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on Econometric Time Series |
| By: | Taiane S. Prass; S\'ilvia R. C. Lopes |
| Abstract: | We consider the Fractionally Integrated Exponential Generalized Autoregressive Conditional Heteroskedasticity process, denoted by FIEGARCH(p,d,q), introduced by Bollerslev and Mikkelsen (1996). We present a simulated study regarding the estimation of the risk measure $VaR_p$ on FIEGARCH processes. We consider the distribution function of the portfolio log-returns (univariate case) and the multivariate distribution function of the risk-factor changes (multivariate case). We also compare the performance of the risk measures $VaR_p$, $ES_p$ and MaxLoss for a portfolio composed by stocks of four Brazilian companies. |
| Date: | 2013–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1305.5238&r=ets |
| By: | J. D. Deuschel; P. K. Friz; A. Jacquier; S. Violante |
| Abstract: | In the compagnion paper [Marginal density expansions for diffusions and stochastic volatility, part I] we discussed density expansions for multidimensional diffusions $(X^1,...,X^d)$, at fixed time $T$ and projected to their first $l$ coordinates, in the small noise regime. Global conditions were found which replace the well-known "not-in-cutlocus" condition known from heat-kernel asymptotics. In the present paper we discuss financial applications; these include tail and implied volatility asymptotics in some correlated stochastic volatility models. In particular, we solve a problem left open by A. Gulisashvili and E.M. Stein (2009). |
| Date: | 2013–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1305.6765&r=ets |
| By: | Michael McAleer (University of Canterbury); Felix Chan; Les Oxley |
| Abstract: | The papers in this special issue of Mathematics and Computers in Simulation cover the following topics. Improving judgmental adjustment of model-based forecasts, whether forecast updates are progressive, on a constrained mixture vector autoregressive model, whether all estimators are born equal. The empirical properties of some estimators of long memory, characterising trader manipulation in a limitorder driven market, measuring bias in a term-structure model of commodity prices through the comparison of simultaneous and sequential estimation, modeling tail credit risk using transition matrices, evaluation of the DPC-based inclusive payment system in Japan for cataract operations by a new model, the matching of lead underwriters and issuing firms in the Japanese corporate bond market, stochastic life table forecasting. A time-simultaneous fan chart application, adaptive survey designs for sampling rare and clustered populations, income distribution inequality, globalization, and innovation. A general equilibrium simulation, whether exchange rates affect consumer prices. A comparative analysis for Australia, China and India, the impacts of exchange rates on Australia's domestic and outbound travel markets, clean development mechanism in China. Regional distribution and prospects, design and implementation of a Web-based groundwater data management system, the impact of serial correlation on testing for structural change in binary choice model. Monte Carlo evidence, and coercive journal self citations, impact factor, journal influence and article influence. |
| Keywords: | Modeling, simulation, forecasting, time series models, trading, credit risk, empirical finance, health economics, sampling, groundwater systems, exchange rates, structural change, citations |
| JEL: | C15 C63 E27 E37 E47 F37 F47 |
| Date: | 2013–05–20 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:13/18&r=ets |
| By: | BAUWENS, Luc (Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium); otranto, EDOARDO (University of Messina, Italy) |
| Abstract: | Several models have been developed to capture the dynamics of the conditional correlations between time series of financial returns, but few studies have investigated the determinants of the correlation dynamics. A common opinion is that the market volatility is a major determinant of the correlations. We extend some models to capture explicitly the dependence of the correlations on the volatility of the market of interest. The models differ in the way by which the volatility influences the correlations, which can be transmitted through linear or nonlinear, and direct or indirect effects. They are applied to different data sets to verify the presence and possible regularity of the volatility impact on correlations. |
| Keywords: | volatility effects, conditional correlation, DCC, Markov switching |
| JEL: | C32 C58 |
| Date: | 2013–05–06 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2013014&r=ets |
| By: | HAFNER, Christian (Université catholique de Louvain, CORE & ISBA, Belgium); LINTON, Oliver (Faculty of Economics, Cambridge University, UK) |
