Showing papers by "Oliver Linton published in 2006"

Quantile autoregression. Commentary

Abstract: We consider quantile autoregression (QAR) models in which the autoregressive coefficients can be expressed as monotone functions of a single, scalar random variable. The models can capture systematic influences of conditioning variables on the location, scale, and shape of the conditional distribution of the response, and thus constitute a significant extension of classical constant coefficient linear time series models in which the effect of conditioning is confined to a location shift. The models may be interpreted as a special case of the general random-coefficient autoregression model with strongly dependent coefficients. Statistical properties of the proposed model and associated estimators are studied. The limiting distributions of the autoregression quantile process are derived. QAR inference methods are also investigated. Empirical applications of the model to the U.S. unemployment rate, short-term interest rate, and gasoline prices highlight the model's potential.

Estimating Features of a Distribution from Binomial Data

Abstract: A statistical problem that arises in several fields is that of estimating the features of an unknown distribution, which may be conditioned on covariates, using a sample of binomial observations on whether draws from this distribution exceed threshold levels set by experimental design. Applications include bioassay and destructive duration analysis. The empirical application we consider is referendum contingent valuation in resource economics, where one is interested in features of the distribution of values (willingness to pay) placed by consumers on a public good such as endangered species. Sample consumers are asked whether they favor a referendum that would provide the good at a cost specified by experimental design. This paper provides estimators for moments and quantiles of the unknown distribution in this problem under both nonparametric and semiparametric specifications.

A closed-form estimator for the garch(1,1) model

Abstract: We propose a closed-form estimator for the linear GARCH(1,1) model. The estimator has the advantage over the often used quasi-maximum likelihood estimator (QMLE) that it can be easily implemented and does not require the use of any numerical optimization procedures or the choice of initial values of the conditional variance process. We derive the asymptotic properties of the estimator, showing T(κ−1)/κ-consistency for some κ ∈ (1,2) when the fourth moment exists and -asymptotic normality when the eighth moment exists. We demonstrate that a finite number of Newton–Raphson iterations using our estimator as starting point will yield asymptotically the same distribution as the QMLE when the fourth moment exists. A simulation study confirms our theoretical results.The first author's research was supported by the Shoemaker Foundation. The second author's research was supported by the Economic and Social Science Research Council of the United Kingdom.

Estimating Quadratic Variation Consistently in the Presence of Correlated Measurement Error

Abstract: We propose an econometric model that captures the e¤ects of market microstructure on a latent price process. In particular, we allow for correlation between the measurement error and the return process and we allow the measurement error process to have a diurnal heteroskedasticity. We propose a modification of the TSRV estimator of quadratic variation. We show that this estimator is consistent, with a rate of convergence that depends on the size of the measurement error, but is no worse than n1=6. We investigate in simulation experiments the finite sample performance of various proposed implementations.

Flexible term structure estimation: which method is preferred?

Abstract: We show that the recently developed non-parametric procedure for fitting the term structure of interest rates developed by Linton, Mammen, Nielsen, and Tanggaard (J Econ 105(1):185–223, 2001) overall performs notably better than the highly flexible McCulloch (J Finon 30:811–830, 1975) cubic spline and Fama and Bliss (Am Econ Rev 77:680–692, 1987) bootstrap methods. However, if interest is limited to the Treasury-bill region alone then the Fama–Bliss method demonstrates superior performance. We further show, via simulation, that using the estimated short rate from the Linton–Mammen–Nielsen–Tanggaard procedure as a proxy for the short rate has higher precision then the commonly used proxies of the one and three month Treasury-bill rates. It is demonstrated that this precision is important when using proxies to estimate the stochastic process governing the evolution of the short rate

Identification and Nonparametric Estimation of a Transformed Additively Separable Model

Abstract: Let r (x, z) be a function that, along with its derivatives, can be consistently estimated nonparametrically. This paper discusses identification and consistent estimation of the unknown functions H, M, G and F, where r (x, z) = H [M (x, z)] and M (x, z) = G(x) + F (z). An estimation algorithm is proposed for each of the model's unknown components when r (x, z) represents a conditional mean function. The resulting estimators use marginal integration, and are shown to have a limiting Normal distribution with a faster rate of convergence than unrestricted nonparametric alternatives. Their small sample performance is studied in a Monte Carlo experiment. We empirically apply our results to nonparametrically estimate and test generalized homothetic production functions in four industries within the Chinese economy.

Testing for stochasticmonotonicity

Abstract: We propose a test of the hypothesis of stochastic monotonicity. This hypothesis isof interest in many applications. Our test is based on the supremum of a rescaledU-statistic. We show that its asymptotic distribution is Gumbel. The proof is difficultbecause the approximating Gaussian stochastic process contains both a stationaryand a nonstationary part and so we have to extend existing results that only applyto either one or the other case.

