économétrie_24/06/2008

Source : NEP (New Economics Papers) | RePEc

Parameter Estimation in Nonlinear AR-GARCH Models
Date: 2008; By: Mika Meitz; Pentti Saikkonen
This paper develops an asymptotic estimation theory for nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a functional coefficient autoregression of order p (AR(p)) with the conditional variance specified as a general nonlinear first order generalized autoregressive conditional heteroskedasticity (GARCH(1,1)) model. Strong consistency and asymptotic normality of the global Gaussian quasi maximum likelihood (QML) estimator are established under conditions comparable to those recently used in the corresponding linear case. To the best of our knowledge, this paper provides the first results on consistency and asymptotic normality of the QML estimator in nonlinear autoregressive models with GARCH errors.
Keywords: AR-GARCH, asymptotic normality, consistency, nonlinear time series, quasi maximum likelihood estimation
JEL: C13 C22

Empirical Likelihood Block Bootstrapping
Date: 2008; By: Jason Allen; Allan W. Gregory; Katsumi Shimotsu
Monte Carlo evidence has made it clear that asymptotic tests based on generalized method of moments (GMM) estimation have disappointing size. The problem is exacerbated when the moment conditions are serially correlated. Several block bootstrap techniques have been proposed to correct the problem, including Hall and Horowitz (1996) and Inoue and Shintani (2006). We propose an empirical likelihood block bootstrap procedure to improve inference where models are characterized by nonlinear moment conditions that are serially correlated of possibly infinite order. Combining the ideas of Kitamura (1997) and Brown and Newey (2002), the parameters of a model are initially estimated by GMM which are then used to compute the empirical likelihood probability weights of the blocks of moment conditions. The probability weights serve as the multinomial distribution used in resampling. The first-order asymptotic validity of the p roposed procedure is proven, and a series of Monte Carlo experiments show it may improve test sizes over conventional block bootstrapping.
Keywords: Econometric and statistical methods
JEL: C14 C22

Unit Root Testing with Unstable Volatility
Date: 2008-05-05; By: Brendan K. Beare (Nuffield College, Oxford University)
It is known that unit root test statistics may not have the usual asymptotic properties when the variance of innovations is unstable. In particular, persistent changes in volatility can cause the size of unit root tests to differ from the nominal level. In this paper we propose a class of modified unit root test statistics that are robust to the presence of unstable volatility. The modification is achieved by purging heteroskedasticity from the data using a kernel estimate of volatility prior to the application of standard tests. In the absence of deterministic trend components, this approach delivers test statistics that achieve standard asymptotics under the null hypothesis of a unit root. When the data are homoskedastic, the local power of unit root tests is unchanged by our modification. We use Monte Carlo simulations to compare the finite sample performance of our modified tests with that of existing methods o f correcting for unstable volatility.
Keywords: unit root, heteroskedasticity, nonstationary volatility.
JEL: C14 C22

Asymptotic and bootstrap properties of rank regressions
Date: 2008-03-20; By: Subbotin, Viktor
The paper develops the bootstrap theory and extends the asymptotic theory of rank estimators, such as the Maximum Rank Correlation Estimator (MRC) of Han (1987), Monotone Rank Estimator (MR) of Cavanagh and Sherman (1998) or Pairwise-Difference Rank Estimators (PDR) of Abrevaya (2003). It is known that under general conditions these estimators have asymptotic normal distributions, but the asymptotic variances are difficult to find. Here we prove that the quantiles and the variances of the asymptotic distributions can be consistently estimated by the nonparametric bootstrap. We investigate the accuracy of inference based on the asymptotic approximation and the bootstrap, and provide bounds on the associated error. In the case of MRC and MR, the bound is a function of the sample size of order close to n^{-1/6}. The PDR estimators belong to a special subclass of rank estimators for which the bound is vanishing with th e rate close to n^{-1/2}. The theoretical findings are illustrated with Monte-Carlo experiments and a real data example.
Keywords: Rank Estimators; Bootstrap; M-Estimators; U-Statistics; U-Processes
JEL: C14 C12 C15

Bayesian Covariance Matrix Estimation using a Mixture of Decomposable Graphical Models
Date: 2007-04; By: Helen Armstrong (School of Mathematics, University of New South Wales); Christopher K. Carter (School of Economics, University of New South Wales); Kevin K. F. Wong (Graduate University for Advanced Studies, Tokyo, Japan); Robert Kohn (School of Economics, University of New South Wales)
Estimating a covariance matrix efficiently and discovering its structure are important statistical problems with applications in many fields. This article takes a Bayesian approach to estimate the covariance matrix of Gaussian data. We use ideas from Gaussian graphical models and model selection to construct a prior for the covariance matrix that is a mixture over all decomposable graphs, where a graph means the configuration of nonzero offdiagonal elements in the inverse of the covariance matrix. Our prior for the covariance matrix is such that the probability of each graph size is specified by the user and graphs of equal size are assigned equal probability. Most previous approaches assume that all graphs are equally probable. We give empirical results that show the prior that assigns equal probability over graph sizes outperforms the prior that assigns equal probability over all graphs, both in identifying the c orrect decomposable graph and in more efficiently estimating the covariance matrix. The advantage is greatest when the number of observations is small relative to the dimension of the covariance matrix. The article also shows empirically that there is minimal change in statistical efficiency in using the mixture over decomposable graphs prior for estimating a general covariance compared to the Bayesian estimator by Wong et al. (2003), even when the graph of the covariance matrix is nondecomposable. However, our approach has some important advantages over that of Wong et al. (2003). Our method requires the number of decomposable graphs for each graph size. We show how to estimate these numbers using simulation and that the simulation results agree with analytic results when such results are known. We also show how to estimate the posterior distribution of the covariance matrix using Markov chain Monte Carlo with the elements of the covariance matrix integrated out and give em pirical results that show the sampler is computationally efficient an d converges rapidly. Finally, we note that both the prior and the simulation method to evaluate the prior apply generally to any decomposable graphical model.
Keywords: Covariance selection; Graphical models; Reduced conditional sampling; Variable selection

