating exogeneity. Econom Lett. 1990;34:33–35]. A real data example is provided to illustrate the methods. Finite sample properties of the estimators are also examined through a Monte Carlo simulation.     

门限协整套利:理论与实证研究

 不同市场上的同质或相似商品的价格存在长期均衡关系,当价格偏离均衡时,由于套利交易的存在,偏离会迅速回到均衡。在一定的门限值以外,二者服从协整关系,在门限值以内,二者没有协整关系,这种关系称为门限协整。本文在Balke,Fomby(1997)[1]和Hasen（1996）[6]的基础上提出了基于门限向量误差修正模型（T-VECM）的sup-Wald检验,用Bootstrap方法模拟统计量的渐进分布,验证了英国富时指数期货（uk100）和德国法兰克福指数期货（ger30）的门限协整关系,并用Hasen,Seo（2002）[11]提出的极大似然估计方法（MLE）同时估计出门限参数和协整向量,并给出了在这种门限协整关系下进行跨市场无风险套利的策略。     

A Parametric approach to the Estimation of Cointegration Vectors in Panel Data

In this article, a parametric framework for estimation and inference in cointegrated panel data models is considered that is based on a cointegrated VAR(p) model. A convenient two-step estimator is suggested where, in the first step, all individual specific parameters are estimated, and in the second step, the long-run parameters are estimated from a pooled least-squares regression. The two-step estimator and related test procedures can easily be modified to account for contemporaneously correlated errors, a feature that is often encountered in multi-country studies. Monte Carlo simulations suggest that the two-step estimator and related test procedures outperform semiparametric alternatives such as the fully modified OLS approach, especially if the number of time periods is small.     

The impact of integrated measurement errors on modeling long-run macroeconomic time series

ABSTRACT

Data spanning long time periods, such as that over 1860–2012 for the UK, seem likely to have substantial errors of measurement that may even be integrated of order one, but which are probably cointegrated for cognate variables. We analyze and simulate the impacts of such measurement errors on parameter estimates and tests in a bivariate cointegrated system with trends and location shifts which reflect the many major turbulent events that have occurred historically. When trends or shifts therein are large, cointegration analysis is not much affected by such measurement errors, leading to conventional stationary attenuation biases dependent on the measurement error variance, unlike the outcome when there are no offsetting shifts or trends.     

Interval forecasting in cointegrated systems

In this paper interval forecasting of cointegrated systems is examined. If the estimated coefficients are used to construct the forecasting intervals the error component due to the estimation of the coefficients is omitted in most cases. Analogous to the stationary case of vectorautoregressive models a correction term is derived basing on Johansen’s error correction representation of cointegrated systems. Its usefulness is analysed by means of a Monte Carlo study. The Monte Carlo study firstly demonstrates the difference between the nominal level of the confidence interval of forecasting and the observed level of the interval construction with known coefficients of variance calculation. Secondly, the forecast interval with estimated coefficients is investigated. Thirdly, it is illustrated that the approximation of forecast intervals can be improved by the proposed correction term for a small sample size, if the true cointegration rank is specified.     

Accelerated Estimation of Switching Algorithms: The Cointegrated VAR Model and Other Applications

Restricted versions of the cointegrated vector autoregression are usually estimated using switching algorithms. These algorithms alternate between two sets of variables but can be slow to converge. Acceleration methods are proposed that combine simplicity and effectiveness. These methods also outperform existing proposals in some applications of the expectation–maximization method and parallel factor analysis.     

Estimating systems of trending variables

A survey is given of some results on inference in cointegrated systems. We discuss some regression methods, and contrast them with the analysis of the vector autoregressive model. We discuss determination of cointegrating rank and estimation of parameters, as well as asymptotic inference. The problems are treated for 1(1) and for 1(2) variables.     

Estimating systems of trending variables

A survey is given of some results on inference in cointegrated systems. We discuss some regression methods, and contrast them with the analysis of the vector autoregressive model. We discuss determination of cointegrating rank and estimation of parameters, as well as asymptotic inference. The problems are treated for 1(1) and for 1(2) variables.     

