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on Econometric Time Series |
| By: | Dominique Guegan (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris); Zhiping Lu (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, ECNU - East China Normal University) |
| Abstract: | Long memory processes have been extensively studied over the past decades. When dealing with the financial and economic data, seasonality and time-varying long-range dependence can often be observed and thus some kind of non-stationarity can exist inside financial data sets. To take into account this kind of phenomena, we propose a new class of stochastic process : the locally stationary k-factor Gegenbauer process. We describe a procedure of estimating consistently the time-varying parameters by applying the discrete wavelet packet transform (DWPT). The robustness of the algorithm is investigated through simulation study. An application based on the error correction term of fractional cointegration analysis of the Nikkei Stock Average 225 index is proposed. |
| Keywords: | Discrete wavelet packet transform ; Gegenbauer process ; Nikkei Stock Average 225 index ; non-stationarity ; ordinary least square estimation |
| Date: | 2009–03 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00375531_v1&r=ets |
| By: | Dominique Guegan (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris) |
| Abstract: | This paper focuses on the use of dynamical chaotic systems in Economics and Finance. In these fields, researchers employ different methods from those taken by mathematicians and physicists. We discuss this point. Then, we present statistical tools and problems which are innovative and can be useful in practice to detect the existence of chaotic behavior inside real data sets. |
| Keywords: | Chaos ; Deterministic dynamical system ; Economics ; Estimation theory ; Finance ; Forecasting |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00375713_v1&r=ets |
| By: | Lanouar Charfeddine (OEP - Université de Marne-la-Vallée); Dominique Guegan (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris) |
| Abstract: | Are structural breaks models true switching models or long memory processes ? The answer to this question remain ambiguous. A lot of papers, in recent years, have dealt with this problem. For instance, Diebold and Inoue (2001) and Granger and Hyung (2004) show, under specific conditions, that switching models and long memory processes can be easily confused. In this paper, using several generating models like the mean-plus-noise model, the STOchastic Permanent BREAK model, the Markov switching model, the TAR model, the sign model and the Structural CHange model (SCH) and several estimation techiques like the GPH technique, the Exact Local Whittle (ELW) and the Wavelet methods, we show that, if the answer is quite simple in some cases, it can be mitigate in other cases. Using French and American inflation rates, we show that these series cannot be characterized by the same class of models. The main result of this study suggests that estimating the long memory parameter without taking account existence of breaks in the data sets may lead to misspecification and to overestimate the true parameter. |
| Keywords: | Structural breaks models, spurious long memory behavior, inflation series. |
| Date: | 2009–04 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00377485_v1&r=ets |
| By: | Dominique Guegan (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris); Jing Zhang (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, ECNU - East China Normal University) |
| Abstract: | This paper proposes a new approach to measure the dependence in multivariate financial data. Data in finance and insurance often cover a long time period. Therefore, the economic factors may induce some changes inside the dependence structure. Recently, two methods using copulas have been proposed to analyze such changes. The first approach investigates the changes of copula's parameters. The second one tests the changes of copulas by determining the best copulas using moving windows. In this paper we take into account the non stationarity of the data and analyze : (1) the changes of parameters while the copula family keeps static ; (2) the changes of copula family. We propose a series of tests based on conditional copulas and goodness-of-fit (GOF) tests to decide the type of change, and further give the corresponding change analysis. We illustrate our approach with Standard & Poor 500 and Nasdaq indices, and provide dynamic risk measures. |
| Keywords: | Dynamic copula - goodness-of-fit test - change-point - time-varying parameter - VaR - ES |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00368334_v1&r=ets |
| By: | Abdou Kâ Diongue (UFR SAT - Université Gaston Berger - Université Gaston Berger de Saint-Louis); Dominique Guegan (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris); Rodney C. Wolff (School of Mathematical Sciences - Queensland University of Technology) |