Testing for the Cointegrating Rank of a Vector Autoregressive Process with Uncertain Deterministic Trend Term
Date: 2008; By: Matei Demetrescu; Helmut Luetkepohl; Pentti Saikkonen
When applying Johansen’s procedure for determining the cointegrating rank to systems of variables with linear deterministic trends, there are two possible tests to choose from. One test allows for a trend in the cointegration relations and the other one restricts the trend to be orthogonal to the cointegration relations. The first test is known to have reduced power relative to the second one if there is in fact no trend in the cointegration relations, whereas the second one is based on a misspecified model if the linear trend is not orthogonal to the cointegration relations. Hence, the treatment of the linear trend term is crucial for the outcome of the rank determination procedure. We compare two alternative testing strategies which are applicable if there is uncertainty regarding the proper trend specification. In the first one a specific cointegrating rank is rejected if one of the two tests rejects and in the second one the trend term is decided upon by a pretest. The first strategy is shown to be preferable in applied work.
Keywords: Cointegration analysis, likelihood ratio test, vector autoregressive model, vector error correction model
JEL: C32

A Statistical Comparison of Alternative Identification Schemes for Monetary Policy Shocks
Date: 2008; By: Markku Lanne; Helmut Luetkepohl
Different identification schemes for monetary policy shocks have been proposed in the literature. They typically specify just-identifying restrictions in a standard structural vector autoregressive (SVAR) framework. Thus, in this framework the different schemes cannot be checked against the data with statistical tests. We consider different approaches how to use the data properties to augment the standard SVAR setup for identifying the shocks. Thereby it becomes possible to test models which are just identified in a standard setting. For monthly US data it is found that a model where monetary shocks are induced via the federal funds rate is the only one which cannot be rejected when the data properties are used for identification.
Keywords: Mixed normal distribution, structural vector autoregressive model, vector autoregressive process
JEL: C32

Asymptotics for LS, GLS, and Feasible GLS Statistics in an AR(1) Model with Conditional Heteroskedaticity
Date: 2008-06; By: Donald W.K. Andrews (Cowles Foundation, Yale University); Patrik Guggenberger (Dept. of Economics, UCLA)
This paper considers a first-order autoregressive model with conditionally heteroskedastic innovations. The asymptotic distributions of least squares (LS), infeasible generalized least squares (GLS), and feasible GLS estimators and t statistics are determined. The GLS procedures allow for misspecification of the form of the conditional heteroskedasticity and, hence, are referred to as quasi-GLS procedures. The asymptotic results are established for drifting sequences of the autoregressive parameter and the distribution of the time series of innovations. In particular, we consider the full range of cases in which the autoregressive parameter rho_n satisfies (i) n(1 – rho_n) -> infinity and (ii) n(1 – rho_n) -> h_1 < infinity as n -> infinity, where n is the sample size. Results of this type are needed to establish the uniform asymptotic properties of the LS and quasi-GLS statistics.
Keywords: Asymptotic distribution, Autoregression, Conditional heteroskedasticity, Generalized least squares, Least squares
JEL: C22

Model Averaging in Risk Management with an Application to Futures Markets
Date: 2008-01; By: Pesaran, M.H.; Schleicher, C.; Zaffaroni, P.
This paper considers the problem of model uncertainty in the case of multi-asset volatility models and discusses the use of model averaging techniques as a way of dealing with the risk of inadvertently using false models in portfolio management. Evaluation of volatility models is then considered and a simple Value-at-Risk (VaR) diagnostic test is proposed for individual as well as `average’ models. The asymptotic as well as the exact ¯nite-sample distribution of the test statistic, dealing with the possibility of parameter uncertainty, are established. The model averaging idea and the VaR diagnostic tests are illustrated by an application to portfolios of daily returns on six currencies, four equity indices, four ten year government bonds and four commodities over the period 1991-2007. The empirical evidence supports the use of `thick’ model averaging strategies over single models or Bayesian type model averaging procedures.
Keywords: Model Averaging, Value-at-Risk, Decision Based Evaluations.
JEL: C32 C52 C53 G11

Further results on bias in dynamic unbalanced panel data models with an application to firm R&D investment
Date: 2008; By: Lokshin, Boris (UNU-MERIT, and Maastricht University)
This paper extends the LSDV bias-corrected estimator in [Bun, M., Carree, M.A. 2005. Bias-corrected estimation in dynamic panel data models, Journal of Business and Economic Statistics, 23(2): 200-10] to unbalanced panels and discusses the analytic method of obtaining the solution. Using a Monte Carlo approach the paper compares the performance of this estimator with three other available techniques for dynamic panel data models. Simulation reveals that LSDV-bc estimator is a good choice except for samples with small T, where it may be unpractical. The methodology is applied to examine the impact of internal and external R&D on labor productivity in an unbalanced panel of innovating firms.
Keywords: Bias Correction, Unbalanced Panel Data, GMM, Dynamic Models
JEL: C23

