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Full-Text Articles in Economics
Understanding Temporal Aggregation Effects On Kurtosis In Financial Indices, Offer Lieberman, Peter C.B. Phillips
Understanding Temporal Aggregation Effects On Kurtosis In Financial Indices, Offer Lieberman, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Indices of financial returns typically display sample kurtosis that declines towards the Gaussian value 3 as the sampling interval increases. This paper uses stochastic unit root (STUR) and continuous time analysis to explain the phenomenon. Limit theory for the sample kurtosis reveals that STUR specifications provide two sources of excess kurtosis, both of which decline with the sampling interval. Limiting kurtosis is shown to be random and is a functional of the limiting price process. Using a continuous time version of the model under no-drift, local drift, and drift inclusions, we suggest a new continuous time kurtosis measure for financial …
Hybrid Stochastic Local Unit Roots, Offer Lieberman, Peter C.B. Phillips
Hybrid Stochastic Local Unit Roots, Offer Lieberman, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Two approaches have dominated formulations designed to capture small departures from unit root autoregressions. The first involves deterministic departures that include local-to-unity (LUR) and mildly (or moderately) integrated (MI) specifications where departures shrink to zero as the sample size n→∞. The second approach allows for stochastic departures from unity, leading to stochastic unit root (STUR) specifications. This paper introduces a hybrid local stochastic unit root (LSTUR) specification that has both LUR and STUR components and allows for endogeneity in the time varying coefficient that introduces structural elements to the autoregression. This hybrid model generates trajectories that, upon normalization, have non-linear …
Iv And Gmm Estimation And Testing Of Multivariate Stochastic Unit Root Models, Offer Lieberman, Peter C.B. Phillips
Iv And Gmm Estimation And Testing Of Multivariate Stochastic Unit Root Models, Offer Lieberman, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Lieberman and Phillips (2016; Journal of Econometrics; LP) introduced a multivariate stochastic unit root (STUR) model, which allows for random, time varying local departures from a unit root (UR) model, where nonlinear least squares (NLLS) may be used for estimation and inference on the STUR coefficient. In a structural version of this model where the driver variables of the STUR coefficient are endogenous, the NLLS estimate of the STUR parameter is inconsistent, as are the corresponding estimates of the associated covariance parameters. This paper develops a nonlinear instrumental variable (NLIV) as well as GMM estimators of the STUR parameter which …
Asymptotics For Ls, Gls, And Feasible Gls Statistics In An Ar(1) Model With Conditional Heteroskedasticity, Donald W.K. Andrews, Patrik Guggenberger
Asymptotics For Ls, Gls, And Feasible Gls Statistics In An Ar(1) Model With Conditional Heteroskedasticity, Donald W.K. Andrews, Patrik Guggenberger
Cowles Foundation Discussion Papers
This paper considers a first-order autoregressive model with conditionally heteroskedastic innovations. The asymptotic distributions of least squares (LS), infeasible generalized least squares (GLS), and feasible GLS estimators and t statistics are determined. The GLS procedures allow for misspecification of the form of the conditional heteroskedasticity and, hence, are referred to as quasi-GLS procedures. The asymptotic results are established for drifting sequences of the autoregressive parameter and the distribution of the time series of innovations. In particular, we consider the full range of cases in which the autoregressive parameter ρ n satisfies (i) n(1 - ρ n ) → ∞ and …
Asymptotics For Ls, Gls, And Feasible Gls Statistics In An Ar(1) Model With Conditional Heteroskedaticity, Donald W.K. Andrews, Patrik Guggenberger
Asymptotics For Ls, Gls, And Feasible Gls Statistics In An Ar(1) Model With Conditional Heteroskedaticity, Donald W.K. Andrews, Patrik Guggenberger
Cowles Foundation Discussion Papers
This paper considers a first-order autoregressive model with conditionally heteroskedastic innovations. The asymptotic distributions of least squares (LS), infeasible generalized least squares (GLS), and feasible GLS estimators and t statistics are determined. The GLS procedures allow for misspecification of the form of the conditional heteroskedasticity and, hence, are referred to as quasi-GLS procedures. The asymptotic results are established for drifting sequences of the autoregressive parameter and the distribution of the time series of innovations. In particular, we consider the full range of cases in which the autoregressive parameter ρ n satisfies (i) n (1 - ρ n ) → ∞ …
