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on Econometric Time Series |
| By: | Antoine Lejay (TOSCA - TO Simulate and CAlibrate stochastic models - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en Automatique - IECL - Institut Élie Cartan de Lorraine - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique); Paolo Pigato (LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées - UPEM - Université Paris-Est Marne-la-Vallée - Fédération de Recherche Bézout - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12 - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | This technical report presents the methodology and the numerical results for 21 stock prices under the assumption they follow a Drifted Geometric Oscillating Brownian motion model. Such a model takes leverage and mean-reversion effects into account. Ce rapport completes the article "A threshold model for local volatility: evidence of leverage and mean reversion effects on historical data" |
| Abstract: | Ce rapport technique présente la méthodologie et les résultats numériques pour les prix de 21 actifs boursiers sous l’hypothèse qu’ils se comportent comme un mouvement brownien oscillant avec dérive. Un tel modèle prend en compte les effets de levier et de retour à la moyenne. Ce rapport complète l’article A threshold model for local volatility: evidence of leverage and mean reversion effects on historical data. |
| Keywords: | Financial Mathematics, geometric Oscillating Brownian motion, Realized volatility estimator, Maximum likelihood, mean-reversion, leverage effect,mathématiques financières,Mouvement brownien géométrique oscillant,estimateur de l...,maximum de vrai...,estimateur de la volatilité réalisée,effet de levier,retour à la moy... |
| Date: | 2017–12–20 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01668975&r=ets |
| By: | Antoine Lejay (TOSCA - TO Simulate and CAlibrate stochastic models - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en Automatique - IECL - Institut Élie Cartan de Lorraine - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique); Paolo Pigato (WIAS - Weierstrass Institute for Applied Analysis and Stochastics - Forschungsverbund Berlin e.V. (FVB)) |
| Abstract: | In financial markets, low prices are generally associated with high volatilities and vice-versa, this well known stylized fact usually being referred to as leverage effect. We propose a local volatility model, given by a stochastic differential equation with piecewise constant coefficients, which accounts of leverage and mean-reversion effects in the dynamics of the prices. This model exhibits a regime switch in the dynamics accordingly to a certain threshold. It can be seen as a continuous time version of the Self-Exciting Threshold Autoregressive (SETAR) model. We propose an estimation procedure for the volatility and drift coefficients as well as for the threshold level. Tests are performed on the daily prices of 21 assets. They show empirical evidence for leverage and mean-reversion effects, consistent with the results in the literature. |
| Keywords: | realized volatility,Self-Exciting Threshold Autoregressive model,mean-reversion,leverage effect,Oscillating Brownian motion, Regime-Switching |
| Date: | 2017–12–20 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01669082&r=ets |
| By: | Jerry Hausman (Institute for Fiscal Studies and MIT); Maxim L. Pinkovskiy (Institute for Fiscal Studies) |
| Abstract: | We propose a new estimator for the dynamic panel model, which solves the failure of strict exogeneity by calculating the bias in the first-order conditions as a function of the autoregressive parameter and solving the resulting equation. The estimator does well in a wide variety of situations where other estimators do not perform well: stationary initial condition, predetermined but not strictly exogenous regressors, and the presence of correlation between the error terms and the fixed effects. We also propose a general method for including predetermined variables infixed-effects panel regressions. |
| JEL: | C01 C22 C23 |
| Date: | 2017–11–30 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:53/17&r=ets |
| By: | Korobilis, D; Yilmaz, K |
| Abstract: | We estimate a large Bayesian time-varying parameter vector autoregressive (TVP-VAR) model of daily stock return volatilities for 35 U.S. and European financial institutions. Based on that model we extract a connectedness index in the spirit of Diebold and Yilmaz(2014)(DYCI).We show that the connectedness index from the TVP-VAR model captures abrupt turning points better than the one obtained from rolling-windows VAR estimates. As the TVP-VAR based DYCI shows more pronounced jumps during important crisis moments, it captures the intensification of tensions in financial markets more accurately and timely than the rolling-windows based DYCI. Finally, we show that the TVP-VAR based index performs better in forecasting systemic events in the American and European financial sectors as well. |
