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A new approach to the economic analysis of nonstationarytime seriesandthe business cycle
 Econometrica
, 1989
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Cited by 1021 (12 self)
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A Simple Estimator of Cointegrating Vectors in Higher Order Cointegrated Systems," Econometrica 61
, 1993
"... Efficient estimators of cointegrating vectors are presented for systems involving deterministic components and variables of differing, higher orders of integration. The estimators are computed using GLS or OLS, and Wald Statistics constructed from these estimators have asymptotic x2 distributions. T ..."
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Cited by 261 (3 self)
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Efficient estimators of cointegrating vectors are presented for systems involving deterministic components and variables of differing, higher orders of integration. The estimators are computed using GLS or OLS, and Wald Statistics constructed from these estimators have asymptotic x2 distributions. These and previously proposed estimators of cointegrating vectors are used to study longrun U.S. money (Ml) demand. Ml demand is found to be stable over 19001989; the 95 % confidence intervals for the income elasticity and interest rate semielasticity are (.88,1.06) and (.13,.08), respectively. Estimates based on the postwar data alone, however, are unstable, with variances which indicate substantial sampling uncertainty.
Testing for Common Trends
 Journal of the American Statistical Association
, 1988
"... Cointegrated multiple time series share at least one common trend. Two tests are developed for the number of common stochastic trends (i.e., for the order of cointegration) in a multiple time series with and without drift. Both tests involve the roots of the ordinary least squares coefficient matrix ..."
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Cited by 229 (6 self)
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Cointegrated multiple time series share at least one common trend. Two tests are developed for the number of common stochastic trends (i.e., for the order of cointegration) in a multiple time series with and without drift. Both tests involve the roots of the ordinary least squares coefficient matrix obtained by regressing the series onto its first lag. Critical values for the tests are tabulated, and their power is examined in a Monte Carlo study. Economic time series are often modeled as having a unit root in their autoregressive representation, or (equivalently) as containing a stochastic trend. But both casual observation and economic theory suggesthat many series might contain the same stochastic trendso that they are cointegrated. If each of n series is integrated of order 1 but can be jointly characterized by k < n stochastic trends, then the vecto representation of these series has k unit roots and n k distinct stationary linear combinations. Our proposed tests can be viewed alternatively as tests of the number of common trends, linearly independent cointegrating vectors, or autoregressive unit roots of the vector process. Both of the proposed tests are asymptotically similar. The firstest (qf) is developed under the assumption that certain components of the process have a finiteorder vector autoregressive (VAR) representation, and the nuisance parameters are handled by estimating this VAR. The second test (q,) entails computing the eigenvalues of a corrected sample firstorder autocorrelation matrix, where the correction is essentially a sum of the autocovariance matrices. Previous researchers have found that U.S. postwar interest rates, taken individually, appear to be integrated of order 1. In addition, the theory of the term structure implies that yields on similar assets of different maturities will be cointegrated. Applying these tests to postwar U.S. data on the federal funds rate and the three and twelvemonth treasury bill rates providesupport for this prediction: The three interest rates appear to be cointegrated.
Critical values for cointegration tests
 Eds.), LongRun Economic Relationship: Readings in Cointegration
, 1991
"... This paper provides tables of critical values for some popular tests of cointegration and unit roots. Although these tables are necessarily based on computer simulations, they are much more accurate than those previously available. The results of the simulation experiments are summarized by means of ..."
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Cited by 203 (2 self)
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This paper provides tables of critical values for some popular tests of cointegration and unit roots. Although these tables are necessarily based on computer simulations, they are much more accurate than those previously available. The results of the simulation experiments are summarized by means of response surface regressions in which critical values depend on the sample size. From these regressions, asymptotic critical values can be read off directly, and critical values for any finite sample size can easily be computed with a hand calculator. Added in 2010 version: A new appendix contains additional results that are more accurate and cover more cases than the ones in the original paper.
Inference in Linear Time Series Models with Some Unit Roots," Econometrica
, 1990
"... This paper considers estimation and hypothesis testing in linear time series models when some or all of the variables have unit roots. Our motivating example is a vector autoregression with some unit roots in the companion matrix, which might include polynomials in time as regressors. In the general ..."
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Cited by 174 (7 self)
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This paper considers estimation and hypothesis testing in linear time series models when some or all of the variables have unit roots. Our motivating example is a vector autoregression with some unit roots in the companion matrix, which might include polynomials in time as regressors. In the general formulation, the variable might be integrated or cointegrated of arbitrary orders, and might have drifts as well. We show that parameters that can be written as coefficients on mean zero, nonintegrated regressors have jointly normal asymptotic distributions, converging at the rate T'/2. In general, the other coefficients (including the coefficients on polynomials in time) will have nonnormal asymptotic distributions. The results provide a formal characterization of which t or F testssuch as Granger causality testswill be asymptotically valid, and which will have nonstandard limiting distributions.
Stochastic Trends and Economic Fluctuations
 American Economic Review
, 1991
"... Are business cycles mainly the result of permanent shocks to productivity? This paper uses a longrun restriction implied by a large class of realbusinesscycle modelsidentifying permanent productivity shocks as shocks to the common stochastic trend in output, consumption, and investmentto provid ..."
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Cited by 137 (4 self)
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Are business cycles mainly the result of permanent shocks to productivity? This paper uses a longrun restriction implied by a large class of realbusinesscycle modelsidentifying permanent productivity shocks as shocks to the common stochastic trend in output, consumption, and investmentto provide new evidence on this question. Econometric tests indicate that this commonstochastictrend / cointegration implication is consistent with postwar U.S. data. However, in systems with nominal variables, the estimates of this common stochastic trend indicate that permanent productivity shocks typically explain less than half of the businesscycle variability in output, consumption, and investment. (JEL E32, C32) A central, surprising, and controversial result of some current research on real business cycles is the claim that a common stochastic trendthe cumulative effect of permanent shocks to productivityunderlies the bulk of economic fluctuations. If confirmed, this finding would imply that many other forces have been relatively unimportant over historical business cycles, including the monetary and fiscal policy shocks stressed in traditional macroeconomic analysis. This paper shows that the hypothesis of a common stochastic productivity trend has a set of econometric implications that allows us to test for its presence, measure its importance, and extract estimates of its realized value. Applying these procedures to consumption, investment, and output for the postwar United States, we find results that both support and contradict this claim in the realbusinesscycle literature. The U.S. data are consis
Forecasting and Testing in Cointegrated Systems
 Journal of Econometrics
, 1987
"... This paper examines the behavior of forecasts made from a cointegrated system as introduced by ..."
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Cited by 110 (0 self)
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This paper examines the behavior of forecasts made from a cointegrated system as introduced by