A New Look at the Forward Premium Puzzle

This paper analyzes the sampling properties of the widely documented large negative slope estimates in regressions of future exchange returns on current forward premium. We argue that the abnormal behavior of the slope estimators in these regressions arises from the simultaneous presence of high persistence, low signal-to-noise ratio, strong endogeneity and an omitted variable problem. The paper develops the limiting theory for the slope parameter estimators in the levels and differenced forward premium regressions under some assumptions that match the empirical properties of the data. The asymptotic results derived in the paper help to reconcile the findings from the levels and difference specifications and provide important insights about the time series properties of the implied risk premium.Forward premium anomaly, high persistence, low signal-to-noise ratio, local-to-unity asymptotics

A Moment-Matching Method for Approximating Vector Autoregressive Processes by Finite-State Markov Chains

This paper proposes a moment-matching method for approximating vector autoregressions by finite-state Markov chains. The Markov chain is constructed by targeting the conditional moments of the underlying continuous process. The proposed method is more robust to the number of discrete values and tends to outperform the existing methods for approximating multivariate processes over a wide range of the parameter space, especially for highly persistent vector autoregressions with roots near the unit circle.Markov Chain, Vector Autoregressive Processes, Functional Equation, Numerical Methods, Moment Matching

"Time Series Nonparametric Regression Using Asymmetric Kernels with an Application to Estimation of Scalar Diffusion Processes"

This paper considers a nonstandard kernel regression for strongly mixing processes when the regressor is nonnegative. The nonparametric regression is implemented using asymmetric kernels [Gamma (Chen, 2000b), Inverse Gaussian and Reciprocal Inverse Gaussian (Scaillet, 2004) kernels] that possess some appealing properties such as lack of boundary bias and adaptability in the amount of smoothing. The paper investigates the asymptotic and finite-sample properties of the asymmetric kernel Nadaraya-Watson, local linear, and re-weighted Nadaraya-Watson estimators. Pointwise weak consistency, rates of convergence and asymptotic normality are established for each of these estimators. As an important economic application of asymmetric kernel regression estimators, we reexamine the problem of estimating scalar diffusion processes.

Specification Testing in Models with Many Instruments

This paper studies the asymptotic validity of the Anderson-Rubin (AR) test and the J test of overidentifying restrictions in linear models with many instruments. When the number of instruments increases at the same rate as the sample size, we establish that the conventional AR and J tests are asymptotically incorrect. Some versions of these tests, that are developed for situations with moderately many instruments, are also shown to be asymptotically invalid in this framework. We propose modifications of the AR and J tests that deliver asymptotically correct sizes. Importantly, the corrected tests are robust to the numerosity of the moment conditions in the sense that they are valid for both few and many instruments. The simulation results illustrate the excellent properties of the proposed tests.Instrumental variables, many instruments, Bekker?s asymptotics, Anderson? Rubin test, test for overidentifying restrictions.

Nonparametric Estimation of Scalar Diffusion Processes of Interest Rates Using Asymmetric Kernels

This paper proposes a nonparametric regression using asymmetric kernel functions for nonnegative, absolutely regular processes, and specializes this technique to estimating scalar diffusion models of spot interest rate. We illustrate the advantages of asymmetric kernel estimators for bias correction and efficiency gains. The finite-sample properties and the practical relevance of the proposed estimators are evaluated in the context of bond and option pricing. We also present estimation results from empirical analysis of the term structure of U.S. interest rates.Nonparametric regression; Gamma kernel; diffusion estimation; spot interest rate; derivative pricing

Local GMM Estimation of Time Series Models with Conditional Moment Restrictions

This paper investigates statistical properties of the local GMM (LGMM) estimator for some time series models defined by conditional moment restrictions. First, we consider Markov processes with possible conditional heteroskedasticity of unknown form and establish the consistency, asymptotic normality, and semi-parametric efficiency of the estimator. Second, inspired by simulation results showing that the LGMM estimator has a significantly smaller bias than the OLS estimator, we undertake a higher-order asymptotic expansion and analyze the bias properties of the LGMM estimator. The structure of the asymptotic expansion of the LGMM estimator reveals an interesting contrast with the OLS estimator that helps to explain the bias reduction in the LGMM estimator. The practical importance of these findings is evaluated in terms of a bond and option pricing exercise based on a diffusion model for spot interest rate.Conditional moment restrictions; Local GMM; Higher-order expansion; Conditional heteroskedasticity

Modeling Financial Return Dynamics by Decomposition

While the predictability of excess stock returns is statistically small, their sign and volatility exhibit a substantially larger degree of dependence over time. We capitalize on this observation and consider prediction of excess stock returns by decomposing the equity premium into a product of sign and absolute value components and carefully modeling the marginal predictive densities of the two parts. Then we construct the joint density of a positively valued (absolute returns) random variable and a discrete binary (sign) random variable by copula methods and discuss computation of the conditional mean predictor. Our empirical analysis of US stock return data shows among other interesting ndings that despite the large unconditional correlation between the two multiplicative components they are conditionally very weakly dependent.Stock returns predictability; Directional forecasting; Absolute returns; Joint predictive distribution; Copulas.

Bootstrap Unit Root Tests in Models with GARCH(1,1) Errors

This paper proposes a bootstrap unit root test in models with GARCH(1,1) errors and establishes its asymptotic validity under mild moment and distributional restrictions. While the proposed bootstrap test for a unit root shares the power enhancing properties of its asymptotic counterpart (Ling and Li, 2003), it offers a number of important advantages. In particular, the bootstrap procedure does not require explicit estimation of nuisance parameters that enter the distribution of the test statistic and corrects the substantial size distortions of the asymptotic test that occur for strongly heteroskedastic processes. The simulation results demonstrate the excellent finite-sample properties of the bootstrap unit root test for a wide range of GARCH specifications.Unit root test; GARCH; Bootstrap

A new method for approximating vector autoregressive processes by finite-state Markov chains

This paper proposes a new method for approximating vector autoregressions by a finite-state Markov chain. The method is more robust to the number of discrete values and tends to outperform the existing methods over a wide range of the parameter space, especially for highly persistent vector autoregressions with roots near the unit circle.Markov Chain, Vector Autoregressive Processes, Functional Equation, Numerical Methods, Moment Matching, Numerical Integration