| Keywords: | Connectedness, Vector autoregression, Time-varying parameter model, Rolling window estimation, Systemic risk, Financial institutions |
| Date: | 2018–01 |
| URL: | http://d.repec.org/n?u=RePEc:esy:uefcwp:20937&r=ets |
| By: | Guy Melard; Rajae R. Azrak |
| Abstract: | The paper provides a kind of Klimko-Nelson theoremsalternative in the case of conditional estimators for array timeseries, when the assumptions of almost sure convergence cannot be established.We do not assume stationarity nor even local stationarity.In addition, we provide sufficient conditions for two of the assumptionsand two theorems for the evaluation of the information matrixin array time series. |
| Keywords: | properties least-square array time series |
| Date: | 2017–12–31 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/263350&r=ets |
| By: | Georgiev, I; Harvey, DI; Leybourne, SJ; Taylor, AMR |
| Abstract: | We examine how the familiar spurious regression problem can manifest itself in the context of recently proposed predictability tests. For these tests to provide asymptotically valid inference, account has to be taken of the degree of persistence of the putative predictors. Failure to do so can lead to spurious over-rejections of the no predictability null hypothesis. A number of methods have been developed to achieve this. However, these approaches all make an underlying assumption that any predictability in the variable of interest is purely attributable to the predictors under test, rather than to any unobserved persistent latent variables, themselves uncorrelated with the predictors being tested. We show that where this assumption is violated, something that could very plausibly happen in practice, sizeable (spurious) rejections of the null can occur in cases where the variables under test are not valid predictors. In response, we propose a screening test for predictive regression invalidity based on a stationarity testing approach. In order to allow for an unknown degree of persistence in the putative predictors, and for both conditional and unconditional heteroskedasticity in the data, we implement our proposed test using a fixed regressor wild bootstrap procedure. We establish the asymptotic validity of this bootstrap test, which entails establishing a conditional invariance principle along with its bootstrap counterpart, both of which appear to be new to the literature and are likely to have important applications beyond the present context. We also show how our bootstrap test can be used, in conjunction with extant predictability tests, to deliver a two-step feasible procedure. Monte Carlo simulations suggest that our proposed bootstrap methods work well in finite samples. An illustration employing U.S. stock returns data demonstrates the practical usefulness of our procedures. |
| Keywords: | Predictive regression; causality; persistence; spurious regression; stationarity test; fixed regressor wild bootstrap; conditional distribution. |
| Date: | 2018–01 |
| URL: | http://d.repec.org/n?u=RePEc:esy:uefcwp:21006&r=ets |
| By: | Christian Gouriéroux (CREST; University of Toronto); Alain Monfort (CREST); Jean-Paul Renne (University of Lausanne) |
| Abstract: | The basic assumption of a structural VARMA model (SVARMA) is that it is driven by a white noise whose components are independent and can be interpreted as economic shocks, called "structural" shocks. When the errors are Gaussian, independence is equivalent to noncorrelation and these models face two kinds of identi?cation issues. The ?rst identi?cation problem is "static" and is due to the fact that there is an in?nite number of linear transformations of a given random vector making its components uncorrelated. The second identi?cation problem is "dynamic" and is a consequence of the fact that the SVARMA process may have a non invertible AR and/or MA matrix polynomial but, still, has the same second-order properties as a VARMA process in which both the AR and MA matrix polynomials are invertible (the fundamental representation). Moreover the standard Box-Jenkins approach [Box and Jenkins (1970)] automatically estimates the fundamental representation and, therefore, may lead to misspeci?ed Impulse Response Functions. The aim of this paper is to explain that these dif?culties are mainly due to the Gaussian assumption, and that both identi?cation challenges are solved in a non-Gaussian framework. We develop new simple parametric and semi-parametric estimation methods when there is non-fundamentalness in the moving average dynamics. The functioning and performances of these methods are illustrated by applications conducted on both simulated and real data. |
