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913
Time series regression with a unit root
 Econometrica
, 1987
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Cited by 398 (35 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Linear Regression Limit Theory for Nonstationary Panel Data
 ECONOMETRICA
, 1999
"... This paper develops a regression limit theory for nonstationary panel data with large numbers of cross section Ž n. and time series Ž T. observations. The limit theory allows for both sequential limits, wherein T� � followed by n��, and joint limits where T, n�� simultaneously; and the relationship ..."
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Cited by 300 (22 self)
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This paper develops a regression limit theory for nonstationary panel data with large numbers of cross section Ž n. and time series Ž T. observations. The limit theory allows for both sequential limits, wherein T� � followed by n��, and joint limits where T, n�� simultaneously; and the relationship between these multidimensional limits is explored. The panel structures considered allow for no time series cointegration, heterogeneous cointegration, homogeneous cointegration, and nearhomogeneous cointegration. The paper explores the existence of longrun average relations between integrated panel vectors when there is no individual time series cointegration and when there is heterogeneous cointegration. These relations are parameterized in terms of the matrix regression coefficient of the longrun average covariance matrix. In the case of homogeneous and near homogeneous cointegrating panels, a panel fully modified regression estimator is developed and studied. The limit theory enables us to test hypotheses about the long run average parameters both within and between subgroups of the full population.
Consumption Strikes Back? Measuring LongRun Risk
, 2008
"... We characterize and measure a longterm riskreturn tradeoff for the valuation of cash flows exposed to fluctuations in macroeconomic growth. This tradeoff features risk prices of cash flows that are realized far into the future but continue to be reflected in asset values. We apply this analysis ..."
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Cited by 231 (30 self)
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We characterize and measure a longterm riskreturn tradeoff for the valuation of cash flows exposed to fluctuations in macroeconomic growth. This tradeoff features risk prices of cash flows that are realized far into the future but continue to be reflected in asset values. We apply this analysis to claims on aggregate cash flows and to cash flows from value and growth portfolios by imputing values to the longrun dynamic responses of cash flows to macroeconomic shocks. We explore the sensitivity of our results to features of the economic valuation model and of the model cash flow dynamics.
An Adaptive Metropolis algorithm
 Bernoulli
, 1998
"... A proper choice of a proposal distribution for MCMC methods, e.g. for the MetropolisHastings algorithm, is well known to be a crucial factor for the convergence of the algorithm. In this paper we introduce an adaptive Metropolis Algorithm (AM), where the Gaussian proposal distribution is updated al ..."
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Cited by 213 (8 self)
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A proper choice of a proposal distribution for MCMC methods, e.g. for the MetropolisHastings algorithm, is well known to be a crucial factor for the convergence of the algorithm. In this paper we introduce an adaptive Metropolis Algorithm (AM), where the Gaussian proposal distribution is updated along the process using the full information cumulated so far. Due to the adaptive nature of the process, the AM algorithm is nonMarkovian, but we establish here that it has the correct ergodic properties. We also include the results of our numerical tests, which indicate that the AM algorithm competes well with traditional MetropolisHastings algorithms, and demonstrate that AM provides an easy to use algorithm for practical computation. 1991 Mathematics Subject Classification: 65C05, 65U05. Keywords: adaptive MCMC, comparison, convergence, ergodicity, Markov Chain Monte Carlo, MetropolisHastings algorithm 1 Introduction It is generally acknowledged that the choice of an effective proposal...
On adaptive markov chain monte carlo algorithm
 BERNOULLI
, 2005
"... We look at adaptive MCMC algorithms that generate stochastic processes based on sequences of transition kernels, where each transition kernel is allowed to depend on the past of the process. We show under certain conditions that the generated stochastic process is ergodic, with appropriate stationar ..."
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Cited by 122 (29 self)
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We look at adaptive MCMC algorithms that generate stochastic processes based on sequences of transition kernels, where each transition kernel is allowed to depend on the past of the process. We show under certain conditions that the generated stochastic process is ergodic, with appropriate stationary distribution. We then consider the Random Walk Metropolis (RWM) algorithm with normal proposal and scale parameter σ. We propose an adaptive version of this algorithm that sequentially adjusts σ using a RobbinsMonro type algorithm in order to nd the optimal scale parameter σopt as in Roberts et al. (1997). We show, under some additional conditions that this adaptive algorithm is ergodic and that σn, the sequence of scale parameter obtained converges almost surely to σopt. Our algorithm thus automatically determines and runs the optimal RWM scaling, with no manual tuning required. We close with a simulation example.
Basic Properties of Strong Mixing Conditions. A Survey and Some Open Questions
 PROBABILITY SURVEYS
, 2005
"... This is an update of, and a supplement to, the author’s earlier survey paper [18] on basic properties of strong mixing conditions. That paper appeared in 1986 in a book containing survey papers on various types of dependence conditions and the limit theory under them. The survey here will include pa ..."
