Showing papers on "Cointegration published in 1996"

Likelihood-Based Inference in Cointegrated Vector Autoregressive Models

Abstract: This book gives a detailed mathematical and statistical analysis of the cointegrated vector autoregresive model. This model had gained popularity because it can at the same time capture the short-run dynamic properties as well as the long-run equilibrium behaviour of many non-stationary time series. It also allows relevant economic questions to be formulated in a consistent statistical framework. Part I of the book is planned so that it can be used by those who want to apply the methods without going into too much detail about the probability theory. The main emphasis is on the derivation of estimators and test statistics through a consistent use of the Guassian likelihood function. It is shown that many different models can be formulated within the framework of the autoregressive model and the interpretation of these models is discussed in detail. In particular, models involving restrictions on the cointegration vectors and the adjustment coefficients are discussed, as well as the role of the constant and linear drift. In Part II, the asymptotic theory is given the slightly more general framework of stationary linear processes with i.i.d. innovations. Some useful mathematical tools are collected in Appendix A, and a brief summary of weak convergence in given in Appendix B. The book is intended to give a relatively self-contained presentation for graduate students and researchers with a good knowledge of multivariate regression analysis and likelihood methods. The asymptotic theory requires some familiarity with the theory of weak convergence of stochastic processes. The theory is treated in detail with the purpose of giving the reader a working knowledge of the techniques involved. Many exercises are provided. The theoretical analysis is illustrated with the empirical analysis of two sets of economic data. The theory has been developed in close contract with the application and the methods have been implemented in the computer package CATS in RATS as a result of a rcollaboation with Katarina Juselius and Henrik Hansen.

Numerical distribution functions for unit root and cointegration tests

Abstract: SUMMARY This paper employs response surface regressions based on simulation experiments to calculate distribution functions for some well-known unit root and cointegration test statistics. The principal contributions of the paper are a set of data files that contain estimated response surface coefficients and a computer program for utilizing them. This program, which is freely available via the Internet, can easily be used to calculate both asymptotic and finite-sample critical values and P-values for any of the tests. Graphs of some of the tabulated distribution functions are provided. An empirical example deals with interest rates and inflation rates in Canada. Tests of the null hypothesis that a time-series process has a unit root have been widely used in recent years, as have tests of the null hypothesis that two or more integrated series are not cointegrated. The most commonly used unit root tests are based on the work of Dickey and Fuller (1979) and Said and Dickey (1984). These are known as Dickey-Fuller (DF) tests and Augmented Dickey-Fuller (ADF) tests, respectively. These tests have non-standard distributions, even asymptotically. The cointegration tests developed by Engle and Granger (1987) are closely related to DF and ADF tests, but they have different, non-standard distributions, which depend on the number of possibly cointegrated variables. Although the asymptotic theory of these unit root and cointegration tests is well developed, it is not at all easy for applied workers to calculate the marginal significance level, or P-value, associated with a given test statistic. Until a few years ago (MacKinnon, 1991), accurate critical values for cointegration tests were not available at all. In a recent paper (MacKinnon, 1994), I used simulation methods to estimate the asymptotic distributions of a large number of unit root and cointegration tests. I then obtained reasonably simple approximating equations that may be used to obtain approximate asymptotic P-values. In the present paper, I extend the results to allow for up to 12 variables, instead of six, and I correct two deficiencies of the earlier work. The first deficiency is that the approximating equations are considerably less accurate than the underlying estimated asymptotic distributions. The second deficiency is that, even though the simulation experiments provided information about the finite-sample distributions of the test statistics, the approximating equations were obtained only for the asymptotic case. The key to overcoming these two deficiencies is to use tables of response surface coefficients, from which estimated quantiles for any sample size may be calculated, instead of equations to

Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration

Abstract: This paper employs response surface regressions based on simulation experments to calculate asymptotic distribution functions for the likelihood ratio tests for cointegration proposed by Johansen The paper provides tables of critical values that are very much more accurate than those available previously However the principal contributions of the paper are a set of data les that contain estimated asymptotic quantiles obtained from response surface estimation and a computer program for utilizing them This program which is freely available via the Internet can easily be used to calculate asymptotic critical values and P values Graphs of some of the tabulated distribution functions are also provided An empirical example motivated by the European Economic and Monetary Union proposed in the Maastricht Treaty suggests that not all the countries of the European Union may qualify initially for participation in the EMU.

A Time Series Model of Self-employment under Uncertainty

Abstract: This paper applies the techniques of stochastic optimal control to the problem of price-taking agents choosing the optimal balance between self-employment and paid employment. The two principal innovations are the development of an intertemporal optimizing model for heterogeneous agents under conditions of uncertainty, and the application of multivariate maximum likelihood cointegration techniques to test the model and to obtain estimates of the long-run and short-run determinants of self-employment. Both risk and expected returns are found to affect the numbers in self-employment in the long run; there is also evidence that the interest rate acts as a barrier to entry in reducing self-employment in the short run and the long run.