| Abstract: | The EGARCH is a popular model for discrete time volatility since it allows for asymmetric effects and naturally ensures positivity even when including exogenous variables. Estimation and inference is usually done via maximum likelihood. Although some progress has been made recently, a complete distribution theory of MLE for EGARCH models is still missing. Furthermore, the estimation procedure itself may be highly sensitive to starting values, the choice of numerical optimation algorithm, etc. We present an alter- native estimator that is available in a simple closed form and which could be used, for example, as starting values for MLE. The estimator of the dynamic parameter is inde- pendent of the innovation distribution. For the other parameters we assume that the innovation distribution belongs to the class of Generalized Error Distributions (GED), profiling out its parameter in the estimation procedure. We discuss the properties of the proposed estimator and illustrate its performance in a simulation study. |
| Keywords: | autocorrelations, generalized error distribution, method of moments estimator, Newton-Raphson |
| JEL: | C12 C13 C14 |
| Date: | 2013–05–22 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2013022&r=ets |
| By: | Christian Gouriéroux (CREST and University of Toronto); Jean-Michel Zakoian (CREST and University Lille 3) |
| Abstract: | The linear mixed causal and noncausal autoregressive processes provide often a better fit to economic and financial time series than the standard causal linear autoregressive processes. By considering the example of the noncausal Cauchy autoregressive process, we show that it might be explained by the special associated nonlinear causal dynamics. Indeed, this causal dynamics can include unit root, bubble phenomena, or asymmetric cycles often observed on financial markets. The noncausal Cauchy autoregressive process provides a new modelling for explosive multiple bubbles and their transmission in a multivariate dynamic framework. We also explain why standard unit root tests will fail in detecting such explosive bubbles |
| Keywords: | Causal Innovation, Explosive Bubble, Noncausal Process, Unit Root, Bubble Cointegration |
| Date: | 2013–02 |
| URL: | http://d.repec.org/n?u=RePEc:crs:wpaper:2013-04&r=ets |
| By: | Istvan Barra (VU University Amsterdam); Lennart Hoogerheide (VU University Amsterdam); Siem Jan Koopman (VU University Amsterdam); Andre Lucas (VU University Amsterdam) |
| Abstract: | We propose a new methodology for the Bayesian analysis of nonlinear non-Gaussian state space models with a Gaussian time-varying signal, where the signal is a function of a possibly high-dimensional state vector. The novelty of our approach is the development of proposal densities for the joint posterior density of parameter and state vectors: a mixture of Student's t-densities as the marginal proposal density for the parameter vector, and a Gaussian density as the conditional proposal density for the signal given the parameter vector. We argue that a highly efficient procedure emerges when these proposal densities are used in an independent Metropolis-Hastings algorithm. A particular feature of our approach is that smoothed estimates of the states and an estimate of the marginal likelihood are obtained directly as an output of the algorithm. Our methods are computationally efficient and produce more accurate estimates when compared to recently proposed alternativ es. We present extensive simulation evidence for stochastic volatility and stochastic intensity models. For our empirical study, we analyse the performance of our method for stock return data and corporate default panel data. |
| Keywords: | nonlinear non-Gaussian state space model, Bayesian inference, Monte Carlo estimation, Metropolis-Hastings algorithm, mixture of Student's t-distributions |
| JEL: | C11 C15 C22 C32 C58 |
| Date: | 2012–03–26 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2013050&r=ets |
| By: | Manabu Asai (Soka University, Japan); Massimiliano Caporin (University of Padova, Italy); Michael McAleer (Erasmus University Rotterdam, The Netherlands, Complutense University of Madrid, Spain, and Kyoto University, Japan) |
| Abstract: | Most multivariate variance or volatility models suffer from a common problem, the “curse of dimensionality”. For this reason, most are fitted under strong parametric restrictions that reduce the interpretation and flexibility of the models. Recently, the literature has focused on multivariate models with milder restrictions, whose purpose is to combine the need for interpretability and efficiency faced by model users with the computational problems that may emerge when the number of assets can be very large. We contribute to this strand of the literature by proposing a block-type parameterization for multivariate stochastic volatility models. The empirical analysis on stock returns on the US market shows that 1% and 5 % Value-at-Risk thresholds based on one-step-ahead forecasts of covariances by the new specification are satisfactory for the period including the Global Financial Crisis. |