Asymptotics For Ls, Gls, And Feasible Gls Statistics In An Ar(1) Model With Conditional Heteroskedaticity, Donald W.K. Andrews, Patrik Guggenberger
Asymptotics For Ls, Gls, And Feasible Gls Statistics In An Ar(1) Model With Conditional Heteroskedaticity, Donald W.K. Andrews, Patrik Guggenberger
Cowles Foundation Discussion Papers
This paper considers a first-order autoregressive model with conditionally heteroskedastic innovations. The asymptotic distributions of least squares (LS), infeasible generalized least squares (GLS), and feasible GLS estimators and t statistics are determined. The GLS procedures allow for misspecification of the form of the conditional heteroskedasticity and, hence, are referred to as quasi-GLS procedures. The asymptotic results are established for drifting sequences of the autoregressive parameter and the distribution of the time series of innovations. In particular, we consider the full range of cases in which the autoregressive parameter rhon satisfies (i) n (1 – ρ n ) → ∞ and …
Adaptive Estimation Of Autoregressive Models With Time-Varying Variances, Ke-Li Xu, Peter C.B. Phillips
Adaptive Estimation Of Autoregressive Models With Time-Varying Variances, Ke-Li Xu, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Stable autoregressive models of known finite order are considered with martingale differences errors scaled by an unknown nonparametric time-varying function generating heterogeneity. An important special case involves structural change in the error variance, but in most practical cases the pattern of variance change over time is unknown and may involve shifts at unknown discrete points in time, continuous evolution or combinations of the two. This paper develops kernel-based estimators of the residual variances and associated adaptive least squares (ALS) estimators of the autoregressive coefficients. These are shown to be asymptotically efficient, having the same limit distribution as the infeasible generalized …
Adaptive Estimation Of Autoregressive Models With Time-Varying Variances, Ke-Li Xu, Peter C.B. Phillips
Adaptive Estimation Of Autoregressive Models With Time-Varying Variances, Ke-Li Xu, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Stable autoregressive models of known finite order are considered with martingale differences errors scaled by an unknown nonparametric time-varying function generating heterogeneity. An important special case involves structural change in the error variance, but in most practical cases the pattern of variance change over time is unknown and may involve shifts at unknown discrete points in time, continuous evolution or combinations of the two. This paper develops kernel-based estimators of the residual variances and associated adaptive least squares (ALS) estimators of the autoregressive coefficients. These are shown to be asymptotically efficient, having the same limit distribution as the infeasible generalized …
Indirect Inference For Dynamic Panel Models, Christian Gouriéroux, Peter C.B. Phillips, Jun Yu
Indirect Inference For Dynamic Panel Models, Christian Gouriéroux, Peter C.B. Phillips, Jun Yu
Cowles Foundation Discussion Papers
It is well-known that maximum likelihood (ML) estimation of the autoregressive parameter of a dynamic panel data model with fixed effects is inconsistent under fixed time series sample size ( T ) and large cross section sample size ( N ) asymptotics. The estimation bias is particularly relevant in practical applications when T is small and the autoregressive parameter is close to unity. The present paper proposes a general, computationally inexpensive method of bias reduction that is based on indirect inference (Gouriéroux et al., 1993), shows unbiasedness and analyzes efficiency. The method is implemented in a simple linear dynamic panel …
Gaussian Inference In Ar(1) Time Series With Or Without A Unit Root, Peter C.B. Phillips, Chirok Han
Gaussian Inference In Ar(1) Time Series With Or Without A Unit Root, Peter C.B. Phillips, Chirok Han
Cowles Foundation Discussion Papers
This note introduces a simple first-difference-based approach to estimation and inference for the AR(1) model. The estimates have virtually no finite sample bias, are not sensitive to initial conditions, and the approach has the unusual advantage that a Gaussian central limit theory applies and is continuous as the autoregressive coefficient passes through unity with a uniform / n rate of convergence. En route, a useful CLT for sample covariances of linear processes is given, following Phillips and Solo (1992). The approach also has useful extensions to dynamic panels.
