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Full-Text Articles in Social and Behavioral Sciences
Estimating And Applying Autoregression Models Via Their Eigensystem Representation, Leo Krippner
Estimating And Applying Autoregression Models Via Their Eigensystem Representation, Leo Krippner
Sim Kee Boon Institute for Financial Economics
This article introduces the eigensystem autoregression (EAR) framework, which allows an AR model to be specified, estimated, and applied directly in terms of its eigenvalues and eigenvectors. An EAR estimation can therefore impose various constraints on AR dynamics that would not be possible within standard linear estimation. Examples are restricting eigenvalue magnitudes to control the rate of mean reversion, additionally imposing that eigenvalues be real and positive to avoid pronounced oscillatory behavior, and eliminating the possibility of explosive episodes in a time-varying AR. The EAR framework also produces closed-form AR forecasts and associated variances, and forecasts and data may be …
Hybrid Stochastic Local Unit Roots, Offer Lieberman, Peter C. B. Phillips
Hybrid Stochastic Local Unit Roots, Offer Lieberman, Peter C. B. Phillips
Research Collection School Of Economics
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 -> infinity. 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, …
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 …
Limit Theory For Mildly Integrated Process With Intercept, Yijie Fei
Limit Theory For Mildly Integrated Process With Intercept, Yijie Fei
Research Collection School Of Economics
Some asymptotic results are given for first-order autoregressive (AR(1)) time series with two features: (i). a nonzero constant intercept (ii). a root moderately deviating from unity. Both stationary and explosive sides are studied. It is shown that the inclusion of intercept will change drastically the large sample properties of the least-squares (LS) estimator obtained in Phillips and Magdalinos (2007, PM hereafter). For near-stationary case, only an unusual convergence of a linear combination of intercept and AR coefficient can be derived. For near-explosive case, on the other hand, the limiting distributions of two estimators will be independent and Gaussian, with conventional …
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 …
An Investigation Into The Relative Importance Of Civil Institutions On Subjective Well-Being, Samuel Fleming
An Investigation Into The Relative Importance Of Civil Institutions On Subjective Well-Being, Samuel Fleming
Graduate Student Theses, Dissertations, & Professional Papers
Poverty is not a material problem; in fact, it is a much greater problem, the problem of social, natural, and economic disconnect from the institutions of stability, wealth, justice, and well-being. When considering human flourishing, we must look beyond the material at “lives that are not necessarily morally good, but good for us” (Tiberius, 2006, p. 493). In the vein of Sen’s Capabilities Theory, this paper uses subjective well-being as a comprehensive measure of an individual’s life and circumstances examines how civil institutions impact an individual’s non-monetary welfare function. This paper conducts a series of regression models in an attempt …
A Multivariate Stochastic Unit Root Model With An Application To Derivative Pricing, Offer Lieberman, Peter C. B. Phillips
A Multivariate Stochastic Unit Root Model With An Application To Derivative Pricing, Offer Lieberman, Peter C. B. Phillips
Research Collection School Of Economics
This paper extends recent findings of Lieberman and Phillips (2014) on stochastic unit root (STUR) models to a multivariate case including asymptotic theory for estimation of the model's parameters. The extensions are useful for applications of STUR modeling and because they lead to a generalization of the Black-Scholes formula for derivative pricing. In place of the standard assumption that the price process follows a geometric Brownian motion, we derive a new form of the Black-Scholes equation that allows for a multivariate time varying coefficient element in the price equation. The corresponding formula for the value of a European-type call option …
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 …
Optimal Jackknife For Unit Root Models, Ye Chen, Jun Yu
Optimal Jackknife For Unit Root Models, Ye Chen, Jun Yu
Research Collection School Of Economics
A new jackknife method is introduced to remove the first order bias in unit root models. It is optimal in the sense that it minimizes the variance among all the jackknife estimators of the form considered in Phillips and Yu (2005) and Chambers and Kyriacou (2013) after the number of subsamples is selected. Simulations show that the new jackknife reduces the variance of that of Chambers and Kyriacou by about 10% for any selected number of subsamples without compromising bias reduction. The results continue to hold true in near unit root models. (C) 2014 Elsevier B.V. All rights reserved.