| Keywords: | block structures; multivariate stochastic volatility; curse of dimensionality; leverage effects; multi-factors; heavy-tailed distribution |
| JEL: | C32 C51 C10 |
| Date: | 2013–05–27 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2013073&r=ets |
| By: | David Ardia; Lennart F. Hoogerheide |
| Abstract: | We investigate the time-variation of the cross-sectional distribution of asymmetric GARCH model parameters over the S&P 500 constituents for the period 2000-2012. We find the following results. First, the unconditional variances in the GARCH model obviously show major time-variation, with a high level after the dot-com bubble and the highest peak in the latest financial crisis. Second, in these more volatile periods it is especially the persistence of deviations of volatility from is unconditional mean that increases. Particularly in the latest financial crisis, the estimated models tend to Integrated GARCH models, which can cope with an abrupt regime-shift from low to high volatility levels. Third, the leverage effect tends to be somewhat higher in periods with higher volatility. Our findings are mostly robust across sectors, except for the technology sector, which exhibits a substantially higher volatility after the dot-com bubble. Further, the financial sector shows the highest volatility during the latest financial crisis. Finally, in an analysis of different market capitalizations, we find that small cap stocks have a higher volatility than large cap stocks where the discrepancy between small and large cap stocks increased during the latest financial crisis. Small cap stocks also have a larger conditional kurtosis and a higher leverage effect than mid cap and large cap stocks. |
| Keywords: | GARCH, GJR, equity, leverage effect, S&P 500 universe |
| JEL: | C22 C52 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:lvl:lacicr:1313&r=ets |
| By: | Jennifer Castle; David Hendry |
| Abstract: | We consider model selection for non-linear dynamic equations with more candidate variables than observations, based on a general class of non-linear-in-the-variables functions, addressing possible location shifts by impulse-indicator saturation. After an automatic search delivers a simplified congruent terminal model, an encompassing test can be implemented against an investigator's preferred non-linear function. When that is non-linear in the parameters, such as a threshold model, the overall approach can only be semi-automatic. The method is applied to re-analyze an empirical model of real wages in the UK over 1860-2004, updated and extended to 2005-2011 for forecast evaluation. |
| Keywords: | Non-linear models, location shifts, model selection, autometrics, impulse-indicator saturation |
| JEL: | C51 C22 |
| Date: | 2013–05–16 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:654&r=ets |
| By: | Giuseppe Cavaliere (University of Bologna); Morten Ørregaard Nielsen (Queen's University and CREATES); A.M. Robert Taylor (University of Nottingham) |
| Abstract: | We propose bootstrap implementations of the asymptotic Wald, likelihood ratio and Lagrange multiplier tests for the order of integration of a fractionally integrated time series. Our main purpose in doing so is to develop tests which are robust to both conditional and unconditional heteroskedasticity of a quite general and unknown form in the shocks. We show that neither the asymptotic tests nor the analogues of these which obtain from using a standard i.i.d. bootstrap admit pivotal asymptotic null distributions in the presence of heteroskedasticity, but that the corresponding tests based on the wild bootstrap principle do. An heteroskedasticity-robust Wald test, based around a sandwich estimator of the variance, is also shown to deliver asymptotically pivotal inference under the null, and we show that it can be successfully bootstrapped using either i.i.d. resampling or the wild bootstrap. We quantify the dependence of the asymptotic size and local power of the asymptotic tests on the degree of heteroskedasticity present. An extensive Monte Carlo simulation study demonstrates that significant improvements in finite sample behaviour can be obtained by the bootstrap vis-Ã -vis the corresponding asymptotic tests in both heteroskedastic and homoskedastic environments. The results also suggest that a bootstrap algorithm based on model estimates obtained under the null hypothesis is preferable to one which uses unrestricted model estimates. |
| Keywords: | Bootstrap, conditional heteroskedasticity, fractional integration, likelihood-based inference, unconditional heteroskedasticity |
| JEL: | C12 C22 |
| Date: | 2013–05 |
| URL: | http://d.repec.org/n?u=RePEc:qed:wpaper:1309&r=ets |