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Articles 1 - 26 of 26
Full-Text Articles in Social and Behavioral Sciences
Power Maximization And Size Control Of Heteroscedasticity And Autocorrelation Robust Tests With Exponentiated Kernels, Yixiao Sun, Peter C. B. Phillips, Sainan Jin
Power Maximization And Size Control Of Heteroscedasticity And Autocorrelation Robust Tests With Exponentiated Kernels, Yixiao Sun, Peter C. B. Phillips, Sainan Jin
Research Collection School Of Economics
Using the power kernels of Phillips, Sun, and Jin (2006, 2007), we examine the large sample asymptotic properties of the t-test for different choices of power parameter (ρ). We show that the nonstandard fixed-ρ limit distributions of the t-statistic provide more accurate approximations to the finite sample distributions than the conventional large-ρ limit distribution. We prove that the second-order corrected critical value based on an asymptotic expansion of the nonstandard limit distribution is also second-order correct under the large-ρ asymptotics. As a further contribution, we propose a new practical procedure for selecting the test-optimal power parameter that addresses the central …
Uniform Asymptotic Normality In Stationary And Unit Root Autoregression, Chirok Han, Peter C. B. Phillips, Donggyu Sul
Uniform Asymptotic Normality In Stationary And Unit Root Autoregression, Chirok Han, Peter C. B. Phillips, Donggyu Sul
Research Collection School Of Economics
While differencing transformations can eliminate nonstationarity, they typically reduce signal strength and correspondingly reduce rates of convergence in unit root autoregressions. The present paper shows that aggregating moment conditions that are formulated in differences provides an orderly mechanism for preserving information and signal strength in autoregressions with some very desirable properties. In first order autoregression, a partially aggregated estimator based on moment conditions in differences is shown to have a limiting normal distribution that holds uniformly in the autoregressive coefficient rho, including stationary and unit root cases. The rate of convergence is root n when vertical bar rho vertical bar < 1 and the limit distribution is the same as the Gaussian maximum likelihood estimator (MLE), but when rho = 1 the rate of convergence to the normal distribution is within a slowly varying factor of n. A fully aggregated estimator (FAE) is shown to have the same limit behavior in the stationary case and to have nonstandard limit distributions in unit root and near integrated cases, which reduce both the bias and the variance of the MLE. This result shows that it is possible to improve on the asymptotic behavior of the MLE without using an artificial shrinkage technique or otherwise accelerating convergence at unity at the cost of performance in the neighborhood of unity. Confidence intervals constructed from the FAE using local asymptotic theory around unity also lead to improvements over the MLE.
A Simple And Robust Method Of Inference For Spatial Lag Dependence, Zhenlin Yang, Yan Shen
A Simple And Robust Method Of Inference For Spatial Lag Dependence, Zhenlin Yang, Yan Shen
Research Collection School Of Economics
A simple and reliable method of inference for the spatial parameter in spatial autoregressive models is introduced, based on a statistic obtained by centering and rescaling the numerator of the concentrated Gaussian score function. The resulted tests and confidence intervals are robust against the distributional misspecifications and are insensitive to the spatial layouts and the error standard deviation. In contrast, the standard methods based on Gaussian score and information matrix may lead to inconsistent inference when errors are non normal, and can be quite sensitive to the spatial layouts and the error standard deviation even when errors are normally distributed. …
Singapore Consumer’S Inflation Expectations And Creation Of Singapore Index Of Inflation Expectations, Aurobindo Ghosh, Jun Yu
Singapore Consumer’S Inflation Expectations And Creation Of Singapore Index Of Inflation Expectations, Aurobindo Ghosh, Jun Yu
Research Collection School Of Economics
The aim of this report is to highlight a broad spectrum of issues that brings about the measurement of the disagreement and the uncertainity and the formation of inflation expectations among economic agents in Singapore.
