Victoria Zinde-Walsh | McGill University (original) (raw)
Papers by Victoria Zinde-Walsh
Journal of Multivariate Analysis, 2009
Many processes can be represented in a simple form as infinite-order linear series. In such cases... more Many processes can be represented in a simple form as infinite-order linear series. In such cases, an approximate model is often derived as a truncation of the infinite-order process, for estimation on the finite sample. The literature contains a number of asymptotic distributional results for least squares estimation of such finite truncations, but for quantile estimation, results are not available at a level of generality that accommodates time series models used as finite approximations to processes of potentially unbounded order. Here we establish consistency and asymptotic normality for conditional quantile estimation of truncations of such infinite-order linear models, with the truncation order increasing in sample size. We focus on estimation of the model at a given quantile. The proofs use the generalized functions approach and allow for a wide range of time series models as well as other forms of regression model. The results are illustrated with both analytical and simulation examples.
Journal of Multivariate Analysis, 2009
Many processes can be represented in a simple form as infinite-order linear series. In such cases... more Many processes can be represented in a simple form as infinite-order linear series. In such cases, an approximate model is often derived as a truncation of the infinite-order process, for estimation on the finite sample. The literature contains a number of asymptotic distributional results for least squares estimation of such finite truncations, but for quantile estimation, results are not available at a level of generality that accommodates time series models used as finite approximations to processes of potentially unbounded order. Here we establish consistency and asymptotic normality for conditional quantile estimation of truncations of such infinite-order linear models, with the truncation order increasing in sample size. We focus on estimation of the model at a given quantile. The proofs use the generalized functions approach and allow for a wide range of time series models as well as other forms of regression model. The results are illustrated with both analytical and simulation examples.
Journal of Multivariate Analysis, 2009
Many processes can be represented in a simple form as infinite-order linear series. In such cases... more Many processes can be represented in a simple form as infinite-order linear series. In such cases, an approximate model is often derived as a truncation of the infinite-order process, for estimation on the finite sample. The literature contains a number of asymptotic distributional results for least squares estimation of such finite truncations, but for quantile estimation, results are not available at a level of generality that accommodates time series models used as finite approximations to processes of potentially unbounded order. Here we establish consistency and asymptotic normality for conditional quantile estimation of truncations of such infinite-order linear models, with the truncation order increasing in sample size. We focus on estimation of the model at a given quantile. The proofs use the generalized functions approach and allow for a wide range of time series models as well as other forms of regression model. The results are illustrated with both analytical and simulation examples.
Journal of Multivariate Analysis, 2009
Many processes can be represented in a simple form as infinite-order linear series. In such cases... more Many processes can be represented in a simple form as infinite-order linear series. In such cases, an approximate model is often derived as a truncation of the infinite-order process, for estimation on the finite sample. The literature contains a number of asymptotic distributional results for least squares estimation of such finite truncations, but for quantile estimation, results are not available at a level of generality that accommodates time series models used as finite approximations to processes of potentially unbounded order. Here we establish consistency and asymptotic normality for conditional quantile estimation of truncations of such infinite-order linear models, with the truncation order increasing in sample size. We focus on estimation of the model at a given quantile. The proofs use the generalized functions approach and allow for a wide range of time series models as well as other forms of regression model. The results are illustrated with both analytical and simulation examples.
Nous utilisons des techniques d'estimation de modèle reliées à ceux de Galbraith et Zinde-Walsh (... more Nous utilisons des techniques d'estimation de modèle reliées à ceux de Galbraith et Zinde-Walsh (2000) pour les modèles ARCH et GARCH, basées sur la realized volatility (Andersen et Bollerslev 1998, et autres), afin d'obtenir les quantiles conditionnels de volatilité quotidienne dans les données provenant des marchés boursiers et des marchés de devises étrangères. Ces méthodes nous permettent en principe de caractériser la distribution entière de volatilité en utilisant la volatilité réalisée et les retours carrés. Nous prenons des échantillons de rendements quotidiens et intrajournaliers de l'indice 35 du TSE, et des taux de change DM/$ US et Yen/$ US. Nos résultats montrent également que les percentiles inférieurs de la distribution conditionnelle augmentent proportionnellement moins en périodes de volatilité extrême que les percentiles supérieurs.
