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on Econometric Time Series |
| By: | Johan Dahlin; Fredrik Lindsten; Thomas B. Sch\"on |
| Abstract: | Particle Metropolis-Hastings enables Bayesian parameter inference in general nonlinear state space models (SSMs). However, in many implementations a random walk proposal is used and this can result in poor mixing if not tuned correctly using tedious pilot runs. Therefore, we consider a new proposal inspired by quasi-Newton algorithms that achieves better mixing with less tuning. Compared to other Hessian based proposals, it only requires estimates of the gradient of the log-posterior. A possible application of this new proposal is parameter inference in the challenging class of SSMs with intractable likelihoods. We exemplify this application and the benefits of the new proposal by modelling log-returns of future contracts on coffee by a stochastic volatility model with symmetric $\alpha$-stable observations. |
| Date: | 2015–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1502.03656&r=ets |
| By: | Markus Bibinger; Moritz Jirak; Mathias Vetter; |
| Abstract: | This work develops change-point methods for statistics of high-frequency data. The main interest is the volatility of an Itˆo semi-martingale, which is discretely observed over a fixed time horizon. We construct a minimax-optimal test to discriminate different smoothness classes of the underlying stochastic volatility process. In a high-frequency framework we prove weak convergence of the test statistic under the hypothesis to an extreme value distribution. As a key example, under extremely mild smoothness assumptions on the stochastic volatility we thereby derive a consistent test for volatility jumps. A simulation study demonstrates the practical value in finite-sample applications. |
| Keywords: | high-frequency data, nonparametric change-point test, minimax-optimal test, stochastic volatility, volatility jumps |
| JEL: | C12 C14 |
| Date: | 2015–02 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2015-008&r=ets |
| By: | Ricardo Crisostomo |
| Abstract: | This paper analyses the implementation and calibration of the Heston Stochastic Volatility Model. We first explain how characteristic functions can be used to estimate option prices. Then we consider the implementation of the Heston model, showing that relatively simple solutions can lead to fast and accurate vanilla option prices. We also perform several calibration tests, using both local and global optimization. Our analyses show that straightforward setups deliver good calibration results. All calculations are carried out in Matlab and numerical examples are included in the paper to facilitate the understanding of mathematical concepts. |
| Date: | 2015–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1502.02963&r=ets |
| By: | Nikolaos Halidias; Ioannis Stamatiou |
| Abstract: | In this paper we want to exploit further the semi-discrete method appeared in \cite{halidias_stamatiou:2014}. We are interested in the numerical solution of mean reverting CEV processes that appear in financial mathematics and are described as non negative solutions of certain stochastic differential equations with sub-linear diffusion coefficients of the form $(x_t)^q,$ where $\frac{1}{2}<q<1.$ Our goal is to construct explicit numerical schemes that preserve positivity. We prove convergence of the proposed SD scheme with rate depending on the parameter $q.$ Furthermore, we verify our findings through numerical experiments. |
| Date: | 2015–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1502.03018&r=ets |
| By: | Malefaki, Valia |
| Abstract: | In this thesis I discuss flexible Bayesian treatment of the linear factor stochastic volatility model with latent factors, which proves to be essential in order to preserve parsimony when the number of cross section in the data grows. Based on the Bayesian model selection literature, I introduce a flexible prior specification which allows carrying out restriction search on the mean equation coefficients of the factor model – the loadings matrix. I use this restriction search as a data-based alternative to evaluate the cross sectional restrictions suggested by arbitrage pricing theory. A mixture innovation model is also proposed which generalizes the standard stochastic volatility specification and can also be interpreted as a restriction search in variance equation parameters. I comment on how to use the mixture innovation model to catch both gradual and abrupt changes in the stochastic evolution of the covariance matrix of high-dimensional financial datasets. This approach has the additional advantages of dating when large jumps in volatility have occurred in the data and determining whether these jumps are attributed to any of the factors, the innovation errors, or combinations of those. |
| Keywords: | Factor model; Bayesian prior |
| JEL: | C01 C11 G11 G12 |
| Date: | 2015–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:62216&r=ets |
| By: | Anindya Banerjee; Josep Lluis Carrion-i-Silvestre |
| Abstract: | Spurious regression analysis in panel data when the time series are cross-section dependent is analyzed in the paper. We show that consistent estimation of the long-run average parameter is possible once we control for cross-section dependence using cross-section averages in the spirit of the common correlated effects approach in Pesaran (2006). This result is used to design a panel cointegration test statistic accounting for cross-section dependence. The performance of the proposal is investigated in comparison with factor-based methods to control for cross-section dependence when strong, semi-weak and weak cross-section dependence may be present. |
