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on Econometrics |
| By: | Francq, Christian; Zakoian, Jean-Michel |
| Abstract: | This paper studies the asymptotic properties of the quasi-maximum likelihood estimator of ARCH(1) models without strict stationarity constraints, and considers applications to testing problems. The estimator is unrestricted, in the sense that the value of the intercept, which cannot be consistently estimated in the explosive case, is not fixed. A specific behavior of the estimator of the ARCH coefficient is obtained at the boundary of the stationarity region, but this estimator remains consistent and asymptotically normal in every situation. The asymptotic variance is different in the stationary and non stationary situations, but is consistently estimated, with the same estimator, in both cases. Tests of strict stationarity and non stationarity are proposed. Their behaviors are studied under the null assumption and under local alternatives. The tests developed for the ARCH(1) model are able to detect non-stationarity in more general GARCH models. A numerical illustration based on stock indices is proposed. |
| Keywords: | ARCH model; Inconsistency of estimators; Local power of tests; Nonstationarity; Quasi Maximum Likelihood Estimation |
| JEL: | C13 C12 C22 C01 |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:22414&r=ecm |
| By: | Heitor Almeida; Murillo Campello; Antonio F. Galvao Jr. |
| Abstract: | We use Monte Carlo simulations and real data to assess the performance of alternative methods that deal with measurement error in investment equations. Our experiments show that individual-fixed effects, error heteroscedasticity, and data skewness severely affect the performance and reliability of methods found in the literature. In particular, estimators that use higher-order moments are shown to return biased coefficients for (both) mismeasured and perfectly-measured regressors. These estimators are also very inefficient. Instrumental variables-type estimators are more robust and efficient, although they require fairly restrictive assumptions. We estimate empirical investment models using alternative methods. Real-world investment data contain firm-fixed effects and heteroscedasticity, causing high-order moments estimators to deliver coefficients that are unstable across different specifications and not economically meaningful. Instrumental variables methods yield estimates that are robust and seem to conform to theoretical priors. Our analysis provides guidance for dealing with the problem of measurement error under circumstances empirical researchers are likely to find in practice. |
| JEL: | G3 |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:15951&r=ecm |
| By: | Tim Bollerslev (Department of Economics, Duke University, and NBER and CREATES); Viktor Todorov (Department of Finance, Kellogg School of Management, Northwestern University) |
| Abstract: | We propose a new and flexible non-parametric framework for estimating the jump tails of Itô semimartingale processes. The approach is based on a relatively simple-to-implement set of estimating equations associated with the compensator for the jump measure, or its "intensity", that only utilizes the weak assumption of regular variation in the jump tails, along with in-fill asymptotic arguments for uniquely identifying the "large" jumps from the data. The estimation allows for very general dynamic dependencies in the jump tails, and does not restrict the continuous part of the process and the temporal variation in the stochastic volatility. On implementing the new estimation procedure with actual high-frequency data for the S&P 500 aggregate market portfolio, we find strong evidence for richer and more complex dynamic dependencies in the jump tails than hitherto entertained in the literature. |
| Keywords: | Extreme events, jumps, high-frequency data, jump tails, non-parametric estimation, stochastic volatility |
| JEL: | C13 C14 G10 G12 |
| Date: | 2010–04–14 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2010-16&r=ecm |
| By: | Giovanni De Luca (Dipartimento di Statistica e Matematica per la Ricerca Economica Università di Napoli Parthenope.); Giampiero Gallo (Università degli Studi di Firenze, Dipartimento di Statistica "G. Parenti") |
| Abstract: | In this paper we model the dynamics of realized volatility as a Multiplicative Error Model with a mixture of distributions for the innovation term with time-varying mixing weights forced by past behavior of volatility. The mixture considers innovations as a source of time-varying volatility of volatility and is able to capture the right tail behavior of the distribution of volatility. The empirical results show that there is no substantial difference in the one-step ahead conditional expectations obtained according to various mixing schemes but that fixity of mixing weights may be a binding constraint in deriving accurate quantiles of the predicted distribution. |
| Keywords: | Multiplicative Error Models, Realized Volatility, Mixture Distributions |
| JEL: | C22 C51 C53 |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:fir:econom:wp2010_03&r=ecm |
| By: | Ole E. Barndorff–Nielsen (Thiele Center, Department of Mathematical Sciences and CREATES); Fred Espen Benth (Centre of Mathematics for Applications, University of Oslo and Faculty of Economics University of Agder); Almut E. D. Veraart (CREATES, School of Economics and Management Aarhus University) |
| Abstract: | This paper introduces a new modelling framework for energy spot prices based on Lévy semistationary processes. Lévy semistationary processes are special cases of the general class of ambit processes. We provide a detailed analysis of the probabilistic properties of such models and we show how they are able to capture many of the stylised facts observed in energy markets. Furthermore, we derive forward prices based on our spot price model. As it turns out, many of the classical spot models can be embedded into our novel modelling framework. |
| Keywords: | Energy markets, forward price, Lévy semistationary process, stochastic integration, spot price |
| JEL: | C0 C1 C5 G1 |
| Date: | 2010–04–27 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2010-18&r=ecm |
| By: | Sinha, Pankaj; Jayaraman, Prabha |
| Abstract: | Abstract In this paper we derive the Bayes estimates of the location parameter of normal and lognormal distribution under the hierarchical priors for the vector parameter, . The ML-II ε-contaminated class of priors are employed at the second stage of hierarchical priors to examine the robustness of Bayes estimates with respect to possible misspecification at the second stage. The simulation studies for both normal and lognormal distributions confirm Berger’s (1985) assertion that form of the second stage prior does not affect the Bayes decisions. |
| Keywords: | Hierarchical Bayes; Hierarchical priors; ML-II ε-contaminated class of priors |
| JEL: | C00 C44 C02 C11 |
| Date: | 2010–04–30 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:22416&r=ecm |
| By: | Claudia Miani (Bank of Italy); Stefano Siviero (Bank of Italy) |
| Abstract: | It has increasingly become standard practice to supplement point macroeconomic forecasts with an appraisal of the degree of uncertainty and the prevailing direction of risks. Several alternative approaches have been proposed in the literature to compute the probability distribution of macroeconomic forecasts; all of them rely on combining the predictive density of model-based forecasts with subjective judgment about the direction and intensity of prevailing risks. We propose a non-parametric, model-based simulation approach, which does not require specific assumptions to be made regarding the probability distribution of the sources of risk. The probability distribution of macroeconomic forecasts is computed as the result of model-based stochastic simulations which rely on re-sampling from the historical distribution of risk factors and are designed to deliver the desired degree of skewness. By contrast, other approaches typically make a specific, parametric assumption about the distribution of risk factors. The approach is illustrated using the Bank of Italy’s Quarterly Macroeconometric Model. The results suggest that the distribution of macroeconomic forecasts quickly tends to become symmetric, even if all risk factors are assumed to be asymmetrically distributed. |
| Keywords: | macroeconomic forecasts, stochastic simulations, balance of risks, uncertainty, fan-charts |
| JEL: | C14 C53 E37 |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:bdi:wptemi:td_758_10&r=ecm |
| By: | Frauke Kreuter; Carolina Casas-Cordero |
| Abstract: | Paradata – data about the process of survey production – have drawn increasing attention as the statistical world moves towards the implementation of quality metrics and measures to improve quality and save costs. This paper gives examples of various uses of paradata and discusses access to paradata as well as future developments. |
| Keywords: | paradata, process data, responsive design, measurement error, nonresponse, adjustment |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:rsw:rswwps:rswwps96&r=ecm |