Ce document est publié dans l'intention de rendre accessibles les résultats préliminaires de la r... more Ce document est publié dans l'intention de rendre accessibles les résultats préliminaires de la recherche effectuée au CIRANO, afin de susciter des échanges et des suggestions. Les idées et les opinions émises sont sous l'unique responsabilité des auteurs, et ne représentent pas nécessairement les positions du CIRANO ou de ses partenaires. This paper presents preliminary research carried out at CIRANO and aims at encouraging discussion and comment. The observations and viewpoints expressed are the sole responsibility of the authors. They do not necessarily represent positions of CIRANO or its partners.
In models with a large number of 'nuisance' effects which must be controlled for, dimensi... more In models with a large number of 'nuisance' effects which must be controlled for, dimension reduction on these effects can be an effective strategy for obtaining estimates of a smaller number of parameters of interest. Galbraith and Zinde-Walsh (2005) show, in a general linear regression context with exogenous regressors and a set of explanatory series of unknown and possibly unbounded dimension, that one can obtain consistent and asymptotically normal estimation of a parameter of interest. The dimension reduction uses orthogonal components derived from the eigenvectors of the moment matrix of the controls, and may be selected by largest eigenvalue (principal components) or by mod- ified methods adapted to the problem. In the present study we show that this method can be employed in more general contexts involving endogenous regressors, requiring in- strumental variable methods for consistent estimation, with dimension reduction on both endogenous and exogenous regressors.
The binary-response maximum score estimator is a robust estimator, which can accomodate heterosce... more The binary-response maximum score estimator is a robust estimator, which can accomodate heteroscedasticity of an unknown form. However, the asymptotic properties of the estimator are known only for the case of i.i.d. errors. J. Horowitz (1992) has suggested smoothing of this estimator and derived its asymptotic distribution. In this paper asymptotic prop- erties of the smoothed estimator are examined for a class of smoothing functions by using the generalized functions methodology . The results show that variance reduction is possible when a set of smoothing schemes is applied to the data; a Monte Carlo study evaluates these gains. The method is robust to the choice of bandwidth and is fully automatic. We also propose a reliable formula for an optimal bandwidth, which does not depend on the characteristics of the sample but incorporates certain parameters of smoothing functions.
In models with a large number of 'nuisance' effects which must be controlled for, dimensi... more In models with a large number of 'nuisance' effects which must be controlled for, dimension reduction on these effects can be an effective strategy for obtaining estimates of a smaller number of parameters of interest. Galbraith and Zinde-Walsh (2005) show, in a general linear regression context with exogenous regressors and a set of explanatory series of unknown and possibly unbounded dimension, that one can obtain consistent and asymptotically normal estimation of a parameter of interest. The dimension reduction uses orthogonal components derived from the eigenvectors of the moment matrix of the controls, and may be selected by largest eigenvalue (principal components) or by modified methods adapted to the problem. In the present study we show that this method can be employed in more general time series contexts permitting non-stationary (in particular, integrated fractionally integrated) regressors, without a priori knowledge of orders of integration or pre-testing for or...
We consider estimates of the parameters of GARCH models of daily financial returns, obtained usin... more We consider estimates of the parameters of GARCH models of daily financial returns, obtained using intra-day (high-frequency) returns data to estimate the daily conditional volatility.Two potential bases for estimation are considered. One uses aggregation of high-frequency Quasi- ML estimates, using aggregation results of Drost and Nijman (1993). The other uses the integrated volatility of Andersen and Bollerslev (1998), and obtains coefficients from a model estimated by LAD or OLS, in the former case providing consistency and asymptotic normality in some cases where moments of the volatility estimation error may not exist. In particular, we consider estimation in this way of an ARCH approximation, and obtain GARCH parameters by a method related to that of Galbraith and Zinde-Walsh (1997) for ARMA processes. We offer some simulation evidence on small-sample performance, and characterize the gains relative to standard quasi-ML estimates based on daily data alone. Nous considérons les...
This paper describes a parameter estimation method for both stationary and non-stationary ARFIMA ... more This paper describes a parameter estimation method for both stationary and non-stationary ARFIMA (p,d,q) models, based on autoregressive approximation. We demonstrate consistency of the estimator for -1/2 < d < 1, and in the stationary case we provide a Normal approximation to the finite-sample distribution which can be used for inference. The method provides good finite-sample performance, comparable with that of ML, and stable performance across a range of stationary and non-stationary values of the fractional differencing parameter. In addition, it appears to be relatively robust to mis-specification of the ARFIMA model to be estimated, and is computationally straightforward. Nous décrivons une méthode d'estimation pour les paramètres des modèles ARFIMA stationnaires ou non-stationnaires, basée sur l'approximation auto-régressive. Nous démontrons que la procédure est consistante pour -1/2 < d < 1, et dans le cas stationnaire nous donnons une approximation Norm...