Comment: The Future of Administrative Records in the Economic Programs of the Census Bureau

Using recently developed statistical tools for analyzing cointegrated 1(2) data, this article models money, income, prices, and interest rates in Denmark. The final model describes the dynamic adjustment to short-run changes of the process, to deviations from long-run steady states, and to several political interventions. It provides new insights about the effects of the liberalization of trade and capital in a small open European economy.     

Cointegration and Long-Horizon Forecasting

We consider the forecasting of cointegrated variables, and we show that at long horizons nothing is lost by ignoring cointegration when forecasts are evaluated using standard multivariate forecast accuracy measures. In fact, simple univariate Box–Jenkins forecasts are just as accurate. Our results highlight a potentially important deficiency of standard forecast accuracy measures—they fail to value the maintenance of cointegrating relationships among variables—and we suggest alternatives that explicitly do so.     

Relative Commodity Prices and Cointegration

The Prebisch–Singer hypothesis of a secular decline in the relative price of primary commodities is reassessed, on the basis of recently available time series data, for 1900–1986. Special attention is given to adequate dynamic modeling of price fluctuations. Primary and manufactured-goods prices are found to be cointegrated. The hypothesis of stationarity for the long-run relative-price movements cannot be rejected. The empirical evidence does not support the Prebisch–Singer hypothesis.     

The role of the constant and linear terms in cointegration analysis of nonstationary variables

The autoregressive model for cointegrated variables is analyzed with respect to the role of the constant and linear terms. Various models for 1(1) variables defined by restrictions on the deterministic terms are discussed, and it is shown that statistical inference can be performed by reduced rank regression. The asymptotic distributions of the test statistics and estimators are found. A similar analysis is given for models for 1(2) variables with a constant term.     

The role of the constant and linear terms in cointegration analysis of nonstationary variables

The autoregressive model for cointegrated variables is analyzed with respect to the role of the constant and linear terms. Various models for 1(1) variables defined by restrictions on the deterministic terms are discussed, and it is shown that statistical inference can be performed by reduced rank regression. The asymptotic distributions of the test statistics and estimators are found. A similar analysis is given for models for 1(2) variables with a constant term.     

Finite Sample Modifications of the Granger Non Causality Test in Cointegrated Vector Autoregressions

This article deals with the Granger non causality test in cointegrated vector autoregressive processes. We propose a new testing procedure that yields an asymptotically standard distribution and performs well in small samples by combining the standard Wald test and the generalized inverse procedure. We also propose a few simple modifications to the test statistics in order to help our procedure perform better in finite samples. Monte Carlo simulations show that our procedure works better than the conventional approach.     

Testing for autocorrelation in non-stationary dynamic systems of equations

Using Monte Carlo methods, the properties of systemwise generalizations of the Breusch-Godfrey test for autocorrelated errors are studied in integrated cointegrated systems of equations. Our analysis, regarding the size of the test, reveals that the corrected LR tests have been shown to perform satisfactorily even in cases when the exogenous variables follow a unit root process, whilst the commonly used TR2 test behaves badly even in single equations. All tests perform badly, however, when the number of equations increases and the exogenous variables are highly autocorrelated.     

Exploring the Impact of Multivariate GARCH Innovations on Hypothesis Testing for Cointegrating Vectors

This article investigates the impact of multivariate generalized autoregressive conditional heteroskedastic (GARCH) errors on hypothesis testing for cointegrating vectors. The study reviews a cointegrated vector autoregressive model incorporating multivariate GARCH innovations and a regularity condition required for valid asymptotic inferences. Monte Carlo experiments are then conducted on a test statistic for a hypothesis on the cointegrating vectors. The experiments demonstrate that the regularity condition plays a critical role in rendering the hypothesis testing operational. It is also shown that Bartlett-type correction and wild bootstrap are useful in improving the small-sample size and power performance of the test statistic of interest.     

Aggregate consumption functions for India: A cointegration analysis under structural changes, 1919-86

This paper extends cointegration methodology to include the effect of possible structural changes on aggregate consumption behaviour in India during 1919-86. The only cointegrated relation is found to be a dynamic linear regression of lag order two, with 1944 as the year in which structural change began. The estimated short-run marginal propensity to consume (MPC) is greater than the long-run MPC. The estimates of the MPC are different from previous estimates for the Indian economy based on conventional econometrics. The initial year of structural change has been selected by extending the method of Perron and that of Zivot and Andrews.