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617
Time series regression with a unit root
 Econometrica
, 1987
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Cited by 203 (27 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 146 (14 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Consumption Strikes Back?: Measuring Long Run Risk, Unpublished working paper
, 2006
"... 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 115 (13 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. I.
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 102 (4 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...
Tail Bounds for Occupancy and the Satisfiability Threshold Conjecture
, 1995
"... The classical occupancy problem is concerned with studying the number of empty bins resulting from a random allocation of m balls to n bins. We provide a series of tail bounds on the distribution of the number of empty bins. These tail bounds should find application in randomized algorithms and prob ..."
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Cited by 98 (2 self)
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The classical occupancy problem is concerned with studying the number of empty bins resulting from a random allocation of m balls to n bins. We provide a series of tail bounds on the distribution of the number of empty bins. These tail bounds should find application in randomized algorithms and probabilistic analysis. Our motivating application is the following wellknown conjecture on threshold phenomenon for the satisfiability problem. Consider random 3SAT formulas with cn clauses over n variables, where each clause is chosen uniformly and independently from the space of all clauses of size 3. It has been conjectured that there is a sharp threshold for satisfiability at c ß 4:2. We provide a strong upper bound on the value of c , showing that for c ? 4:758 a random 3SAT formula is unsatisfiable with high probability. This result is based on a structural property, possibly of independent interest, whose proof needs several applications of the occupancy tail bounds. Supporte...
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 74 (25 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.
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 69 (2 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.
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 66 (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...
Ultra high frequency volatility estimation with dependent microstructure noise
"... We analyze the impact of time series dependence in market microstructure noise on the properties of estimators of the integrated volatility of an asset price based on data sampled at frequencies high enough for that noise to be a dominant consideration. We show that combining two time scales for tha ..."
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Cited by 63 (10 self)
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We analyze the impact of time series dependence in market microstructure noise on the properties of estimators of the integrated volatility of an asset price based on data sampled at frequencies high enough for that noise to be a dominant consideration. We show that combining two time scales for that purpose will work even when the noise exhibits time series dependence, analyze in that context a refinement of this approach based on multiple time scales, and compare empirically our different estimators to the standard realized volatility.
On the ergodicity properties of some adaptive MCMC algorithms
 Annals of Applied Probability
"... In this paper we study the ergodicity properties of some adaptive Monte Carlo Markov chain algorithms (MCMC) that have been recently proposed in the literature. We prove that under a set of verifiable conditions, ergodic averages calculated from the output of a socalled adaptive MCMC sampler conver ..."
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Cited by 56 (7 self)
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In this paper we study the ergodicity properties of some adaptive Monte Carlo Markov chain algorithms (MCMC) that have been recently proposed in the literature. We prove that under a set of verifiable conditions, ergodic averages calculated from the output of a socalled adaptive MCMC sampler converge to the required value and can even, under more stringent assumptions, satisfy a central limit theorem. We prove that the conditions required are satisfied for the Independent MetropolisHastings algorithm and the Random Walk Metropolis algorithm with symmetric increments. Finally we propose an application of these results to the case where the proposal distribution of the MetropolisHastings update is a mixture of distributions from a curved exponential family.