A distance measureinthe appropriate space of stochastic processes can be used to measure the qual... more A distance measureinthe appropriate space of stochastic processes can be used to measure the qualityofapproximation when oneprocess is taken as a model of another, either deliberatelyorbymis-specification. We examine the problem of approximating an ARMA processby a model fromthe AR(p) class, emphasizing a distance measurebased on the Hilbert metric. This measure can be used to calculate distances between particular processes, andtheminimum distance to a classofprocesses such as the AR(p) class. We show that this measure provides a good apriori indication of the impact of substitution of an approximate process for the true process. We alsoprovide comparison with the Kullback-Leibler-Jeffreys information metric, and applicationstochoice of order in selecting an approximating AR model onafinite sample, testing of dynamic specification, forecast performance of approximate models, and evaluation of information criteria for selection of approximating models. Key words: autoregressiveappro...
We examine a simple estimator for the multivariate moving average model based on vector autoregre... more We examine a simple estimator for the multivariate moving average model based on vector autoregressive approximation. In finite samples the estimator has a bias which is low where roots of the determinantal equation are well away from the unit circle, and more substantial where one or more roots have modulus near unity. We also examine the sacrifice involved in specifying a vector model for processes which are in fact univariate, and show that the representation estimated by this multivariate technique is asymptotically invertible. This estimator has significant computational advantages over Maximum Likelihood. Moreover, as reported by Galbraith and Zinde-Walsh (1994) for the special case of the univariate model, this estimator can be more robust to mis-specification than ML. The estimation method is applied to a VMA model of wholesale and retail inventories, using Canadian data on overall aggregate, non-durable and durable inventory investment, and allows us to examine the propagat...
Many processes can be represented in a simple form as infinite-order linear series. In such cases... more Many processes can be represented in a simple form as infinite-order linear series. In such cases, an approximate model is often derived as a truncation of the infinite-order process, for estimation on the finite sample. The literature contains a number of asymptotic distributional results for least squares estimation of such finite truncations, but for quantile estimation, only results for finite-order processes are available at a level of generality that accommodates time series processes. Here we establish consistency and asymptotic normality for conditional quantile estimation of truncations of such infinite-order linear models, with the truncation order increasing in sample size. The proofs use the generalized functions approach and allow for a wide range of time series models as well as other forms of regression model. As an example, many time series processes may be represented as an AR(1) or an MA(1); here we use a simulation to illustrate the degree of conformity of finites...
Many important models, such as index models widely used in limited dependent variables, partial l... more Many important models, such as index models widely used in limited dependent variables, partial linear models and nonparametric demand studies utilize estimation of average derivatives (sometimes weighted) of the conditional mean function. Asymptotic results in the literature focus on situations where the ADE converges at parametric rates (as a result of averaging); this requires making stringent assumptions on smoothness of the underlying density; in practice such assumptions may be violated. We extend the existing theory by relaxing smoothness assumptions and obtain a full range of asymptotic results with both parametric and non-parametric rates. We consider both the possibility of lack of smoothness and lack of precise knowledge of degree of smoothness and propose an estimation strategy that produces the best possible rate without a priori knowledge of degree of density smoothness. The new combined estimator is a linear combination of estimators corresponding to di�erent bandwidt...
Econometric Theory
We provide a proof of the consistency and asymptotic normality of the estimator suggested by Heck... more We provide a proof of the consistency and asymptotic normality of the estimator suggested by Heckman (1990) for the intercept of a semiparametrically estimated sample selection model. The estimator is based on 'identification at infinity' which leads to non-standard convergence rate. Andrews and Schafgans (1998) derived asymptotic results for a smoothed version of the estimator. We examine the optimal bandwidth selection for the estimators and derive asymptotic MSE rates under a wide class of distributional assumptions. We also provide some comparisons of the estimators and practical guidelines.