Dynamic Factors in the Presence of Block Structure
Date: 2008; By: Marc Hallin; Roman Liska
Macroeconometric data often come under the form of large panels of time series, themselves decomposing into smaller but still quite large subpanels or blocks. We show how the dynamic factor analysis method proposed in Forni et al (2000), combined with the identification method of Hallin and Liska (2007), allows for identifying and estimating joint and block-specific common factors. This leads to a more sophisticated analysis of the structures of dynamic interrelations within and between the blocks in such datasets, along with an informative decomposition of explained variances. The method is illustrated with an analysis of the Industrial Production Index data for France, Germany, and Italy.
Keywords: Panel data; Time series; High dimensional data; Dynamic factor model; Business cycle; Block specific factors; Dynamic principal components; Information criterion.

Modeling Expectations with Noncausal Autoregressions
Date: 2008; By: Markku Lanne; Pentti Saikkonen
This paper is concerned with univariate noncausal autoregressive models and their potential usefulness in economic applications. We argue that noncausal autoregressive models are especially well suited for modeling expectations. Unlike conventional causal autoregressive models, they explicitly show how the considered economic variable is affected by expectations and how expectations are formed. Noncausal autoregressive models can also be used to examine the related issue of backward-looking or forward-looking dynamics of an economic variable. We show in the paper how the parameters of a noncausal autoregressive model can be estimated by the method of maximum likelihood and how related test procedures can be obtained. Because noncausal autoregressive models cannot be distinguished from conventional causal autoregressive models by second order properties or Gaussian likelihood, a detailed discussion on their specific ation is provided. Motivated by economic applications we explicitly use a forward-looking autoregressive polynomial in the formulation of the model. This is di¤erent from the practice used in previous statistics literature on noncausal autoregressions and, in addition to its economic motivation, it is also convenient from a statistical point of view. In particular, it facilitates obtaining likelihood based diagnostic tests for the specified orders of the backward-looking and forward-looking autoregressive polynomials. Such test procedures are not only useful in the specification of the model but also in testing economically interesting hypotheses such as whether the considered variable only exhibits forward-looking behavior. As an empirical application, we consider modeling the U.S. in.ation dynamics which, according to our results, is purely forward-looking.

Forecasting Economic and Financial Variables with Global VARs
Date: 2008-01; By: Pesaran, M.H.; Schuermann, T.; Smit, L.V.
This paper considers the problem of forecasting real and financial macroeconomic variables across a large number of countries in the global economy. To this end a global vector autoregressive (GVAR) model previously estimated over the 1979Q1-2003Q4 period by Dees, de Mauro, Pesaran, and Smith (2007), is used to generate out-of-sample one quarter and four quarters ahead forecasts of real output, inflation, real equity prices, exchange rates and interest rates over the period 2004Q1-2005Q4. Forecasts are obtained for 134 variables from 26 regions made up of 33 countries covering about 90% of world output. The forecasts are compared to typical benchmarks: univariate autoregressive and random walk models. Building on the forecast combination literature, the effects of model and estimation uncertainty on forecast outcomes are examined by pooling forecasts obtained from different GVAR models estimated over alternative sa mple periods. Given the size of the modeling problem, and the heterogeneity of economies considered — industrialised, emerging, and less developed countries — as well as the very real likelihood of possibly multiple structural breaks, averaging forecasts across both models and windows makes a significant difference. Indeed the double-averaged GVAR forecasts performed better than the benchmark competitors, especially for output, inflation and real equity prices.
Keywords: Forecasting using GVAR, structural breaks and forecasting, average forecasts across models and windows, financial and macroeconomic forecasts.
JEL: C32 C51 C53

Extracting the Cyclical Component in Hours Worked: a Bayesian Approach
Date: 2008-05; By: Bernardi, Mauro; Della Corte, Giuseppe; Proietti, Tommaso
The series on average hours worked in the manufacturing sector is a key leading indicator of the U.S. business cycle. The paper deals with robust estimation of the cyclical component for the seasonally adjusted time series. This is achieved by an unobserved components model featuring an irregular component that is represented by a Gaussian mixture with two components. The mixture aims at capturing the kurtosis which characterizes the data. After presenting a Gibbs sampling scheme, we illustrate that the Gaussian mixture model provides a satisfactory representation of the data, allowing for the robust estimation of the cyclical component of per capita hours worked. Another important piece of evidence is that the outlying observations are not scattered randomly throughout the sample, but have a distinctive seasonal pattern. Therefore, seasonal adjustment plays a role. We ¯nally show that, if a °exible seasonal mode l is adopted for the unadjusted series, the level of outlier contamination is drastically reduced.
Keywords: Gaussian Mixtures; Robust signal extraction; State Space Models; Bayesian model selection; Seasonality
JEL: E32 C52 C22 C11