Cointegration for the applied economist

Abstract: Preface - The Contributors - Introduction - A Primer on Cointegration with an Application to Money and Income DADickey, DWJJansen & DLThornton - Unit Roots and Cointegration: An Introduction DHolden & RPerman - Trend, Unit Root and Structural Change in Macroeconomic Time Series PPerron - Wage Growth and the Inflation Process: An Empirical Approach YPMehra - Diagnostic Testing: An Application to the Demand for M1 GOtto - Bibliography - Index

Periodicity and Stochastic Trends in Economic Time Series

Abstract: Concepts in time series analysis an introduction to seasonal time series seasonal adjustment seasonal integration and cointegration are seasons, trends and cycles always independent? periodic autoregressive time series models periodic integration periodic cointegration.

Real Exchange Rate Levels, Productivity and Demand Shocks: Evidence from a Panel of 14 Countries

Abstract: We investigate the long-run relationship between the real exchange rate, traded and non-traded productivity levels, and government spending for 14 OECD countries, using recently developed panel cointegration tests. The results indicate that under certain assumptions it is easier to detect cointegration in panel data than in the available time series; moreover, the rate of reversion to long-run equilibrium is estimated with greater precision.

Periodicity and Stochastic Trends in Economic Time Series

Abstract: This book provides a self-contained account of periodic models for seasonally observed economic time series with stochastic trends. Two key concepts are periodic integration and periodic cointegration. Periodic integration implies that a seasonally varying differencing filter is required to remove a stochastic trend. Period cointegration amounts to allowing cointegration part-term adjustment parameters to vary with the season. The emphasis is on econometric models that explicitly describe seasonal variation and can reasonably be interpreted in terms of economic behaviour. The analysis considers econometric theory, Monte Carlo simulation, and forecasting, and it is illustrated with numerous empirical time series. A key feature of the proposed models is that changing seasonal fluctuations depend on the trend and business cycle fluctuations. In the case of such dependence, it is shown that seasonal adjustment leads to inappropriate results.

Assessing forecast performance in a cointegrated system

Abstract: This paper examines the forecast performance of a cointegrated system relative to the forecast performance of a comparable VAR that fails to recognize that the system is characterized by cointegration. The cointegrated system we examine is composed of three vectors, a money demand representation, a Fisher equation, and a risk premium captured by an interest rate differential. The forecasts produced by the vector error correction model (VECM) associated with this system are compared with those obtained from a corresponding differenced vector autoregression, (DVAR) as well as a vector autoregression based upon the levels of the data (LVAR). Forecast evaluation is conducted using both the ‘full-system’ criterion proposed by Clements and Hendry (1993) and by comparing forecast performance for specific variables. Overall our findings suggest that selective forecast performance improvement (especially at long forecast horizons) may be observed by incorporating knowledge of cointegration rank. Our general conclusion is that when the advantage of incorporating cointegration appears, it is generally at longer forecast horizons. This is consistent with the predictions of Engle and Yoo (1987). But we also find, consistent with Clements and Hendry (1995) that relative gain in forecast performance clearly depends upon the chosen data transformation.

Long‐Run Diversification Potential in Emerging Stock Markets

Abstract: In this paper we use cointegration tests to examine the long-run diversification potential of 13 emerging capital markets. The Johansen [18] and Johansen and Juselius [19] cointegration procedures are applied to the U.S. and 13 emerging capital markets in three geographical regions of the world. None of the three regions examined possesses cointegrated markets. The lack of cointegration indicates that the correlation between returns from each market is independent of the investment horizon Return correlations using weekly data correspond to the long-run investment horizon correlation. Correlations among the returns from these countries are low on average and occasionally negative. The apparent independence of markets within these three emerging regions suggests that diversification across these countries is effective.

Spatial aggregation, spatial dependence and predictability in the UK housing market

Abstract: Most time‐series studies of UK housing markets are carried out on national data. However, housing markets may be better characterised as a series of interconnected sub‐national markets. In this paper, we use methods taken from the spatial econometrics literature and from cointegration to explore the nature of spatial interactions in UK regional house prices and housing starts. The three central spatial issues are the extent to which markets are (a) homogeneous (b) dependent and (c) convergent, across the English regions. We find that housing starts equations are remarkably similar across regions and hence construction can be characterised as a national market. There is a high degree of spatial dependence in terms of both house prices and starts; dependence is uni‐directional in the former, but not the latter. Finally, cointegration results suggest that regional prices converge to long‐run relationships, despite major short‐term variation.