| Keywords: | Structural VARMA; Fundamental Representation; Identi?cation; Shocks; Impulse Response Function; Incomplete Likelihood; Composite Likelihood; Economic Scenario Generators |
| JEL: | C01 C15 C32 E37 |
| URL: | http://d.repec.org/n?u=RePEc:crs:wpaper:2017-08&r=ets |
| By: | Dominik Bertsche (University of Konstanz, Department of Economics, Box 129, 78457 Konstanz, Germany); Robin Braun (University of Konstanz, Graduate School of Decision Science, Department of Economics, Box 129, 78457 Konstanz, Germany) |
| Abstract: | In Structural Vector Autoregressive (SVAR) models, heteroskedasticity can be exploited to identify structural parameters statistically. In this paper, we propose to capture time variation in the second moment of structural shocks by a stochastic volatility (SV) model, assuming that their log variances follow latent AR(1) processes. Estimation is performed by Gaussian Maximum Likelihood and an efficient Expectation Maximization algorithm is developed for that purpose. Since the smoothing distributions required in the algorithm are intractable, we propose to approximate them either by Gaussian distributions or with the help of Markov Chain Monte Carlo (MCMC) methods. We provide simulation evidence that the SV-SVAR model works well in estimating the structural parameters also under model misspecification. We use the proposed model to study the interdependence between monetary policy and the stock market. Based on monthly US data, we find that the SV specification provides the best fit and is favored by conventional information criteria if compared to other models of heteroskedasticity, including GARCH, Markov Switching, and Smooth Transition models. Since the structural shocks identified by heteroskedasticity have no economic interpretation, we test conventional exclusion restrictions as well as Proxy SVAR restrictions which are overidentifying in the heteroskedastic model. |
| Keywords: | Structural Vector Autoregression (SVAR), Identification via heteroskedasticity, Stochastic Volatility, Proxy SVAR |
| JEL: | C32 |
| Date: | 2017–12–21 |
| URL: | http://d.repec.org/n?u=RePEc:knz:dpteco:1711&r=ets |
| By: | PREMINGER Arie; STORTI Giuseppe (Universita degli Studi di Salerno) |
| Abstract: | GARCH (1,1) models are widely used for modelling processes with time varying volatility. These include financial time series, which can be particularly heavy tailed. In this paper, we propose a novel log-transform-based least squares approach to the estimation of GARCH(1,1) models. Within this approach the scale of the estimated volatility is dependent on an unknown tuning constant. By means of a backtesting exercise on both real and simulated data we show that knowledge of the tuning constant is not crucial for Value at Risk prediction. However, this does not apply to many other applications where correct identification of the volatility scale is required. In order to overcome this di culty, we propose two alternative two-stage least squares estimators (LSE) and derive their asymptotic properties under very mild moment conditions for the errors. In particular, we establish the consistency and asymptotic normality at the standard convergence rate of √n for our estimators. Their finite sample properties are assessed by means of an extensive simulation study |
| Keywords: | GARCH (1,1), least squares estimation, heavy tails, consistency, asymptotic normality, two-step esti-mator |
| JEL: | C12 C13 C15 C22 C53 C58 |
| Date: | 2017–04–21 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2017015&r=ets |
| By: | Christian Gouriéroux (CREST; University of Toronto); Alain Monfort (CREST); Jean-Paul Renne (University of Lausanne) |
| Abstract: | The well-known problem of non-identifiability of structural VAR models disappears if the structural shocks are independent and if at most one of them is Gaussian. In that case, the relevant estimation technique is the Independent Component Analysis (ICA). Since the introduction of ICA by Comon (1994), various semi-parametric estimation methods have been proposed for "orthogonalizing" the error terms. These methods include pseudo maximum likelihood (PML) approaches and recursive PML. The aim of our paper is to derive the asymptotic properties of the PML approaches, in particular to study their consistency. We conduct Monte Carlo studies exploring the relative performances of these methods. Finally, an application based on real data shows that structural VAR models can be estimated without additional identification restrictions in the non-Gaussian case and that the usual restrictions can be tested. |
| Keywords: | Independent Component Analysis; Pseudo Maximum Likelihood; Identification; Cayley Transform; Structural Shocks; Structural VAR; Impulse Response Functions |
| JEL: | C14 C32 |
| URL: | http://d.repec.org/n?u=RePEc:crs:wpaper:2017-09&r=ets |