Institute of Mathematical Statistics Lecture Notes - Monograph Series, 2003
Brownian motion can be characterized as a generalized random process and, as such, has a generali... more Brownian motion can be characterized as a generalized random process and, as such, has a generalized derivative whose covariance functional is the delta function. In a similar fashion, fractional Brownian motion can be interpreted as a generalized random process and shown to possess a generalized derivative. The resulting process is a generalized Gaussian process with mean functional zero and covariance functional that can be interpreted as a fractional integral or fractional derivative of the delta-function.
Econometric Reviews, 2014
ABSTRACT We consider estimates of the parameters of Generalized Autoregressive Conditional Hetero... more ABSTRACT We consider estimates of the parameters of Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models obtained using auxiliary information on latent variance which may be available from higher-frequency data, for example from an estimate of the daily quadratic variation such as the realized variance. We obtain consistent estimators of the parameters of the infinite Autoregressive Conditional Heteroskedasticity (ARCH) representation via a regression using the estimated quadratic variation, without requiring that it be a consistent estimate; that is, variance information containing measurement error can be used for consistent estimation. We obtain GARCH parameters using a minimum distance estimator based on the estimated ARCH parameters. With Least Absolute Deviations (LAD) estimation of the truncated ARCH approximation, we show that consistency and asymptotic normality can be obtained using a general result on LAD estimation in truncated models of infinite-order processes. We provide simulation evidence on small-sample performance for varying numbers of intra-day observations.
L'Actualité économique, 2004
Résumé Il existe plusieurs critères d’information dont le but est de faciliter la sélection du mo... more Résumé Il existe plusieurs critères d’information dont le but est de faciliter la sélection du modèle statistique représentant le mieux possible la réalité. Ces critères s’appliquent notamment au cas des modèles de séries chronologiques à une seule variable. La théorie asymptotique peut être utilisée pour faire un choix entre ces critères. Par exemple, si le modèle possède un ordre authentique, il peut être démontré que certains critères sont fortement convergents pour cet ordre. Historiquement, l’estimation en échantillon fini se base sur la sélection d’un ordre unique, même si plusieurs auteurs reconnaissent l’importance du cas où il n’existe pas de vrai ordre fini. Nous proposons ici un survol de la littérature sur les critères d’information et sur leur comparaison asymptotique et en échantillons finis. Nous présentons également quelques comparaisons de critères en échantillons finis en ne prenant pas pour acquis un ordre authentique au modèle. Nous utilisons alors une mesure de ...
Journal of Multivariate Analysis, 2009
Many processes can be represented in a simple form as infinite-order linear series. In such cases... more Many processes can be represented in a simple form as infinite-order linear series. In such cases, an approximate model is often derived as a truncation of the infinite-order process, for estimation on the finite sample. The literature contains a number of asymptotic distributional results for least squares estimation of such finite truncations, but for quantile estimation, results are not available at a level of generality that accommodates time series models used as finite approximations to processes of potentially unbounded order. Here we establish consistency and asymptotic normality for conditional quantile estimation of truncations of such infinite-order linear models, with the truncation order increasing in sample size. We focus on estimation of the model at a given quantile. The proofs use the generalized functions approach and allow for a wide range of time series models as well as other forms of regression model. The results are illustrated with both analytical and simulation examples.
Journal of Multivariate Analysis, 2009
Many processes can be represented in a simple form as infinite-order linear series. In such cases... more Many processes can be represented in a simple form as infinite-order linear series. In such cases, an approximate model is often derived as a truncation of the infinite-order process, for estimation on the finite sample. The literature contains a number of asymptotic distributional results for least squares estimation of such finite truncations, but for quantile estimation, results are not available at a level of generality that accommodates time series models used as finite approximations to processes of potentially unbounded order. Here we establish consistency and asymptotic normality for conditional quantile estimation of truncations of such infinite-order linear models, with the truncation order increasing in sample size. We focus on estimation of the model at a given quantile. The proofs use the generalized functions approach and allow for a wide range of time series models as well as other forms of regression model. The results are illustrated with both analytical and simulation examples.
Journal of Multivariate Analysis, 2009
Many processes can be represented in a simple form as infinite-order linear series. In such cases... more Many processes can be represented in a simple form as infinite-order linear series. In such cases, an approximate model is often derived as a truncation of the infinite-order process, for estimation on the finite sample. The literature contains a number of asymptotic distributional results for least squares estimation of such finite truncations, but for quantile estimation, results are not available at a level of generality that accommodates time series models used as finite approximations to processes of potentially unbounded order. Here we establish consistency and asymptotic normality for conditional quantile estimation of truncations of such infinite-order linear models, with the truncation order increasing in sample size. We focus on estimation of the model at a given quantile. The proofs use the generalized functions approach and allow for a wide range of time series models as well as other forms of regression model. The results are illustrated with both analytical and simulation examples.