Multiple Sample Selection in the Estimation of Intergenerational Occupational Mobility
Date: 2008-05; By: Cheti Nicoletti (Institute for Social and Economic Research)
The estimation of occupational mobility across generations can be biased because of different sample selection issues as, for example, selection into employment. Most empirical papers have either neglected sample selection issues or adopted Heckman-type correction methods. These methods are generally not adequate to estimate intergenerational mobility models. In this paper, we show how to use new methods to estimate linear and quantile intergenerational mobility equations taking account of multiple sample selection.
Keywords: intergenerational links, sample selection

Properties of etimated characteristic roots
Date: 2008-05-30; By: Bent Nielsen (Nuffield College, Oxford University); Heino Bohn Nielsen (University of Copenhagen)
Estimated characteristic roots in stationary autoregressions are shown to give rather noisy information about their population equivalents. This is remarkable given the central role of the characteristic roots in the theory of autoregressive processes. In the asymptotic analysis the problems appear when multiple roots are present as this imply a non-differentiability so the d-method does not apply, convergence rates are slow, and the asymptotic distribution is non-normal. In finite samples this has a considerable influence on the finite sample distribution unless the roots are far apart. With increasing order of the autoregressions it becomes increasingly difficult to place the roots far apart giving a very noisy signal from the characteristic roots.
Keywords: Autoregression; Characteristic root.
JEL: C22

Bridging Economic Theory Models and the Cointegrated Vector Autoregressive Model
Date: 2008; By: Framroze Moller, Niels
Examples of simple economic theory models are analyzed as restrictions on the Cointegrated VAR (CVAR). This establishes a correspondence between basic economic concepts and the econometric concepts of the CVAR: The economic relations correspond to cointegrating vectors and exogeneity in the economic model implies the econometric concept of strong exogeneity for â. The economic equilibrium corresponds to the so-called long-run value (Johansen 2005), the comparative statics are captured by the long-run impact matrix, C; and the exogenous variables are the common trends. Also, the adjustment parameters of the CVAR are shown to be interpretable in terms of expectations formation, market clearing, nominal rigidities, etc. The general-partial equilibrium distinction is also discussed.
Keywords: Cointegrated VAR, unit root approximation, economic theory models, expectations, general equilibrium, DSGE models
JEL: C32

Modeling the Phillips curve with unobserved components
Date: 2008-01; By: Harvey, A.
The relationship between in.ation and the output gap can be modeled simply and effectively by including an unobserved random walk component in the model. The dynamic properties match the stylized facts and the random walk component satisfies the properties normally required for core in.ation. The model may be generalized to as to include a term for the expectation of next period’s output, but it is shown that this is difficult to distinguish from the original specification. The model is fited as a single equation and as part of a bivariate model that includes an equation for GDP. Fitting the bivariate model highlights some new aspects of unobserved components modeling. Single equation and bivariate models tell a similar story: an output gap two per cent above trend is associated with an annual inflation rate that is one percent above core inflation.
Keywords: Cycle; hybrid new Keynesian Phillips curve; inflation gap; Kalman filter, output gap.

Datapedia: a Yellow Brick Roadmap
Date: 2008-06-08; By: Freeman, Alan
This note lays out a roadmap to Datapedia: the goal is to share numbers with the same power and ease that the Wiki has delivered for documents. This would transform the quality and usability of economic data. The goal is a system which, by analogy with Wikipedia can establish a world resource for reliable data. The paper discusses a process by which data providers and users can evolve a new set os systems for exchanging, describing and interacting with data to bring this about. The proposal centres on the metadata – additional descriptive data – that is associated with numeric data, and suggests how, in two cases – World GDP and Creative Industry Employment – data could be mapped in such a way that viable Datawiki platforms can be built. The proposal also allows existing communities of users to start reshaping the way they exchange and handle data, to permit, and also to improve existing standards for colla borative use of data. The first step would be Datawiki: an opensource system for recording revisions, changes and sources of data, allowing users to compare different revisions and versions of data with each other. It would be a set of protocols, and simple web tools, to help data researchers pool, compare, scrutinise, and revise datasets from multiple sources. The first step towards Datawiki is Wikidata: rethinking the way that data itself is transmitted between people that collaborate on it a platform-independent standard for exchanging specifically numeric data. I show that the ubiquitous standard for exchanging data – the spreadsheet – is not up to the task of serving as a platform for Datawiki, and assess how alternatives can be developed.
Keywords: Creative Industries; Economic statistics; Datapedia; Wikipedia; Wiki
Keywords: data, wikipedia, creative industries, macroeconomics
JEL: Z1 E01 C8

Likelihood-based Analysis for Dynamic Factor Models
Date: 2008-01-17; By: Borus Jungbacker (VU University Amsterdam); Siem Jan Koopman (VU University Amsterdam)
We present new results for the likelihood-based analysis of the dynamic factor model that possibly includes intercepts and explanatory variables. The latent factors are modelled by stochastic processes. The idiosyncratic disturbances are specified as autoregressive processes with mutually correlated innovations. The new results lead to computationally efficient procedures for the estimation of the factors and parameter estimation by maximum likelihood and Bayesian methods. An illustration is provided for the analysis of a large panel of macroeconomic time series.
Keywords: EM algorithm; Kalman Filter; Forecasting; Latent Factors; Markov chain Monte Carlo; Principal Components; State Space
JEL: C33 C43