| Keywords: | panel cointegration, cross-section dependence, common factors, spatial econometrics |
| JEL: | C12 C22 |
| Date: | 2014–12 |
| URL: | http://d.repec.org/n?u=RePEc:bir:birmec:15-02&r=ets |
| By: | Archil Gulisashvili; Frederi Viens; Xin Zhang |
| Abstract: | We consider a stochastic volatility stock price model in which the volatility is a non-centered continuous Gaussian process with arbitrary prescribed mean and covariance. By exhibiting a Karhunen-Lo\`{e}ve expansion for the integrated variance, and using sharp estimates of the density of a general second-chaos variable, we derive asymptotics for the stock price density and implied volatility in these models in the limit of large or small strikes. Our main result provides explicit expressions for the first three terms in the expansion of the implied volatility, based on three basic spectral-type statistics of the Gaussian process: the top eigenvalue of its covariance operator, the multiplicity of this eigenvalue, and the $L^{2}$ norm of the projection of the mean function on the top eigenspace. Strategies for using this expansion for calibration purposes are discussed. |
| Date: | 2015–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1502.05442&r=ets |
| By: | Tomasz Skoczylas (Faculty of Economic Sciences, University of Warsaw) |
| Abstract: | In this paper an alternative approach to modelling and forecasting single asset returns volatility is presented. A new, bivariate, flexible framework, which may be considered as a development of single-equation ARCH-type models, is proposed. This approach focuses on joint distribution of returns and observed volatility, measured by Garman-Klass variance estimator, and it enables to examine simultaneous dependencies between them. Proposed models are compared with benchmark GARCH and range-based GARCH (RGARCH) models in terms of prediction accuracy. All models are estimated with maximum likelihood method, using time series of EUR/PLN spot rate quotations and WIG20 index. Results are very encouraging especially for foreasting Value-at-Risk. Bivariate models achieved lesser rates of VaR exception, as well as lower coverage tests statistics, without being more conservative than its single-equation counterparts, as their forecasts errors measures are rather similar. |
| Keywords: | bivariate volatility models, joint distribution, range-based volatility estimators, Garman-Klass estimator, observed volatility, volatility modelling, GARCH, leverage, Value-at-Risk, volatility forecasting |
| JEL: | C13 C32 C53 C58 G10 G17 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:war:wpaper:2015-03&r=ets |
| By: | Winker, Peter; Helmut, Lütkepohl; Staszewska-Bystrova, Anna |
| Abstract: | In impulse response analysis estimation uncertainty is typically displayed by constructing bands around estimated impulse response functions. These bands may be based on frequentist or Bayesian methods. If they are based on the joint distribution in the Bayesian framework or the joint asymptotic distribution possibly constructed with bootstrap methods in the frequentist framework often individual con dence intervals or credibility sets are simply connected to obtain the bands. Such bands are known to be too narrow and have a joint con dence content lower than the desired one. If instead the joint distribution of the impulse response coe cients is taken into account and mapped into the band it is shown that such a band is typically rather conservative. It is argued that a smaller band can often be obtained by using the Bonferroni method. While these considerations are equally important for constructing forecast bands, we focus on the case of impulse responses in this study. |
| JEL: | C32 C53 C65 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc14:100597&r=ets |
| By: | Wagner, Martin; Wied, Dominik |
| Abstract: | We propose a monitoring procedure to detect a structural change from stationary to integrated behavior. When the procedure is applied to the errors of a relationship between integrated series it thus monitors a structural change from a cointegrating relationship to a spurious regression. The cointegration monitoring procedure is based on residuals from modified least squares estimation, using either Fully Modified, Dynamic or Integrated Modified OLS. The procedure is inspired by Chu et al. (1996) in that it is based on parameter estimation only on a pre-break ``calibration'' period rather than being based on sequential estimation over the full sample. We investigate the asymptotic behavior of the procedures under the null, for (fixed and local) alternatives and in case of parameter changes. We also study the finite sample performance via simulations. An application to credit default swap spreads illustrates the potential usefulness of the procedure. |
| JEL: | C32 C22 C52 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:vfsc14:100386&r=ets |
| By: | Biqing Cai; Jiti Gao; Dag Tjøstheim |
| Keywords: | β-null recurrent, cointegration, Markov chain, threshold VAR models <i>T</i><sup>1/2</sup>, while the convergence rate for the estimators for the coefficients in the middle regime is <i>T</i>. Also, we show that the convergence rate of the cointegrating coefficient is <i>T</i><sup>1/2</sup>, which is same as linear cointegration model. The Monte Carlo simulation results suggest that the estimators perform reasonably well in finite samples. Applying the proposed model to study the dynamic relationship between Federal funds rate and 3-month Treasury bill rate, we find that cointegrating coefficients are the same for the two regimes while the short run loading coefficients are different. |
| JEL: | C11 C58 G01 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2015-1&r=ets |