Journal of Multivariate Analysis, 2009
Many processes can be represented in a simple form as infinite-order linear series. In such cases... more Many processes can be represented in a simple form as infinite-order linear series. In such cases, an approximate model is often derived as a truncation of the infinite-order process, for estimation on the finite sample. The literature contains a number of asymptotic distributional results for least squares estimation of such finite truncations, but for quantile estimation, results are not available at a level of generality that accommodates time series models used as finite approximations to processes of potentially unbounded order. Here we establish consistency and asymptotic normality for conditional quantile estimation of truncations of such infinite-order linear models, with the truncation order increasing in sample size. We focus on estimation of the model at a given quantile. The proofs use the generalized functions approach and allow for a wide range of time series models as well as other forms of regression model. The results are illustrated with both analytical and simulation examples.
Nous utilisons des techniques d'estimation de modèle reliées à ceux de Galbraith et Zinde-Walsh (... more Nous utilisons des techniques d'estimation de modèle reliées à ceux de Galbraith et Zinde-Walsh (2000) pour les modèles ARCH et GARCH, basées sur la realized volatility (Andersen et Bollerslev 1998, et autres), afin d'obtenir les quantiles conditionnels de volatilité quotidienne dans les données provenant des marchés boursiers et des marchés de devises étrangères. Ces méthodes nous permettent en principe de caractériser la distribution entière de volatilité en utilisant la volatilité réalisée et les retours carrés. Nous prenons des échantillons de rendements quotidiens et intrajournaliers de l'indice 35 du TSE, et des taux de change DM/$ US et Yen/$ US. Nos résultats montrent également que les percentiles inférieurs de la distribution conditionnelle augmentent proportionnellement moins en périodes de volatilité extrême que les percentiles supérieurs.
Ce document est publié dans l'intention de rendre accessibles les résultats préliminaires de la r... more Ce document est publié dans l'intention de rendre accessibles les résultats préliminaires de la recherche effectuée au CIRANO, afin de susciter des échanges et des suggestions. Les idées et les opinions émises sont sous l'unique responsabilité des auteurs, et ne représentent pas nécessairement les positions du CIRANO ou de ses partenaires. This paper presents preliminary research carried out at CIRANO and aims at encouraging discussion and comment. The observations and viewpoints expressed are the sole responsibility of the authors. They do not necessarily represent positions of CIRANO or its partners.
In models with a large number of 'nuisance' effects which must be controlled for, dimensi... more In models with a large number of 'nuisance' effects which must be controlled for, dimension reduction on these effects can be an effective strategy for obtaining estimates of a smaller number of parameters of interest. Galbraith and Zinde-Walsh (2005) show, in a general linear regression context with exogenous regressors and a set of explanatory series of unknown and possibly unbounded dimension, that one can obtain consistent and asymptotically normal estimation of a parameter of interest. The dimension reduction uses orthogonal components derived from the eigenvectors of the moment matrix of the controls, and may be selected by largest eigenvalue (principal components) or by mod- ified methods adapted to the problem. In the present study we show that this method can be employed in more general contexts involving endogenous regressors, requiring in- strumental variable methods for consistent estimation, with dimension reduction on both endogenous and exogenous regressors.
The binary-response maximum score estimator is a robust estimator, which can accomodate heterosce... more The binary-response maximum score estimator is a robust estimator, which can accomodate heteroscedasticity of an unknown form. However, the asymptotic properties of the estimator are known only for the case of i.i.d. errors. J. Horowitz (1992) has suggested smoothing of this estimator and derived its asymptotic distribution. In this paper asymptotic prop- erties of the smoothed estimator are examined for a class of smoothing functions by using the generalized functions methodology . The results show that variance reduction is possible when a set of smoothing schemes is applied to the data; a Monte Carlo study evaluates these gains. The method is robust to the choice of bandwidth and is fully automatic. We also propose a reliable formula for an optimal bandwidth, which does not depend on the characteristics of the sample but incorporates certain parameters of smoothing functions.