Are there Monday effects in stock returns: a stochastic dominance approach

Abstract: We provide a test of the Monday effect in daily stock index returns. Unlike previous studies we define the Monday effect based on the stochastic dominance criterion. This is a stronger criterion than those based on comparing means used in previous work and has a well defined economic meaning. We apply our test to a number of stock indexes including large caps and small caps as well as UK and Japanese indexes. We find strong evidence of a Monday effect in many cases under this stronger criterion. The effect has reversed or weakened in the Dow Jones and SP stock market anomalies; subsamplingJEL Classification: C12, C14, C15, G13, G14

Identification and Nonparametric Estimation of a Transformed Additively Separable Model

Abstract: Let r(x,z) be a function that, along with its derivatives, can be consistently estimated nonparametrically. This paper discusses identification and consistent estimation of the unknown functions H, M, G and F, where r(x, z) = H[M (x, z)] and M(x,z) = G(x) + F(z). An estimation algorithm is proposed for each of the model's unknown components when r(x, z) represents a conditional mean function. The resulting estimators use marginal integration, and are shown to have a limiting Normal distribution with a faster rate of convergence than unrestricted nonparametric alternatives. Their small sample performance is studied in a Monte Carlo experiment. We empirically apply our results to nonparametrically estimate and test generalized homothetic production functions in four industries within the Chinese economy.

Estimating quadratic variation consistently in the presence of correlated measurement error

Abstract: We propose an econometric model that captures the e¤ects of market microstructure on a latent price process. In particular, we allow for correlation between the measurement error and the return process and we allow the measurement error process to have a diurnal heteroskedasticity. We propose a modification of the TSRV estimator of quadratic variation. We show that this estimator is consistent, with a rate of convergence that depends on the size of the measurement error, but is no worse than n1=6. We investigate in simulation experiments the finite sample performance of various proposed implementations.

The Froot-Stein model revisited

Abstract: We investigate the model of Froot & Stein (1998), a model which has very strong implications for risk management. We argue that their conclusions are too strong and need to be qualified. We also argue that their analysis is incorrect and incomplete. Specifically, there are some unusual consequences of their model, which may be linked to the chosen pricing formula.

Nonparametric Transformation to White Noise

Abstract: We consider a semiparametric distributed lag model in which the “news impact curve” m is nonparametric but the response is dynamic through some linear filters. A special case of this is a nonparametric regression with serially correlated errors. We propose an estimator of the news impact curve based on a dynamic transformation that produces white noise errors. This yields an estimating equation for m that is a type two linear integral equation. We investigate both the stationary case and the case where the error has a unit root. In the stationary case we establish the pointwise asymptotic normality. In the special case of a nonparametric regression subject to time series errors our estimator achieves efficiency improvements over the usual estimators, see Xiao, Linton, Carroll, and Mammen (2003). In the unit root case our procedure is consistent and asymptotically normal unlike the standard regression smoother. We also present the distribution theory for the parameter estimates, which is non-standard in the unit root case. We also investigate its finite sample performance through simulation experiments.

Testing for Stochastic Monotonicity

Abstract: We propose a test of the hypothesis of stochastic monotonicity. This hypothesis is of interest in many applications. Our test is based on the supremum of a rescaled U-statistic. We show that its asymptotic distribution is Gumbel. The proof is difficult because the approximating Gaussian stochastic process contains both a stationary and a nonstationary part and so we have to extend existing results that only apply to either one or the other case.

Semiparametric Estimation of aCharacteristic-based Factor Model ofCommon Stock Returns

Abstract: We introduce an alternative version of the Fama-French three-factor model of stockreturns together with a new estimation methodology. We assume that the factorbetas in the model are smooth nonlinear functions of observed securitycharacteristics. We develop an estimation procedure that combines nonparametrickernel methods for constructing mimicking portfolios with parametric nonlinearregression to estimate factor returns and factor betas simultaneously. Themethodology is applied to US common stocks and the empirical findings comparedto those of Fama and French.

Estimating Quadratic VariationConsistently in thePresence of Correlated MeasurementError

Abstract: We propose an econometric model that captures the e¤ects of marketmicrostructure on a latent price process. In particular, we allow for correlationbetween the measurement error and the return process and we allow themeasurement error process to have a diurnal heteroskedasticity. Wepropose a modification of the TSRV estimator of quadratic variation. Weshow that this estimator is consistent, with a rate of convergence thatdepends on the size of the measurement error, but is no worse than n1=6.We investigate in simulation experiments the finite sample performance ofvarious proposed implementations.

Nonparametric Transformation to White Noise

Abstract: We consider a semiparametric distributed lag model in which the "news impact curve" m is nonparametric but the response is dynamic through some linear filters. A special case of this is a nonparametric regression with serially correlated errors. We propose an estimator of the news impact curve based on a dynamic transformation that produces white noise errors. This yields an estimating equation for m that is a type two linear integral equation. We investigate both the stationary case and the case where the error has a unit root. In the stationary case we establish the pointwise asymptotic normality. In the special case of a nonparametric regression subject to time series errors our estimator achieves efficiency improvements over the usual estimators, see Xiao, Linton, Carroll, and Mammen (2003). In the unit root case our procedure is consistent and asymptotically normal unlike the standard regression smoother. We also present the distribution theory for the parameter estimates, which is non-standard in the unit root case. We also investigate its finite sample performance through simulation experiments.