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596
Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test
 REVIEW OF FINANCIAL STUDIES
, 1988
"... In this article we test the random walk hypothesis for weekly stock market returns by comparing variance estimators derived from data sampled at different frequencies. The random walk model is strongly rejected for the entire sample period (19621985) and for all subperiod for a variety of aggrega ..."
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Cited by 408 (18 self)
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In this article we test the random walk hypothesis for weekly stock market returns by comparing variance estimators derived from data sampled at different frequencies. The random walk model is strongly rejected for the entire sample period (19621985) and for all subperiod for a variety of aggregate returns indexes and sizesorted portofolios. Although the rejections are due largely to the behavior of small stocks, they cannot be attributed completely to the effects of infrequent trading or timevarying volatilities. Moreover, the rejection of the random walk for weekly returns does not support a meanreverting model of asset prices.
Lag length selection and the construction of unit root tests with good size and power
 Econometrica
, 2001
"... It is widely known that when there are errors with a movingaverage root close to −1, a high order augmented autoregression is necessary for unit root tests to have good size, but that information criteria such as the AIC and the BIC tend to select a truncation lag (k) that is very small. We conside ..."
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Cited by 400 (14 self)
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It is widely known that when there are errors with a movingaverage root close to −1, a high order augmented autoregression is necessary for unit root tests to have good size, but that information criteria such as the AIC and the BIC tend to select a truncation lag (k) that is very small. We consider a class of Modified Information Criteria (MIC) with a penalty factor that is sample dependent. It takes into account the fact that the bias in the sum of the autoregressive coefficients is highly dependent on k and adapts to the type of deterministic components present. We use a local asymptotic framework in which the movingaverage root is local to −1 to document how the MIC performs better in selecting appropriate values of k. In montecarlo experiments, the MIC is found to yield huge size improvements to the DF GLS and the feasible point optimal PT test developed in Elliott, Rothenberg and Stock (1996). We also extend the M tests developed in Perron and Ng (1996) to allow for GLS detrending of the data. The MIC along with GLS detrended data yield a set of tests with desirable size and power properties.
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 385 (7 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.
Time series regression with a unit root
 Econometrica
, 1987
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 329 (37 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
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 321 (11 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.
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 217 (0 self)
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This paper examines the behavior of forecasts made from a cointegrated system as introduced by
Univariate detrending methods with stochastic trends, H.I.E.R. discussion paper no
, 1985
"... This paper discusses detrending economic time series, when the trend is modelled as a stochastic process. It considers unobserved components models in which the observed series is decomposed into a trend (a random walk with drift) and a residual stationary component. Optimal detrending methods are d ..."
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Cited by 131 (1 self)
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This paper discusses detrending economic time series, when the trend is modelled as a stochastic process. It considers unobserved components models in which the observed series is decomposed into a trend (a random walk with drift) and a residual stationary component. Optimal detrending methods are discussed, as well as problems associated with using these detrended data in regression models. The methods are applied to three time series: GNP, disposable income, and consumption expenditures. The detrended data are used to test a version of the Life Cycle consumption model. 1.
Errorcorrection Mechanism Tests for Cointegration in a Singleequation Framework
 Journal of Times Series Analysis
, 1998
"... Abstract. A new test is proposed for cointegration in a single equation framework where the regressors are weakly exogenous for the parameters of interest. The test is denoted as an error correction mechanism (ECM) test and is based upon the ordinary least squares coef®cient of the lagged dependent ..."
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Cited by 122 (2 self)
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Abstract. A new test is proposed for cointegration in a single equation framework where the regressors are weakly exogenous for the parameters of interest. The test is denoted as an error correction mechanism (ECM) test and is based upon the ordinary least squares coef®cient of the lagged dependent variable in an autoregressive distributed lag model augmented with leads of the regressors. The limit distributions of the standardized coef®cient and t ratio versions of the ECM tests are obtained and critical values are provided. These limit distributions do not depend upon nuisance parameters but they depend on the number of regressors. Finally, we compare their power properties with those of other cointegration tests available in the literature and ®nd the circumstances under which the ECM tests have a better performance.
A PANIC Attack on Unit Roots and Cointegration
, 2003
"... This paper develops a new methodology that makes use of the factor structure of large dimensional panels to understand the nature of nonstationarity in the data. We refer to it as PANIC – a ‘Panel Analysis of Nonstationarity in Idiosyncratic and Common components’. PANIC consists of univariate and ..."
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Cited by 114 (3 self)
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This paper develops a new methodology that makes use of the factor structure of large dimensional panels to understand the nature of nonstationarity in the data. We refer to it as PANIC – a ‘Panel Analysis of Nonstationarity in Idiosyncratic and Common components’. PANIC consists of univariate and panel tests with a number of novel features. It can detect whether the nonstationarity is pervasive, or variablespecific, or both. It tests the components of the data instead of the observed series. Inference is therefore more accurate when the components have different orders of integration. PANIC also permits the construction of valid panel tests even when crosssection correlation invalidates pooling of statistics constructed using the observed data. The key to PANIC is consistent estimation of the components even when the regressions are individually spurious. We provide a rigorous theory for estimation and inference. In Monte Carlo simulations, the tests have very good size and power. PANIC is applied to a panel of inflation series.