In models with a large number of 'nuisance' effects which must be controlled for, dimensi... more In models with a large number of 'nuisance' effects which must be controlled for, dimension reduction on these effects can be an effective strategy for obtaining estimates of a smaller number of parameters of interest. Galbraith and Zinde-Walsh (2005) show, in a general linear regression context with exogenous regressors and a set of explanatory series of unknown and possibly unbounded dimension, that one can obtain consistent and asymptotically normal estimation of a parameter of interest. The dimension reduction uses orthogonal components derived from the eigenvectors of the moment matrix of the controls, and may be selected by largest eigenvalue (principal components) or by modified methods adapted to the problem. In the present study we show that this method can be employed in more general time series contexts permitting non-stationary (in particular, integrated fractionally integrated) regressors, without a priori knowledge of orders of integration or pre-testing for or...
We consider estimates of the parameters of GARCH models of daily financial returns, obtained usin... more We consider estimates of the parameters of GARCH models of daily financial returns, obtained using intra-day (high-frequency) returns data to estimate the daily conditional volatility.Two potential bases for estimation are considered. One uses aggregation of high-frequency Quasi- ML estimates, using aggregation results of Drost and Nijman (1993). The other uses the integrated volatility of Andersen and Bollerslev (1998), and obtains coefficients from a model estimated by LAD or OLS, in the former case providing consistency and asymptotic normality in some cases where moments of the volatility estimation error may not exist. In particular, we consider estimation in this way of an ARCH approximation, and obtain GARCH parameters by a method related to that of Galbraith and Zinde-Walsh (1997) for ARMA processes. We offer some simulation evidence on small-sample performance, and characterize the gains relative to standard quasi-ML estimates based on daily data alone. Nous considérons les...
This paper describes a parameter estimation method for both stationary and non-stationary ARFIMA ... more This paper describes a parameter estimation method for both stationary and non-stationary ARFIMA (p,d,q) models, based on autoregressive approximation. We demonstrate consistency of the estimator for -1/2 < d < 1, and in the stationary case we provide a Normal approximation to the finite-sample distribution which can be used for inference. The method provides good finite-sample performance, comparable with that of ML, and stable performance across a range of stationary and non-stationary values of the fractional differencing parameter. In addition, it appears to be relatively robust to mis-specification of the ARFIMA model to be estimated, and is computationally straightforward. Nous décrivons une méthode d'estimation pour les paramètres des modèles ARFIMA stationnaires ou non-stationnaires, basée sur l'approximation auto-régressive. Nous démontrons que la procédure est consistante pour -1/2 < d < 1, et dans le cas stationnaire nous donnons une approximation Norm...
A distance measureinthe appropriate space of stochastic processes can be used to measure the qual... more A distance measureinthe appropriate space of stochastic processes can be used to measure the qualityofapproximation when oneprocess is taken as a model of another, either deliberatelyorbymis-specification. We examine the problem of approximating an ARMA processby a model fromthe AR(p) class, emphasizing a distance measurebased on the Hilbert metric. This measure can be used to calculate distances between particular processes, andtheminimum distance to a classofprocesses such as the AR(p) class. We show that this measure provides a good apriori indication of the impact of substitution of an approximate process for the true process. We alsoprovide comparison with the Kullback-Leibler-Jeffreys information metric, and applicationstochoice of order in selecting an approximating AR model onafinite sample, testing of dynamic specification, forecast performance of approximate models, and evaluation of information criteria for selection of approximating models. Key words: autoregressiveappro...
We examine a simple estimator for the multivariate moving average model based on vector autoregre... more We examine a simple estimator for the multivariate moving average model based on vector autoregressive approximation. In finite samples the estimator has a bias which is low where roots of the determinantal equation are well away from the unit circle, and more substantial where one or more roots have modulus near unity. We also examine the sacrifice involved in specifying a vector model for processes which are in fact univariate, and show that the representation estimated by this multivariate technique is asymptotically invertible. This estimator has significant computational advantages over Maximum Likelihood. Moreover, as reported by Galbraith and Zinde-Walsh (1994) for the special case of the univariate model, this estimator can be more robust to mis-specification than ML. The estimation method is applied to a VMA model of wholesale and retail inventories, using Canadian data on overall aggregate, non-durable and durable inventory investment, and allows us to examine the propagat...