Time series and dynamic models

Abstract: In this book Christian Gourieroux and Alain Monfort provide an up-to-date and comprehensive analysis of modern time series econometrics. They have succeeded in synthesising in an organised and integrated way a broad and diverse literature. While the book does not assume a deep knowledge of economics, one of its most attractive features is the close attention it pays to economic models and phenomena throughout. The coverage represents a major reference tool for graduate students, researchers and applied economists. The book is divided into four sections. Section one gives a detailed treatment of classical seasonal adjustment or smoothing methods. Section two provides a thorough coverage of various mathematical tools. Section three is the heart of the book, and is devoted to a range of important topics including causality, exogeneity shocks, multipliers, cointegration and fractionally integrated models. The final section describes the main contribution of filtering and smoothing theory to time series econometric problems.

Modelling Quarterly Tourist Flows to Australia Using Cointegration Analysis

Abstract: The purpose of this paper is to use cointegration analysis to estimate the long-run relationship between quarterly tourist flows to Australia from the USA, Japan, to UK and New Zealand and the fact...

Is OPEC a cartel? Evidence from cointegration and causality tests

Abstract: Were the energy shocks of the 1970s engineered by an effective cartel acting to share the market by controlling output and influencing oil prices? If OPEC was an effective cartel sharing the market among its members, there would be a long run relationship between each member's production and total OPEC output. One would also expect OPECs production to significantly affect the price of oil. These implications of cartel behavior are tested via cointegration and causality tests. The likely effects of regime changes are dealt with using techniques developed by Perron (1989). There is evidence of output coordination among members of the organization, especially in the output rationing era (1982-1993). This is also the only period in which the causality from OPEC production to the price of oil is statistically significant.

Asian Pacific Real Exchange Rates and Relative Prices

Abstract: In this paper, the evidence for a relative tradables-nontradables price based explanation for long run movements in East Asian real exchange rates is examined. Using both time series cointegration techniques and panel regression procedures, I find that the real exchange rates are cointegrated with relative prices. Hence, I conclude that there is substantial evidence in favor of such a relativeprice explanation. However, the evidence is by no means conclusive, especially as it relates to some of the countries now growing the most rapidly--China, Indonesia, and Thailand. The fact that the relative price of tradables can exhibit such pronounced nonstationarity (of either a deterministic or stochastic nature) is troubling.

Statistical Analysis of Cointegrated VAR Processes with Markovian Regime Shifts

Abstract: This paper suggests a new methodological approach to the analysis of cointegrated linear systems subject to changes in regime. We consider cointegrated vector autoregressive processes where Markovian shifts occur in the equilibrium mean and the drift of the system. A two-stage maximum likelihood estimation technique is proposed. In the first stage, based on a finite order VAR approximation of the cointegrated VARMA representation, the Johansen cointegration analysis is invoked to determine the cointegration rank and to estimate the cointegration matrix. An EM algorithm delivers the maximum likelihood estimates of the remaining parameters. The methodology is illustrated with an investigation of international and global business cycles.

The Expectations Hypothesis of the Term Structure: The UK Interbank Market

Abstract: Using a high-quality weekly data set, the author provides several tests of the expectations hypothesis using the vector autoregression and cointegration methodologies, for several maturities between one-week and twelve-months, for the U.K. interbank market. On the basis of the Johansen cointegration analysis, there appears to be a 'break' in the term structure when both the six-month and twelve-month maturities are included as a pair. The latter may be due to either the presence of liquidity constraints or market segmentation or a time varying term premium, all of which would invalidate the assumptions underlying the expectations hypothesis. The author provides some tentative explanations of these diverse results. Copyright 1996 by Royal Economic Society.

Stock-Watson dynamic OLS (DOLS) and error-correction modelling approaches to estimating long- and short-run elasticities in a demand function: new evidence and methodological implications from an application to the demand for coal in mainland China

Abstract: In this paper robust elasticity estimates of coal demand for China are derived using annual data 1953-92. In so doing, we illustrate the use of a powerful yet practically convenient and recently developed modelling procedure devised by Stock and Watson (known as Dynamic OLS (DOLS)), who provide evidence, based on Monte Carlo simulations, of this estimator being superior in small samples compared to a number of alternative estimators, as well as being able not only to accommodate higher orders of integration but also to account for possible simultaneity within regressors of a potential demand system. Furthermore, cointegration and error-correction methods are employed to derive short-run price and income elasticities. Estimated results are quite robust not only in terms of statistical prowess but also in terms of economic intuition and indicate that, over the long run, both price and income elasticities are close to unity. While short-run price and income elasticities are less (in absolute value) than their long-run counterparts, there seems to be some divergence in short-run parameters from a subsample analysis. Overall, results seem to imply that for China, coal consumption should remain relatively constant as future modernization strategies for economic development are pursued. In addition, the study has clear methodological implications for estimating the long- and short-run elasticities in a demand function in general, and in a wide variety of fields in future applied research.

RATS handbook for econometric time series

Abstract: Introduction to RATS Stationary Time-Series Modeling Volatility Tests for Trends and Unit Roots Vector Autoregression Analysis Cointegration and Error Correction Statistical Tables References and Additional Readings