Garch Parameter Estimation Using High-Frequency Data
Date: 2008-06-10; By: Visser, Marcel P.
Estimation of the parameters of Garch models for financial data is typically based on daily close-to-close returns. This paper shows that the efficiency of the parameter estimators may be greatly improved by using volatility proxies based on intraday data. The paper develops a Garch quasi maximum likelihood estimator (QMLE) based on these proxies. Examples of such proxies are the realized volatility and the intraday high-low range. Empirical analysis of the S&P 500 index tick data shows that the use of a suitable proxy may reduce the variances of the estimators of the Garch autoregression parameters by a factor 20.
Keywords: volatility estimation; quasi maximum likelihood; volatility proxy; Gaussian QMLE; log-Gaussian QMLE; autoregressive conditional heteroscedasticity
JEL: C51 G1 C14 C22

Parameter Driven Multi-state Duration Models: Simulated vs. Approximate Maximum Likelihood Estimation
Date: 2008-02-27; By: André A. Monteiro (VU University Amsterdam, and University of Western Australia)
Likelihood based inference for multi-state latent factor intensity models is hindered by the fact that exact closed-form expressions for the implied data density are not available. This is a common and well-known problem for most parameter driven dynamic econometric models. This paper reviews, adapts and compares three different approaches for solving this problem. For evaluating the likelihood, two of the methods rely on Monte Carlo integration with importance sampling techniques. The third method, in contrast, is based on fully deterministic numerical procedures. A Monte Carlo study is conducted to illustrate the use of each method, and assess its corresponding finite sample performance.
Keywords: Multi-state Duration models; Parameter Driven models; Simulated Maximum Likelihood; Importance Sampling
JEL: C15 C32 C33 C41

Forecasting Random Walks Under Drift Instability
Date: 2008-03; By: Pesaran, M.H.; Pick, A.
This paper considers forecast averaging when the same model is used but estimation is carried out over different estimation windows. It develops theoretical results for random walks when their drift and/or volatility are subject to one or more structural breaks. It is shown that compared to using forecasts based on a single estimation window, averaging over estimation windows leads to a lower bias and to a lower root mean square forecast error for all but the smallest of breaks. Similar results are also obtained when observations are exponentially down-weighted, although in this case the performance of forecasts based on exponential down-weighting critically depends on the choice of the weighting coefficient. The forecasting techniques are applied to monthly inflation series of 21 OECD countries and it is found that average forecasting methods in general perform better than using forecasts based on a single estimat ion window.
Keywords: Forecast combinations, averaging over estimation windows, exponentially down-weighting observations, structural breaks.
JEL: C22 C53

An Hourly Periodic State Space Model for Modelling French National Electricity Load
Date: 2008-01-17; By: V. Dordonnat (VU University Amsterdam); S.J. Koopman (VU University Amsterdam); M. Ooms (VU University Amsterdam); A. Dessertaine (Electricité de France, Clamart, France); J. Collet (Electricité de France, Clamart, France)
We present a model for hourly electricity load forecasting based on stochastically time-varying processes that are designed to account for changes in customer behaviour and in utility production efficiencies. The model is periodic: it consists of different equations and different parameters for each hour of the day. Dependence between the equations is introduced by covariances between disturbances that drive the time-varying processes. The equations are estimated simultaneously. Our model consists of components that represent trends, seasons at different levels (yearly, weekly, daily, special days and holidays), short-term dynamics and weather regression effects including nonlinear functions for heating effects. The implementation of our forecasting procedure relies on the multivariate linear Gaussian state space framework and is applied to national French hourly electricity load. The analysis focuses on two hours, 9 AM and 12 AM, but forecasting results are presented for all twenty-four hours. Given the time series length of nine years of hourly observations, many features of our model can be readily estimated including yearly patterns and their time-varying nature. The empirical analysis involves an out-of sample forecasting assessment up to seven days ahead. The one-day ahead forecasts from fourty-eight bivariate models are compared with twenty-four univariate models for all hours of the day. We find that the implied forecasting function strongly depends on the hour of the day.
Keywords: Kalman filter; Maximum likelihood estimation; Seemingly Unrelated Regression Equations; Unobserved Components; Time varying parameters; Heating effect
JEL: C22 C32 C52 C53

MDL Mean Function Selection in Semiparametric Kernel Regression Models
Date: 2008-05-07; By: Jan G. De Gooijer (University of Amsterdam); Ao Yuan (Howard University, Washington DC, USA)
We study the problem of selecting the optimal functional form among a set of non-nested nonlinear mean functions for a semiparametric kernel based regression model. To this end we consider Rissanen’s minimum description length (MDL) principle. We prove the consistency of the proposed MDL criterion. Its performance is examined via simulated data sets of univariate and bivariate nonlinear regression models.
Keywords: Kernel density estimator; Maximum likelihood estimator; Minimum description length; Nonlinear regression; Semiparametric model
JEL: C14

