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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, …
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 …
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 …
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 …
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 …
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 …