Many processes can be represented in a simple form as infinite-order linear series. In such cases... more Many processes can be represented in a simple form as infinite-order linear series. In such cases, an approximate model is often derived as a truncation of the infinite-order process, for estimation on the finite sample. The literature contains a number of asymptotic distributional results for least squares estimation of such finite truncations, but for quantile estimation, only results for finite-order processes are available at a level of generality that accommodates time series processes. Here we establish consistency and asymptotic normality for conditional quantile estimation of truncations of such infinite-order linear models, with the truncation order increasing in sample size. The proofs use the generalized functions approach and allow for a wide range of time series models as well as other forms of regression model. As an example, many time series processes may be represented as an AR(1) or an MA(1); here we use a simulation to illustrate the degree of conformity of finites...
Many important models, such as index models widely used in limited dependent variables, partial l... more Many important models, such as index models widely used in limited dependent variables, partial linear models and nonparametric demand studies utilize estimation of average derivatives (sometimes weighted) of the conditional mean function. Asymptotic results in the literature focus on situations where the ADE converges at parametric rates (as a result of averaging); this requires making stringent assumptions on smoothness of the underlying density; in practice such assumptions may be violated. We extend the existing theory by relaxing smoothness assumptions and obtain a full range of asymptotic results with both parametric and non-parametric rates. We consider both the possibility of lack of smoothness and lack of precise knowledge of degree of smoothness and propose an estimation strategy that produces the best possible rate without a priori knowledge of degree of density smoothness. The new combined estimator is a linear combination of estimators corresponding to di�erent bandwidt...
Econometric Theory
We provide a proof of the consistency and asymptotic normality of the estimator suggested by Heck... more We provide a proof of the consistency and asymptotic normality of the estimator suggested by Heckman (1990) for the intercept of a semiparametrically estimated sample selection model. The estimator is based on 'identification at infinity' which leads to non-standard convergence rate. Andrews and Schafgans (1998) derived asymptotic results for a smoothed version of the estimator. We examine the optimal bandwidth selection for the estimators and derive asymptotic MSE rates under a wide class of distributional assumptions. We also provide some comparisons of the estimators and practical guidelines.
Institute of Mathematical Statistics Lecture Notes - Monograph Series, 2003
Brownian motion can be characterized as a generalized random process and, as such, has a generali... more Brownian motion can be characterized as a generalized random process and, as such, has a generalized derivative whose covariance functional is the delta function. In a similar fashion, fractional Brownian motion can be interpreted as a generalized random process and shown to possess a generalized derivative. The resulting process is a generalized Gaussian process with mean functional zero and covariance functional that can be interpreted as a fractional integral or fractional derivative of the delta-function.
Econometric Reviews, 2014
ABSTRACT We consider estimates of the parameters of Generalized Autoregressive Conditional Hetero... more ABSTRACT We consider estimates of the parameters of Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models obtained using auxiliary information on latent variance which may be available from higher-frequency data, for example from an estimate of the daily quadratic variation such as the realized variance. We obtain consistent estimators of the parameters of the infinite Autoregressive Conditional Heteroskedasticity (ARCH) representation via a regression using the estimated quadratic variation, without requiring that it be a consistent estimate; that is, variance information containing measurement error can be used for consistent estimation. We obtain GARCH parameters using a minimum distance estimator based on the estimated ARCH parameters. With Least Absolute Deviations (LAD) estimation of the truncated ARCH approximation, we show that consistency and asymptotic normality can be obtained using a general result on LAD estimation in truncated models of infinite-order processes. We provide simulation evidence on small-sample performance for varying numbers of intra-day observations.
L'Actualité économique, 2004
Résumé Il existe plusieurs critères d’information dont le but est de faciliter la sélection du mo... more Résumé Il existe plusieurs critères d’information dont le but est de faciliter la sélection du modèle statistique représentant le mieux possible la réalité. Ces critères s’appliquent notamment au cas des modèles de séries chronologiques à une seule variable. La théorie asymptotique peut être utilisée pour faire un choix entre ces critères. Par exemple, si le modèle possède un ordre authentique, il peut être démontré que certains critères sont fortement convergents pour cet ordre. Historiquement, l’estimation en échantillon fini se base sur la sélection d’un ordre unique, même si plusieurs auteurs reconnaissent l’importance du cas où il n’existe pas de vrai ordre fini. Nous proposons ici un survol de la littérature sur les critères d’information et sur leur comparaison asymptotique et en échantillons finis. Nous présentons également quelques comparaisons de critères en échantillons finis en ne prenant pas pour acquis un ordre authentique au modèle. Nous utilisons alors une mesure de ...