Speed of Adjustment in Cointegrated Systems
Date: 2007-06; By: Fanelli, Luca; Paruolo, Paolo
This paper considers the speed of adjustment to long-run equilibria, in the context of cointegrated Vector Autoregressive Processes (VAR). We discuss the definition of multivariate p-lives for any indicator of predictive ability, concentrating on cumulated interim multipliers which converge to impact factor for increasing forecasting horizon. Interim multipliers are related to autoregressive Granger-causality coefficients, structural or generalized cumulative impulse responses. We discuss the relation of the present definition of multivariate p-lives with existing definitions for univariate time series and for nonlinear multivariate stationary processes. For multivariate (possibly cointegrated) VAR systems, p-lives are functions of the dynamics of the system only,and do not depend on the history path on which the forecast is based. Hence one can discuss inference on p-lives as (discrete) functions of parameters in the VAR model. We discuss a likelihood-based approach, both for point estimation and for confidence regions. An illustrative application to adjustment to purchasing-power parity (PPP) is presented.
Keywords: p-life; speed of adjustment; impact factors; vector equilibrium correction; shock absorption.
JEL: C32 C52 F31

Confidence sets based on penalized maximum likelihood estimators
Date: 2008-06; By: Pötscher, Benedikt M.; Schneider, Ulrike
The finite-sample coverage properties of confidence intervals based on penalized maximum likelihood estimators like the LASSO, adaptive LASSO, and hard-thresholding are analyzed. It is shown that symmetric intervals are the shortest. The length of the shortest intervals based on the hard-thresholding estimator is larger than the length of the shortest interval based on the adaptive LASSO, which is larger than the length of the shortest interval based on the LASSO, which in turn is larger than the standard interval based on the maximum likelihood estimator. In the case where the penalized estimators are tuned to possess the `sparsity property’, the intervals based on these estimators are larger than the standard interval by an order of magnitude. A simple asymptotic confidence interval construction in the `sparse’ case, that also applies to the smoothly clipped absolute deviation estimator, is also discussed.
Keywords: penalized maximum likelihood; Lasso; adaptive Lasso; hard-thresholding; confidence set; coverage probability; sparsity; model selection.
JEL: C13 C01

Testing for Granger (non)-Causality in a Time Varying Coefficient VAR Model
Date: 2008-01; By: Dimitris K. Christopoulos; Miguel Leon-Ledesma
In this paper we propose Granger (non-)causality tests based on a VAR model allowing for time-varying coefficients. The functional form of the time-varying coefficients is a Logistic Smooth Transition Autoregressive (LSTAR) model using time as the transition variable. The model allows for testing Granger non-causality when the VAR is subject to a smooth break in the coefficients of the Granger causal variables. The proposed test then is applied to the money-output relationship using quarterly US data for the period 1952:2-2002:4. We find that causality from money to output becomes stronger after 1978:4 and the model is shown to have a good out of sample forecasting performance for output relative to a linear VAR model.
Keywords: Granger causality; Time-varying coefficients; LSTAR models
JEL: C51 C52

“Bayesian Estimation of Demand Functions under Block Rate Pricing”
Date: 2008-06; By: Koji Miyawaki (Graduate School of Economics, University of Tokyo); Yasuihro Omori (Faculty of Economics, University of Tokyo); Akira Hibiki (cNational Institute for Environmental Studies and Department of Social Engineering, Tokyo Institute of Technology)
This article proposes a Bayesian estimation method of demand functions under block rate pricing, focusing on increasing one. Under this pricing structure, price changes when consumption exceeds a certain threshold and the consumer faces a utility maximization problem subject to a piecewise-linear budget constraint. We apply the so-called discrete/continuous choice approach to derive the corresponding demand function. Taking a hierarchical Bayesian approach, we implement a Markov chain Monte Carlo simulation to estimate the demand function. Moreover, a separability condition is explicitly considered to obtain proper estimates. We find, however, that the convergence of the distribution of simulated samples to the posterior distribution is slow, requiring an additional scale transformation step for parameters to the Gibbs sampler. The model is also extended to allow random coefficients for panel data and spatial corre lation for spatial data. These proposed methods are applied to estimate the Japanese residential water and electricity demand function.

Instrumental Variable Estimation for Duration Data
Date: 2008-03-27; By: Govert E. Bijwaard (Erasmus University Rotterdam)
In this article we develop an Instrumental Variable estimation procedure that corrects for possible endogeneity of a variable in a duration model. We assume a Generalized Accelerated Failure Time (GAFT) model. This model is based on transforming the durations and assuming a distribution for these transformed durations. The GAFT model encompasses two competing approaches to duration data; the (Mixed) Proportional Hazard (MPH) model and the Accelerated Failure Time (AFT) model. The basis of the Instrumental Variable Linear Rank estimator (IVLR) is that for the true GAFT model the instrument does not influence the hazard of the transformed duration. The inverse of an extended rank test provide the estimation equations the IVLR estimation procedure is based on. We discuss the large sample properties and the efficiency of this estimator. We discuss the practical issues of implementation of the estimator. We apply the IV LR estimation approach to the Illinois re-employment bonus experiment. In this experiment individuals who became unemployed were divided at random in three groups: two bonus groups and a control group. Those in the bonus groups could refuse to participate in the experiment. It is very likely that this decision is related to the unemployment duration. We use the IVLR estimator to obtain the effect of these endogenous claimant and employer bonuses on the re-employment hazard.
Keywords: Endogenous Variable; Duration model; Censoring; Instrumental Variable
JEL: C21 C41 J64