| Abstract: | In this paper, we discuss the class of Bilinear GATRCH (BL-GARCH) models which are capable of capturing simultaneously two key properties of non-linear time series : volatility clustering and leverage effects. It has been observed often that the marginal distributions of such time series have heavy tails ; thus we examine the BL-GARCH model in a general setting under some non-Normal distributions. We investigate some probabilistic properties of this model and we propose and implement a maximum likelihood estimation (MLE) methodology. To evaluate the small-sample performance of this method for the various models, a Monte Carlo study is conducted. Finally, within-sample estimation properties are studied using S&P 500 daily returns, when the features of interest manifest as volatility clustering and leverage effects. |
| Keywords: | BL-GARCH process - elliptical distribution - leverage effects - Maximum Likelihood - Monte Carlo method - volatility clustering |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00368340_v1&r=ets |
| By: | Romain Biard (SAF - EA2429 - Laboratoire de Science Actuarielle et Financière - Université Claude Bernard - Lyon I); Stéphane Loisel (SAF - EA2429 - Laboratoire de Science Actuarielle et Financière - Université Claude Bernard - Lyon I); Claudio Macci (Dipartimento di Matematica - Università di Roma "Tor Vergata"); Noel Veraverbeke (Center for Statistics - Hasselt University) |
| Abstract: | In the renewal risk model, we study the asymptotic behavior of the expected time-integrated negative part of the process. This risk measure has been introduced by Loisel (2005). Both heavy-tailed and light-tailed claim amount distributions are investigated. The time horizon may be finite or infinite. We apply the results to an optimal allocation problem with two lines of business of an insurance company. The asymptotic behavior of the two optimal initial reserves are computed. |
| Keywords: | Ruin theory; heavy-tailed and light-tailed claim size distribution; risk measure; optimal reserve allocation |
| Date: | 2009–03–31 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00372525_v1&r=ets |
| By: | Daisuke Nagakura; Toshiaki Watanabe |
| Abstract: | We call the realized variance (RV) calculated with observed prices contaminated by microstructure noises (MNs) the noise-contaminated RV (NCRV) and refer to the component in the NCRV associated with the MNs as the MN component. This paper develops a state space method for estimating the integrated variance (IV) and MN component simultaneously. We represent the NCRV by a state space form and show that the state space form parameters are not identifiable; however, they can be expressed as functions of fewer identifiable parameters. We illustrate how to estimate these parameters. The proposed method is applied to yen/dollar exchange rate data. |
| Keywords: | Realized Variance, Integrated Variance, Microstructure Noise, State Space, Identification, Exchange Rate |
| Date: | 2009–03 |
| URL: | http://d.repec.org/n?u=RePEc:hst:ghsdps:gd09-055&r=ets |
| By: | Denis Belomestny |
| Abstract: | We consider the problem of estimating the fractional order of a L´evy process from low frequency historical and options data. An estimation methodology is developed which allows us to treat both estimation and calibration problems in a unified way. The corresponding procedure consists of two steps: the estimation of a conditional characteristic function and the weighted least squares estimation of the fractional order in spectral domain. While the second step is identical for both calibration and estimation, the first one depends on the problem at hand. Minimax rates of convergence for the fractional order estimate are derived, the asymptotic normality is proved and a data-driven algorithm based on aggregation is proposed. The performance of the estimator in both estimation and calibration setups is illustrated by a simulation study. |
| Keywords: | regular Lévy processes, Blumenthal-Getoor index, semiparametric estimation |
| JEL: | C12 C13 |
| Date: | 2009–04 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2009-021&r=ets |
| By: | Kilian, Lutz; Kim, Yun Jung |
| Abstract: | It is well documented that the small-sample accuracy of asymptotic and bootstrap approximations to the pointwise distribution of VAR impulse response estimators is undermined by the estimator’s bias. A natural conjecture is that impulse response estimators based on the local projection (LP) method of Jordà (2005, 2007) are less susceptible to this problem and hence potentially more reliable in small samples than VAR-based estimators. We show that - contrary to this conjecture - LP estimators tend to have both higher bias and higher variance, resulting in pointwise impulse response confidence intervals that are typically less accurate and wider on average than suitably constructed VAR-based intervals. Bootstrapping the LP estimator only worsens its finite-sample accuracy. We also evaluate recently proposed joint asymptotic intervals for VAR and LP impulse response functions. Our analysis suggests that the accuracy of joint intervals can be erratic in practice, and neither joint interval is uniformly preferred over the other. |
| Keywords: | Bias; Confidence interval; Impulse response function; Joint interval; Local projection; Vector autoregression |
| JEL: | C32 C52 C53 |
| Date: | 2009–04 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:7266&r=ets |