Uniform Limit Theory For Stationary Autoregression, Liudas Giraitis, Peter C.B. Phillips
Uniform Limit Theory For Stationary Autoregression, Liudas Giraitis, Peter C.B. Phillips
Cowles Foundation Discussion Papers
First order autoregression is shown to satisfy a limit theory which is uniform over stationary values of the autoregressive coefficient ρ = ρ n in [0,1) provided (1 - ρ n )n approaches infinity. This extends existing Gaussian limit theory by allowing for values of stationary rho that include neighbourhoods of unity provided they are wider than ( n 1 ), even by a slowly varying factor. Rates of convergence depend on rho and are at least squareroot of / n but less than n . Only second moments are assumed, as in the case of stationary autoregression with fixed …
Prewhitening Bias In Hac Estimation, Donggyu Sul, Peter C.B. Phillips, Chi-Young Choi
Prewhitening Bias In Hac Estimation, Donggyu Sul, Peter C.B. Phillips, Chi-Young Choi
Cowles Foundation Discussion Papers
HAC estimation commonly involves the use of prewhitening filters based on simple autoregressive models. In such applications, small sample bias in the estimation of autoregressive coefficients is transmitted to the recoloring filter, leading to HAC variance estimates that can be badly biased. The present paper provides an analysis of these issues using asymptotic expansions and simulations. The approach we recommend involves the use of recursive demeaning procedures that mitigate the effects of small sample autoregressive bias. Moreover, a commonly-used restriction rule on the prewhitening estimates (that first order autoregressive coefficient estimates, or largest eigenvalues, greater than 0.97 be replaced by …
Bias In Dynamic Panel Estimation With Fixed Effects, Incidental Trends And Cross Section Dependence, Peter C.B. Phillips, Donggyu Sul
Bias In Dynamic Panel Estimation With Fixed Effects, Incidental Trends And Cross Section Dependence, Peter C.B. Phillips, Donggyu Sul
Cowles Foundation Discussion Papers
Explicit asymptotic bias formulae are given for dynamic panel regression estimators as the cross section sample size N → ∞. The results extend earlier work by Nickell (1981) and later authors in several directions that are relevant for practical work, including models with unit roots, deterministic trends, predetermined and exogenous regressors, and errors that may be cross sectionally dependent. The asymptotic bias is found to be so large when incidental linear trends are fitted and the time series sample size is small that it changes the sign of the autoregressive coefficient. Another finding of interest is that, when there is …
Dynamic Panel Estimation And Homogeneity Testing Under Cross Section Dependence, Peter C.B. Phillips, Donggyu Sul
Dynamic Panel Estimation And Homogeneity Testing Under Cross Section Dependence, Peter C.B. Phillips, Donggyu Sul
Cowles Foundation Discussion Papers
This paper deals with cross section dependence, homogeneity restrictions and small sample bias issues in dynamic panel regressions. To address the bias problem we develop a panel approach to median unbiased estimation that takes account of cross section dependence. The new estimators given here considerably reduce the effects of bias and gain precision from estimating cross section error correlation. The paper also develops an asymptotic theory for tests of coefficient homogeneity under cross section dependence, and proposes a modified Hausman test to test for the presence of homogeneous unit roots. An orthogonalization procedure is developed to remove cross section dependence …
A Bayesian Analysis Of Trend Determination In Economic Time Series, Eric Zivot, Peter C.B. Phillips
A Bayesian Analysis Of Trend Determination In Economic Time Series, Eric Zivot, Peter C.B. Phillips
Cowles Foundation Discussion Papers
In this paper we provide a comprehensive Bayesian posterior analysis of trend determination in general autoregressive models. Multiple lag autoregressive models with fitted drifts and time trends as well as models that allow for certain types of structural change in the deterministic components are considered. We utilize a modified information matrix-based prior that accommodates stochastic nonstationarity, takes into account the interactions between long-run and short-run dynamics and controls the degree of stochastic nonstationarity permitted. We derive analytic posterior densities for all of the trend determining parameters via the Laplace approximation to multivariate integrals. We also address the sampling properties of …
A Shortcut To Lad Estimator Asymptotics, Peter C.B. Phillips
A Shortcut To Lad Estimator Asymptotics, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Using generalized functions of random variables and generalized Taylor series expansions, we provide almost trivial demonstrations of the asymptotic theory for the LAD estimator in a regression model setting. The approach is justified by the smoothing that is delivered in the limit by the asymptotics, whereby the generalized functions are forced to appear as linear functionals wherein they become real valued. Models with fixed and random regressors, autoregressions and autoregressions with infinite variance errors are studied. Some new analytic results are obtained including an asymptotic expansion of the distribution of the LAD estimator and the results of some earlier simulation …
Towards A Unified Asymptotic Theory For Autoregression, Peter C.B. Phillips
Towards A Unified Asymptotic Theory For Autoregression, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper develops an asymptotic theory for a first order autoregression with a root near unity. Deviations from the unit root theory are measured through a noncentrality parameter. When this parameter is negative we have a local alternative that is stationary; when it is positive, the local alternative is explosive; and when it is zero we have the standard unit root theory. Our asymptotic theory accommodates these alternatives and helps to unify earlier theory in which the unit root case appears as a singularity of the asymptotics. The general theory is expressed in terms of functionals of a simple diffusion …