Model-based Estimation of High Frequency Jump Diffusions with Microstructure Noise and Stochastic Volatility
Date: 2008-01-22; By: Charles S. Bos (VU University Amsterdam)
When analysing the volatility related to high frequency financial data, mostly non-parametric approaches based on realised or bipower variation are applied. This article instead starts from a continuous time diffusion model and derives a parametric analog at high frequency for it, allowing simultaneously for microstructure effects, jumps, missing observations and stochastic volatility. Estimation of the model delivers measures of daily variation outperforming their non-parametric counterparts. Both with simulated and actual exchange rate data, the feasibility of this novel approach is shown. The parametric setting is used to estimate the intra-day trend in the Euro/U.S. Dollar exchange rate.
Keywords: High frequency; integrated variation; intra-day; jump diffusions; microstructure noise; stochastic volatility; exchange rates
JEL: C11 C14 D53 E44

Early Detection Techniques for Market Risk Failure
Date: 2008-05; By: Jose Olmo (Department of Economics, City University, London); William Pouliot (Department of Economics, City University, London)
The implementation of appropriate statistical techniques for monitoring conditional VaR models, i.e, backtesting, reported by institutions is fundamental to determine their exposure to market risk. Backtesting techniques are important since the severity of the departures of the VaR model from market results determine the penalties imposed for inadequate VaR models. In this paper we make six contributions to backtesting techniques. In particular, we show that the Kupiec test can be viewed as a combination of CUSUM change point tests; we detail the lack of power of CUSUM methods in detecting violations of VaR as soon as these occur; we develop an alternative technique based on weighted U-statistic type processes that have power against wrong specifications of the risk measure and early detection; we show these new backtesting techniques are robust to the presence of estimation risk; we construct a new class of weight functions that can be used to weight our processes; and our methods are applicable both under conditional and unconditional VaR settings.
Keywords: Asymmetries, crises; Extreme values; Hypothesis testing; Leverage effect; Nonlinearities; Threshold models

Optimal Asset Allocation with Factor Models for Large Portfolios
Date: 2008-03; By: Pesaran, M.H.; Zaffaroni, P.
This paper characterizes the asymptotic behaviour, as the number of assets gets arbitrarily large, of the portfolio weights for the class of tangency portfolios belonging to the Markowitz paradigm. It is as- sumed that the joint distribution of asset returns is characterized by a general factor model, with possibly heteroskedastic components. Under these conditions, we establish that a set of appealing properties, so far unnoticed, characterize traditional Markowitz portfolio trading strategies. First, we show that the tangency portfolios fully diversify the risk associated with the factor component of asset return innovations. Second, with respect to determination of the portfolio weights, the conditional distribution of the factors is of second-order importance as compared to the distribution of the factor loadings and that of the idiosyncratic components. Third, although of crucial importance in forecasting asse t returns, current and lagged factors do not enter the limit portfolio returns. Our theoretical results also shed light on a number of issues discussed in the literature regarding the limiting properties of portfolio weights such as the diversi¯ability property and the number of dominant factors.
Keywords: Asset allocation, Large Porftolios, Factor models, Diversi¯cation.
JEL: C32 C52 C53 G1

A New Procedure to Monitor the Mean of a Quality Characteristic
Date: 2008; By: Kiani, Mehdi; Panaretos, John; Psarakis, Stelios
The Shewhart, Bonferroni-adjustment and analysis of means (ANOM) control chart are typically applied to monitor the mean of a quality characteristic. The Shewhart and Bonferroni procedure are utilized to recognize special causes in production process, where the control limits are constructed by assuming normal distribution for known parameters (mean and standard deviation), and approximately normal distribution regarding to unknown parameters. The ANOM method is an alternative to the analysis of variance method. It can be used to establish the mean control charts by applying equicorrelated multivariate non-central t distribution. In this paper, we establish new control charts, in phases I and II monitoring, based on normal and t distributions having as a cause a known (or unknown) parameter (standard deviation). Our proposed methods are at least as effective as the classical Shewhart methods and have some advantage s.
Keywords: Shewhart; Bonferroni-adjustment; Analysis of means; Average run length; False alarm probability
JEL: C10

Old and new spectral techniques for economic time series
Date: 2008-05; By: Sella Lisa (University of Turin)
This methodological paper reviews different spectral techniques well suitable to the analysis of economic time series. While econometric time series analysis is generally yielded in the time domain, these techniques propose a complementary approach based on the frequency domain. Spectral decomposition and time series reconstruction provide a precise quantitative and formal description of the main oscillatory components of a series: thus, it is possible to formally identify trends, lowfrequency components, business cycles, seasonalities, etc. Since recent developments in spectral techniques allow to manage even with short noisy dataset, nonstationary processes, non purely periodic components these tools could be applied on economic datasets more widely than they nowadays are.

Short-term forecasting of GDP using large monthly datasets – a pseudo real-time forecast evaluation exercise
Date: 2008-04; By: Karim Barhoumi; Szilard Benk; Riccardo Cristadoro; Ard Den Reijer; Audrone Jakaitiene; Piotr Jelonek; António Rua; Gerhard Rünstler (European Central Bank, Kaiserstrasse 29, 60311 Frankfurt am Main, Germany.); Karsten Ruth; Christophe Van Nieuwenhuyze
This paper evaluates different models for the short-term forecasting of real GDP growth in ten selected European countries and the euro area as a whole. Purely quarterly models are compared with models designed to exploit early releases of monthly indicators for the nowcast and forecast of quarterly GDP growth. Amongst the latter, we consider small bridge equations and forecast equations in which the bridging between monthly and quarterly data is achieved through a regression on factors extracted from large monthly datasets. The forecasting exercise is performed in a simulated real-time context, which takes account of publication lags in the individual series. In general, we find that models that exploit monthly information outperform models that use purely quarterly data and, amongst the former, factor models perform best. JEL Classification: E37, C53.
Keywords: Bridge models, Dynamic factor models, real-time data flow.