Norming Rates And Limit Theory For Some Time-Varying Coefficient Autoregressions, Offer Lieberman, Peter C. B. Phillips
Norming Rates And Limit Theory For Some Time-Varying Coefficient Autoregressions, Offer Lieberman, Peter C. B. Phillips
Research Collection School Of Economics
A time-varying autoregression is considered with a similarity-based coefficient and possible drift. It is shown that the random-walk model has a natural interpretation as the leading term in a small-sigma expansion of a similarity model with an exponential similarity function as its AR coefficient. Consistency of the quasi-maximum likelihood estimator of the parameters in this model is established, the behaviours of the score and Hessian functions are analysed and test statistics are suggested. A complete list is provided of the normalization rates required for the consistency proof and for the score and Hessian function standardization. A large family of unit …
X-Differencing And Dynamic Panel Model Estimation, Chirok Han, Peter C. B. Phillips, Donggyu Sul
X-Differencing And Dynamic Panel Model Estimation, Chirok Han, Peter C. B. Phillips, Donggyu Sul
Research Collection School Of Economics
This paper introduces a new estimation method for dynamic panel models with fixed effects and AR(p) idiosyncratic errors. The proposed estimator uses a novel form of systematic differencing, called X-differencing, that eliminates fixed effects and retains information and signal strength in cases where there is a root at or near unity. The resulting "panel fully aggregated" estimator (PFAE) is obtained by pooled least squares on the system of X-differenced equations. The method is simple to implement, consistent for all parameter values, including unit root cases, and has strong asymptotic and finite sample performance characteristics that dominate other procedures, such as …
An Extension Of Cochran-Orcutt Procedure For Generalized Linear Regression Models With Periodically Correlated Errors, Abdullah A. Smadi, Nour H. Abu-Afouna
An Extension Of Cochran-Orcutt Procedure For Generalized Linear Regression Models With Periodically Correlated Errors, Abdullah A. Smadi, Nour H. Abu-Afouna
Journal of Modern Applied Statistical Methods
An important assumption of ordinary regression models is independence among errors. This research considers the case of periodically correlated errors following the periodic AR model of order 1 (PAR(1)). The remedial measure for correlated errors in regression known as the Cochran-Orcutt procedure is generalized to the case of periodically correlated errors. The motivation for making such generalizations is that the response data may inhibit some seasonality, which may not be captured by the traditional AR(1) autoregressive model. The proposed procedure is described and the bias and MSE of the resulting intercept and slope parameter estimates of the simple LR model …
Optimal Jackknife For Discrete Time And Continuous Time Unit Root Models, Ye Chen, Jun Yu
Optimal Jackknife For Discrete Time And Continuous Time Unit Root Models, Ye Chen, Jun Yu
Research Collection School Of Economics
Maximum likelihood estimation of the persistence parameter in the discrete time unit root model is known for su§ering from a downward bias. The bias is more pronounced in the continuous time unit root model. Recently Chambers and Kyriacou (2010) introduced a new jackknife method to remove the Örst order bias in the estimator of the persistence parameter in a discrete time unit root model. This paper proposes an improved jackknife estimator of the persistence parameter that works for both the discrete time unit root model and the continuous time unit root model. The proposed jackknife estimator is optimal in the …
Forecasting Realized Volatility Using A Nonnegative Semiparametric Time Series Model, A. Eriksson, D. Preve, Jun Yu
Forecasting Realized Volatility Using A Nonnegative Semiparametric Time Series Model, A. Eriksson, D. Preve, Jun Yu
Research Collection School Of Economics
This paper introduces a parsimonious and yet flexible nonnegative semiparametric model to forecast financial volatility. The new model extends the linear nonnegative autoregressive model of Barndorff-Nielsen & Shephard (2001) and Nielsen & Shephard (2003) by way of a power transformation. It is semiparametric in the sense that the distributional form of its error component is left unspecified. The statistical properties of the model are discussed and a novel estimation method is proposed. Asymptotic properties are established for the new estimation method. Simulation studies validate the new estimation method. The out-of-sample performance of the proposed model is evaluated against a number …
Forecasting Realized Volatility Using A Nonnegative Semiparametric Model, D. Preve, A. Eriksson, Jun Yu
Forecasting Realized Volatility Using A Nonnegative Semiparametric Model, D. Preve, A. Eriksson, Jun Yu
Research Collection School Of Economics
This paper introduces a parsimonious and yet flexible nonnegative semiparametric model to forecast volatility. The new model extends the linear nonnegative autoregressive model of Barndorff-Nielsen and Shephard (2001) and Nielsen and Shephard (2003) by way of a Box-Cox transformation. It is semiparametric in the sense that the dependency structure and the distributional form of its error component are left unspecified. The statistical properties of the model are discussed and a novel estimation method is proposed. Its out-of-sample performance is evaluated against a number of standard methods, using data on S&P 500 monthly realized volatilities. The competing models include the exponential …
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
Research Collection School Of Economics
Stable autoregressive models 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. Simulations show that efficiency gains are achieved by the adaptive procedure.
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
Research Collection School Of Economics
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. Biases in dynamic models with fixed effects. Econometrica 49, 1417-1426] 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 …
Indirect Inference For Dynamic Panel Models, Christian Gourieroux, Peter C. B. Phillips, Jun Yu
Indirect Inference For Dynamic Panel Models, Christian Gourieroux, Peter C. B. Phillips, Jun Yu
Research Collection School Of Economics
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 and large cross section sample size asymptotics. This paper proposes a general, computationally inexpensive method of bias reduction that is based on indirect inference, shows unbiasedness and analyzes efficiency. Monte Carlo studies show that our procedure achieves substantial bias reductions with only mild increases in variance, thereby substantially reducing root mean square errors. The method is compared with certain consistent estimators and is shown to have superior finite sample properties to the generalized method of …
Indirect Inference For Dynamic Panel Models, Christian Gourieroux, Peter C. B. Phillips, Jun Yu
Indirect Inference For Dynamic Panel Models, Christian Gourieroux, Peter C. B. Phillips, Jun Yu
Research Collection School Of Economics
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 model, but has wider …
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 …