Score Tests For Inverse Gaussian Mixtures, A. F. Desmond, Zhenlin Yang
Score Tests For Inverse Gaussian Mixtures, A. F. Desmond, Zhenlin Yang
Research Collection School Of Economics
The mixed inverse Gaussian given by Whitmore (Scand. J. Statist., 13, 1986, 211–220) provides a convenient way for testing the goodness-of-fit of a pure inverse Gaussian distribution. The test is a one-sided score test with the null hypothesis being the pure inverse Gaussian (i.e. the mixing parameter is zero) and the alternative a mixture. We devise a simple score test and study its finite sample properties. Monte Carlo results show that it compares favourably with the smooth test of Ducharme (Test, 10, 2001, 271-290). In practical applications, when the pure inverse Gaussian distribution is rejected, one is interested in making …
Specification Sensitivity In Right-Tailed Unit Root Testing For Explosive Behavior, Peter C. B. Phillips, Shu-Ping Shi, Jun Yu
Specification Sensitivity In Right-Tailed Unit Root Testing For Explosive Behavior, Peter C. B. Phillips, Shu-Ping Shi, Jun Yu
Research Collection School Of Economics
Right-tailed unit root tests have proved promising for detecting exuberance in economic and financial activities. Like left-tailed tests, the limit theory and test performance are sensitive to the null hypothesis and the model specification used in parameter estimation. This paper aims to provide some empirical guidelines for the practical implementation of right-tailed unit root tests, focusing on the sup ADF test of Phillips, Wu and Yu (2011), which implements a right-tailed ADF test repeatedly on a sequence of forward sample recursions. We analyze and compare the limit theory of the sup ADF test under deferent hypotheses and model specifications. The …
Specification Testing For Nonparametric Structural Models With Monotonicity In Unobservables, Stefan Hoderlein, Liangjun Su, Halbert White
Specification Testing For Nonparametric Structural Models With Monotonicity In Unobservables, Stefan Hoderlein, Liangjun Su, Halbert White
Research Collection School Of Economics
Monotonicity in a scalar unobservable is a now common assumption in economic theory and applications. Among other things, it allows one to recover the underlying structural function from certain conditional quantiles of observables. Nevertheless, monotonicity is a strong assumption, and its failure can have substantive adverse consequences for structural inference. So far, there are no generally applicable nonparametric specification tests designed to detect monotonicity failure. This paper provides such a test for cross-section data. We show how to exploit an exclusion restriction together with a conditional independence assumption, plausible in a variety of applications, to construct a test. Our statistic …
Dating The Timeline Of Financial Bubbles During The Subprime Crisis, Peter C. B. Phillips, Jun Yu
Dating The Timeline Of Financial Bubbles During The Subprime Crisis, Peter C. B. Phillips, Jun Yu
Research Collection School Of Economics
A new recursive regression methodology is introduced to analyze the bubble characteristics of various financial time series during the subprime crisis. The methods modify a technique proposed in Phillips, Wu, and Yu (2011) and provide a technology for identifying bubble behavior with consistent dating of their origination and collapse. The tests serve as an early warning diagnostic of bubble activity and a new procedure is introduced for testing bubble migration across markets. Three relevant financial series are investigated, including a financial asset price (a house price index), a commodity price (the crude oil price), and one bond price (the spread …
Double Asymptotics For An Explosive Continuous Time Model, Xiaohu Wang, Jun Yu
Double Asymptotics For An Explosive Continuous Time Model, Xiaohu Wang, Jun Yu
Research Collection School Of Economics
This paper develops a double asymptotic limit theory for the persistent parameter (θ) in an explosive continuous time model with a large number of time span (N) and a small number of sampling interval (h). The limit theory allows for the joint limits where N → ∞ and h → 0 simultaneously, the sequential limits where N → ∞ is followed by h → 0, and the sequential limits where h → 0 is followed by N → ∞. All three asymptotic distributions are the same. The initial condition, either fixed or random, appears in the limiting distribution. The simultaneous …
Linear Programming-Based Estimators In Simple Linear Regression, Daniel P. A. Preve, Marcelo C. Medeiros
Linear Programming-Based Estimators In Simple Linear Regression, Daniel P. A. Preve, Marcelo C. Medeiros
Research Collection School Of Economics