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Cited by 117 (0 self)
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This is an update of, and a supplement to, the author’s earlier survey paper [18] on basic properties of strong mixing conditions. That paper appeared in 1986 in a book containing survey papers on various types of dependence conditions and the limit theory under them. The survey here will include part (but not all) of the material in [18], and will also describe some relevant material that was not in that paper, especially some new discoveries and developments that have occurred since that paper was published. (Much of the new material described here involves “interlaced ” strong mixing conditions, in which the index sets are not restricted to “past ” and “future.”) At various places in this survey, open problems will be posed. There is a large literature on basic properties of strong mixing conditions. A survey such as this cannot do full justice to it. Here are a few references on important topics not covered in this survey. For the approximation of mixing sequences by martingale differences, see e.g. the book by Hall and Heyde [80]. For the direct approximation of mixing random variables by independent ones,
Multivariate Local Polynomial Regression For Time Series: Uniform Strong Consistency And Rates
 J. Time Ser. Anal
, 1996
"... Local highorder polynomial fitting is employed for the estimation of the multivariate regression function m (x 1 , . . . , x d ) = E [y (Y d )  X 1 = x 1 , . . . , X d = x d ], and of its partial derivatives, for stationary random processes {Y i , X i }. The function y may be selected to yield est ..."
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Cited by 113 (2 self)
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Local highorder polynomial fitting is employed for the estimation of the multivariate regression function m (x 1 , . . . , x d ) = E [y (Y d )  X 1 = x 1 , . . . , X d = x d ], and of its partial derivatives, for stationary random processes {Y i , X i }. The function y may be selected to yield estimates of the conditional mean, conditional moments and conditional distributions. Uniform strong consistency over compact subsets of R d , along with rates, are established for the regression function and its partial derivatives for strongly mixing processes. Short Title: Multivariate Regression Estimation. Key Words: Multivariate regression estimation, local polynomial fitting, mixing processes, uniform strong consistency, rates of convergence. AMS (1991) Subject Classification: 62G07, 62H12, 62M09. ################## This work was supported by the Office of Naval Research under Grant N0001490J1175.  2  1. Introduction Let {Y i , X i } i = be jointly stationary processes on...
Drawing inferences from statistics based on multiyear asset returns
 Journal of Financial Economics
, 1989
"... Researchers investigating the possibility of mean reversion in stock prices with statistics based on multiyear returns have noted difficulties in drawing inferences from these statistics because the approximating asymptotic distributions perform poorly. We develop an alternative asymptotic distribut ..."
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Cited by 112 (5 self)
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Researchers investigating the possibility of mean reversion in stock prices with statistics based on multiyear returns have noted difficulties in drawing inferences from these statistics because the approximating asymptotic distributions perform poorly. We develop an alternative asymptotic distribution theory for statistics involving multiyear returns. These distributions diPier markedly from those implied by the conventional theory. The alternative theory provides substantially better approximations to the relevant finitesample distributions. It also leads to empirical inferences much less at odds with the hypothesis of no mean reversion.
On the asymptotic distribution of the Moran I test statistic with applications
 Journal of Econometrics104
"... By far, the most popular test for spatial correlation is the one based on Moran’s (1950) I test statistic. Despite this, the available results in the literature concerning the large sample distribution of this statistic are limited and have been derived under assumptions that do not cover many appli ..."
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Cited by 107 (13 self)
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By far, the most popular test for spatial correlation is the one based on Moran’s (1950) I test statistic. Despite this, the available results in the literature concerning the large sample distribution of this statistic are limited and have been derived under assumptions that do not cover many applications of interest. In this paper we first give a general result concerning the large sample distribution of Moran I type test statistics. We then apply this result to derive the large sample distribution of the Moran I test statistic for a variety of important models. In order to establish these results we also give a new central limit theorem for linearquadratic forms.
Threshold autoregression with a unit root
 Econometrica
, 2001
"... This paper develops an asymptotic theory of inference for an unrestricted tworegime threshold autoregressive Ž TAR. model with an autoregressive unit root. We find that the asymptotic null distribution of Wald tests for a threshold are nonstandard and different from the stationary case, and suggest ..."
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Cited by 103 (1 self)
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This paper develops an asymptotic theory of inference for an unrestricted tworegime threshold autoregressive Ž TAR. model with an autoregressive unit root. We find that the asymptotic null distribution of Wald tests for a threshold are nonstandard and different from the stationary case, and suggest basing inference on a bootstrap approximation. We also study the asymptotic null distributions of tests for an autoregressive unit root, and find that they are nonstandard and dependent on the presence of a threshold effect. We propose both asymptotic and bootstrapbased tests. These tests and distribution theory allow for the joint consideration of nonlinearity Ž thresholds. and nonstationary Žunit roots.. Our limit theory is based on a new set of tools that combine unit root asymptotics with empirical process methods. We work with a particular twoparameter empirical process that converges weakly to a twoparameter Brownian motion. Our limit distributions involve stochastic integrals with respect to this twoparameter process. This theory is entirely new and may find applications in other contexts. We illustrate the methods with an application to the U.S. monthly unemployment rate. We find strong evidence of a threshold effect. The point estimates suggest that the threshold effect is in the shortrun dynamics, rather than in the dominate root. While the conventional ADF test for a unit root is insignificant, our TAR unit root tests are arguably significant. The evidence is quite strong that the unemployment rate is not a unit root process, and there is considerable evidence that the series is a stationary TAR process.