Analysis of the dependence structure in econometric time series
Date: 2008-06-05; By: Aurélien Hazan (IBISC – Informatique, Biologie Intégrative et Systèmes Complexes – CNRS : FRE2873 – Université d’Evry-Val d’Essonne); Vincent Vigneron (CES – Centre d’économie de la Sorbonne – CNRS : UMR8174 – Université Panthéon-Sorbonne – Paris I, SAMOS – Statistique Appliquée et MOdélisation Stochastique – Université Panthéon-Sorbonne – Paris I)
The various scales of a signal maintain relations of dependence the on es with the others. Those can vary in time and reveal speed changes in the studied phenomenon. In the goal to establish these changes, one shall compute first the wavelet transform of a signal, on various scales. Then one shall study the statistical dependences between these transforms thanks to an estimator of mutual information. One shall then propose to summarize the resulting network of dependences by a graph of dependences by thresholding the values of the mutual information or by quantifying its values. The method can be applied to several types of signals, such as fluctuations of market indexes for instance the S&P 500, or high frequency foreign exchange (FX) rates.
Keywords: wavelet, dependence; mutual information; financial; time-series; FX

Incorporating judgement with DSGE models
Date: 2008-06; By: Jaromír Beneš; Andrew Binning; Kirdan Lees (Reserve Bank of New Zealand)
Central bank policymakers often cast judgement about macroeconomic forecasts in reduced form terms, basing this on off-model information that is not easily mapped to a structural DSGE framework. We show how to compute forecasts conditioned on policymaker judgement that are the most likely conditional forecasts from the perspective of the DSGE model, thereby maximising the influence of the model structure on the forecasts. We suggest using a simple implausibility index to track the magnitude and type of policymaker judgement. This is based on the structural shocks required to return policymaker judgement. We show how to use the methods for practical use in the policy environment and also apply the techniques to condition DSGE model forecasts on: (i) the long history of published forecasts from the Reserve Bank of New Zealand; (ii) constant interest rate forecasts; and (iii) inflation forecasts from a Bayesian VAR cu rrently used in the policy environment at the Reserve Bank of New Zealand.
Keywords: DSGE models; monetary policy; conditional forecasts
JEL: C51 C53

Rational Forecasts or Social Opinion Dynamics? Identification of Interaction Effects in a Business Climate Survey
Date: 2008-06; By: Thomas Lux
This paper develops a methodology for estimating the parameters of dynamic opinion or expectation formation processes with social interactions. We study a simple stochastic framework of a collective process of opinion formation by a group of agents who face a binary decision problem. The aggregate dynamics of the individuals’ decisions can be analyzed via the stochastic process governing the ensemble average of choices. Numerical approximations to the transient density for this ensemble average allow the evaluation of the likelihood function on the base of discrete observations of the social dynamics. This approach can be used to estimate the parameters of the opinion formation process from aggregate data on its average realization. Our application to a well-known business climate index provides strong indication of social interaction as an important element in respondents’ assessment of the business climate
Keywords: business climate, business cycle forecasts, opinion formation, social interactions
JEL: C42 D84 E37

The Information Content of a Stated Choice Experiment
Date: 2008-05-22; By: Jan Rouwendal (VU University Amsterdam); Arianne de Blaeij (LEI, The Hague); Piet Rietveld (VU University Amsterdam); Erik Verhoef (VU University Amsterdam)
This paper presents a method to assess the distribution of values of time, and values of statistical life, over participants to a stated choice experiment, that does not require the researcher to make an a priori assumption on the type of distribution, as is required for example for mixed logit models. The method requires a few assumptions to hold true, namely that the valuations to be determined are constant for each individual, and that respondents make choices according to their preferences. These assumptions allow the derivation of lower and upper bounds on the (cumulative) distribution of the values of interest over respondents, by deriving for each choice set the value(s) for which the respondent would be indifferent between the alternatives offered, and next deriving from the choice actually made the respondent’s implied minimum or maximum value(s). We also provide an extension of the method that incorpora tes the possibility that errors are made. The method is illustrated using data from an experiment investigating the value of time and the value of statistical life. We discuss the possibility to improve the information content of stated choice experiments by optimizing the attribute levels shown to respondents, which is especially relevant because it would help in selecting the appropriate distribution for mixed logit estimates for the same data.
Keywords: stated preferences; value of a statistical life
JEL: C81 D12 D61 R41

Bad Luck When Joining the Shortest Queue
Date: 2008; By: Blanc, J.P.C. (Tilburg University, Center for Economic Research)
A frequent observation in service systems with queues in parallel is that customers in other queues tend to be served faster than those in one?s own queue. This paper quantifies the probability that one?s service would have started earlier if one had joined another queue than the queue that was actually chosen, for exponential multiserver systems with queues in parallel in which customers join one of the shortest queues upon arrival and in which jockeying is not possible.
Keywords: Queueing;Join-the-shortest-queue; Probability of bad luck; Power-series algorithm; Overtaking customers; Dedicated customers.
JEL: C44 C60