In this paper we introduce a linear programming estimator (LPE) for the slope parameter in a constrained linear regression model with a single regressor. The LPE is interesting because it can be superconsistent in the presence of an endogenous regressor and, hence, preferable to the ordinary least squares estimator (LSE). Two different cases are considered as we investigate the statistical properties of the LPE. In the first case, the regressor is assumed to be fixed in repeated samples. In the second, the regressor is stochastic and potentially endogenous. For both cases the strong consistency and exact finite-sample distribution of the …
Tilted Nonparametric Estimation Of Volatility Functions With Empirical Applications, Ke-Li Xu, Peter C. B. Phillips
Tilted Nonparametric Estimation Of Volatility Functions With Empirical Applications, Ke-Li Xu, Peter C. B. Phillips
Research Collection School Of Economics
This article proposes a novel positive nonparametric estimator of the conditional variance function without reliance on logarithmic or other transformations. The estimator is based on an empirical likelihood modification of conventional local-level nonparametric regression applied to squared residuals of the mean regression. The estimator is shown to be asymptotically equivalent to the local linear estimator in the case of unbounded support but, unlike that estimator, is restricted to be nonnegative in finite samples. It is fully adaptive to the unknown conditional mean function. Simulations are conducted to evaluate the finite-sample performance of the estimator. Two empirical applications are reported. One …
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 …
Non-Parametric Regression Under Location Shifts, Peter C. B. Phillips, Liangjun Su
Non-Parametric Regression Under Location Shifts, Peter C. B. Phillips, Liangjun Su
Research Collection School Of Economics
Recent work by Wang and Phillips (2009b, 2011) has shown that ill-posed inverse problems do not arise in non-stationary non-parametric regression and there is no need for non-parametric instrumental variable estimation. Instead, simple Nadaraya–Watson non-parametric estimation of a cointegrating regression equation is consistent irrespective of the endogeneity in the regressor. The present paper shows that some closely related results apply in the case of structural non-parametric regression with independent data when there are continuous location shifts in the regressor. Some interesting cases are discovered where non-parametric regression is consistent, whereas parametric regression is inconsistent even when the true regression functional …
Testing For Multiple Bubbles, Peter C. B. Phillips, Shu-Ping Shi, Jun Yu
Testing For Multiple Bubbles, Peter C. B. Phillips, Shu-Ping Shi, Jun Yu
Research Collection School Of Economics
Identifying explosive bubbles that are characterized by periodically collapsing behavior over time has been a major concern in the literature and is of great importance for practitioners. The complexity of the nonlinear structure in multiple bubble phenomena diminishes the discriminatory power of existing tests, as evidenced in early simulations conducted by Evans (1991). Multiple collapsing bubble episodes within the same sample period make bubble diagnosis particularly difficult and complicate attempts at econometric dating. The present paper systematically investigates these issues and develops new procedures for practical implementation and surveillance strategies by central banks. We show how the testing procedure and …
Simulated Maximum Likelihood Estimation For Latent Diffusion Models, Tore Selland Kleppe, Jun Yu, Hans J. Skaug
Simulated Maximum Likelihood Estimation For Latent Diffusion Models, Tore Selland Kleppe, Jun Yu, Hans J. Skaug
Research Collection School Of Economics
In this paper a method is developed and implemented to provide the simulated maximum likelihood estimation of latent diffusions based on discrete data. The method is applicable to diffusions that either have latent elements in the state vector or are only observed at discrete time with a noise. Latent diffusions are very important in practical applications in financial economics. The proposed approach synthesizes the closed form method of Ait-Sahalia (2008) and the efficient importance sampler of Richard and Zhang (2007). It does not require any infill observations to be introduced and hence is computationally tractable. The Monte Carlo study shows …
Specification Sensitivities In Right-Tailed Unit Root Testing, Shu-Ping Shi, Peter C. B. Phillips, Jun Yu
Specification Sensitivities In Right-Tailed Unit Root Testing, Shu-Ping Shi, Peter C. B. Phillips, Jun Yu
Research Collection School Of Economics
Right-tailed unit root tests have proved promising for detecting exuberance in economic and financial activities. Like left-tailed tests, the limit theory and test performance are sensitive to the null hypothesis and the model specification used in parameter estimation. This paper aims to provide some empirical guidelines for the practical implementation of right-tailed unit root tests, focusing on the sup ADF test of Phillips, Wu and Yu (2011), which implements a right-tailed ADF test repeatedly on a sequence of forward sample recursions. We analyze and compare the limit theory of the sup ADF test under different hypotheses and model specifications. The …
Bayesian Hypothesis Testing In Latent Variable Models, Yong Li, Jun Yu
Bayesian Hypothesis Testing In Latent Variable Models, Yong Li, Jun Yu
Research Collection School Of Economics
Hypothesis testing using Bayes factors (BFs) is known not to be well defined under the improper prior. In the context of latent variable models, an additional problem with BFs is that they are difficult to compute. In this paper, a new Bayesian method, based on decision theory and the EM algorithm, is introduced to test a point hypothesis in latent variable models. The new statistic is a by-product of the Bayesian MCMC output and, hence, easy to compute. It is shown that the new statistic is easy to interpret and appropriately defined under improper priors because the method employs a …
Instrumental Variable Quantile Estimation Of Spatial Autoregressive Models, Liangjun Su, Zhenlin Yang
Instrumental Variable Quantile Estimation Of Spatial Autoregressive Models, Liangjun Su, Zhenlin Yang
Research Collection School Of Economics
We propose a spatial quantile autoregression (SQAR) model, which allows cross-sectional dependence among the responses, unknown heteroscedasticity in the disturbances, and heterogeneous impacts of covariates on different points (quantiles) of a response distribution. The instrumental variable quantile regression (IVQR) method of Chernozhukov and Hansen (2006) is generalized to allow the data to be non-identically distributed and dependent, an IVQR estimator for the SQAR model is then defined, and its asymptotic properties are derived. Simulation results show that this estimator performs well in finite samples at various quantile points. In the special case of spatial median regression, it outperforms the conventional …
Infinite Density At The Median And The Typical Shape Of Stock Return Distributions, Chirok Han, Jin Seo Cho, Peter C. B. Phillips
Infinite Density At The Median And The Typical Shape Of Stock Return Distributions, Chirok Han, Jin Seo Cho, Peter C. B. Phillips
Research Collection School Of Economics
Statistics are developed to test for the presence of an asymptotic discontinuity (or infinite density or peakedness) in a probability density at the median. The approach makes use of work by Knight (1998) on L(1) estimation asymptotics in conjunction with nonparametric kernel density estimation methods. The size and power of the tests are assessed, and conditions under which the tests have good performance are explored in simulations. The new methods are applied to stock returns of leading companies across major U.S. industry groups. The results confirm the presence of infinite density at the median as a new significant empirical evidence …
Bias In Estimating Multivariate And Univariate Diffusions, Xiaohu Wang, Peter C. B. Phillips, Jun Yu
Bias In Estimating Multivariate And Univariate Diffusions, Xiaohu Wang, Peter C. B. Phillips, Jun Yu
Research Collection School Of Economics
Multivariate continuous time models are now widely used in economics and finance. Empirical applications typically rely on some process of discretization so that the system may be estimated with discrete data. This paper introduces a framework for discretizing linear multivariate continuous time systems that includes the commonly used Euler and trapezoidal approximations as special cases and leads to a general class of estimators for the mean reversion matrix. Asymptotic distributions and bias formulae are obtained for estimates of the mean reversion parameter. Explicit expressions are given for the discretization bias and its relationship to estimation bias in both multivariate and …
Asymptotic Theory For Zero Energy Functionals With Nonparametric Regression Applications, Qiying Wang, Peter C. B. Phillips
Asymptotic Theory For Zero Energy Functionals With Nonparametric Regression Applications, Qiying Wang, Peter C. B. Phillips
Research Collection School Of Economics
A local limit theorem is given for the sample mean of a zero energy function of a nonstationary time series involving twin numerical sequences that pass to infinity. The result is applicable in certain nonparametric kernel density estimation and regression problems where the relevant quantities are functions of both sample size and bandwidth. An interesting outcome of the theory in nonparametric regression is that the linear term is eliminated from the asymptotic bias. In consequence and in contrast to the stationary case, the Nadaraya-Watson estimator has the same limit distribution (to the second order including bias) as the local linear …
Explosive Behavior In The 1990s Nasdaq: When Did Exuberance Escalate Asset Values?, Peter C. B. Phillips, Yangru Wu, Jun Yu
Explosive Behavior In The 1990s Nasdaq: When Did Exuberance Escalate Asset Values?, Peter C. B. Phillips, Yangru Wu, Jun Yu
Research Collection School Of Economics
A recursive test procedure is suggested that provides a mechanism for testing explosive behavior, date stamping the origination and collapse of economic exuberance, and providing valid confidence intervals for explosive growth rates. The method involves the recursive implementation of a right-side unit root test and a sup test, both of which are easy to use in practical applications, and some new limit theory for mildly explosive processes. The test procedure is shown to have discriminatory power in detecting periodically collapsing bubbles, thereby overcoming a weakness in earlier applications of unit root tests for economic bubbles. An empirical application to the …
Corrigendum To "A Gaussian Approach For Continuous Time Models Of The Short Term Interest Rate", Peter C. B. Phillips, Jun Yu
Corrigendum To "A Gaussian Approach For Continuous Time Models Of The Short Term Interest Rate", Peter C. B. Phillips, Jun Yu
Research Collection School Of Economics
An error is corrected in Yu and Phillips (2001) (Econometrics Journal, 4, 210-224) where a time transformation was used to induce Gaussian disturbances in the discrete time equivalent model. It is shown that the error process in this model is not a martingale and the Dambis, Dubins-Schwarz (DDS) theorem is not directly applicable. However, a detrended error process is a martingale, the DDS theorem is applicable, and the corresponding stopping time correctly induces Gaussianity. We show that the two stopping time sequences differ by O(a2), where a is the pre-specified normalized timing constant.
Estimation And Forecasting Of Dynamic Conditional Covariance: A Semiparametric Multivariate Model, Xiangdong Long, Liangjun Su, Aman Ullah
Estimation And Forecasting Of Dynamic Conditional Covariance: A Semiparametric Multivariate Model, Xiangdong Long, Liangjun Su, Aman Ullah
Research Collection School Of Economics
We propose a semiparametric conditional covariance (SCC) estimator that combines the first-stage parametric conditional covariance (PCC) estimator with the second-stage nonparametric correction estimator in a multiplicative way. We prove the asymptotic normality of our SCC estimator, propose a nonparametric test for the correct specification of PCC models, and study its asymptotic properties. We evaluate the finite sample performance of our test and SCC estimator and compare the latter with that of PCC estimator, purely nonparametric estimator, and Hafner, Dijk, and Franses’s (2006) estimator in terms of mean squared error and Value-at-Risk losses via simulations and real data analyses.
Model Selection In Validation Sampling Data: An Asymptotic Likelihood-Based Lasso Approach, Chenlei Leng, Denis H. Y. Leung
Model Selection In Validation Sampling Data: An Asymptotic Likelihood-Based Lasso Approach, Chenlei Leng, Denis H. Y. Leung
Research Collection School Of Economics
We propose an asymptotic likelihood-based LASSO approach for model selection in regression analysis when data are subject to validation sampling. The method makes use of an initial estimator of the regression coefficients and their asymptotic covariance matrix to form an asymptotic likelihood. This ``working'' objective function facilitates the formulation of the LASSO and the implementation of a fast algorithm. Our method circumvents the need to use a likelihood set-up that requires full distributional assumptions about the data. We show that the resulting estimator is consistent in model selection and that the method has lower prediction errors than a model that …
Nonparametric And Semiparametric Panel Econometric Models: Estimation And Testing, Liangjun Su, Aman Ullah
Nonparametric And Semiparametric Panel Econometric Models: Estimation And Testing, Liangjun Su, Aman Ullah
Research Collection School Of Economics
This paper gives a selective review on the recent developments of nonparametric and semiparametric panel data models. We focus on the conventional panel data models with one-way error component structure, partially linear panel data models, varying coefficient panel data models, nonparametric panel data models with multi-factor error structure, and nonseparable nonparametric panel data models. For each area, we discuss the basic models and ideas of estimation, and comment on the asymptotic properties of different estimators and specification tests. Much theoretical and empirical research is needed in this emerging area