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on Econometric Time Series |
| By: | Rodríguez, Gabriel (Pontificia Universidad Católica del Perú); Tramontana, Roxana (Pontificia Universidad Católica del Perú) |
| Abstract: | Empirical research indicates that the volatility of stock return time series have long memory. However, it has been demonstrated that short memory processes contaminated with random level shifts can often be confused as being long memory. Often this feature is referred to as spurious long memory. This paper represents an empirical study of the random level shift (RLS) model using the approach of Lu and Perron (2010) and Li and Perron (2013) for the volatility of daily stocks returns data for ve Latin American countries. The RLS model consists of the sum of a short term memory component and a level shift component, where the level shift component is governed by a Bernoulli process with a shift probability . The estimation results suggest that the level shifts in the volatility of daily stocks returns data are infrequent but once they are taken into account, the long memory characteristic and the GARCH e¤ects disappear. An out-of-sample forecasting exercise is also provided. |
| Date: | 2015–07 |
| URL: | http://d.repec.org/n?u=RePEc:rbp:wpaper:2015-004&r=all |
| By: | Kim, Jaeho |
| Abstract: | This paper provides two Bayesian algorithms to efficiently estimate non-linear/non-Gaussian switching state space models by extending a standard Particle Markov chain Monte Carlo (PMCMC) method. Instead of iteratively running separate PMCMC steps using conventional approaches, the proposed methods generate continuous-state and discrete-regime indicator variables together from their joint smoothing distribution in one Gibbs block. The proposed Bayesian algorithms that are built upon the novel ideas of ancestor sampling and particle rejuvenation are robust to small numbers of particles and degenerate state transition equations. Moreover, the algorithms are applicable to any switching state space models, regardless of the Markovian property. The difficulty in conducting Bayesian model comparisons is overcome by adopting the Deviance Information Criterion (DIC). For illustration, a regime-dependent leverage effect in the U.S. stock market is investigated using the newly developed methods. A conventional regime switching stochastic volatility model is generalized to encompass the regime-dependent leverage effect and is applied to Standard and Poor’s 500 and NASDAQ daily return data. The resulting Bayesian posterior estimates indicate that the stronger (weaker) financial leverage effect is associated with a high (low) volatility regime. |
| Keywords: | Particle Markov Chain Monte Carlo, Regime switching, State space model, Leverage effect |
| JEL: | C11 C15 |
| Date: | 2015–10–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:67153&r=all |
| By: | Francq, Christian; Sucarrat, Genaro |
| Abstract: | Estimation of large financial volatility models is plagued by the curse of dimensionality: As the dimension grows, joint estimation of the parameters becomes infeasible in practice. This problem is compounded if covariates or conditioning variables (``X") are added to each volatility equation. In particular, the problem is especially acute for non-exponential volatility models (e.g. GARCH models), since there the variables and parameters are restricted to be positive. Here, we propose an estimator for a multivariate log-GARCH-X model that avoids these problems. The model allows for feedback among the equations, admits several stationary regressors as conditioning variables in the X-part (including leverage terms), and allows for time-varying covariances of unknown form. Strong consistency and asymptotic normality of an equation-by-equation least squares estimator is proved, and the results can be used to undertake inference both within and across equations. The flexibility and usefulness of the estimator is illustrated in two empirical applications. |
| Keywords: | Exponential GARCH, multivariate log-GARCH-X, VARMA-X, Equation-by-Equation Estimation (EBEE), Least Squares |
| JEL: | C13 C22 C32 C51 C58 |
| Date: | 2015–10–08 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:67140&r=all |
| By: | Sergio Afonso Lago Alves; Angelo Marsiglia Fasolo |
| Abstract: | This paper presents a new algorithm, based on a two-part Gibbs sampler with FFBS method, to recover the joint distribution of missing observations in a mixed-frequency dataset. The new algorithm relaxes most of the constraints usually presented in the literature, namely: (i) it does not require at least one time series to be observed every period; (ii) it provides an easy way to add linear restrictions based on the state space representation of the VAR; (iii) it does not require regularly-spaced time series at lower frequencies; and (iv) it avoids degeneration problems arising when states, or linear combination of states, are actually observed. In addition, the algorithm is well suited for embedding high-frequency real-time information for improving nowcasts and forecasts of lower frequency time series. We evaluate the properties of the algorithm using simulated data. Moreover, as empirical applications, we simulate monthly Brazilian GDP, comparing our results to the Brazilian IBC-BR, and recover what would historical PNAD-C unemployment rates look like prior to 2012 |
| Date: | 2015–09 |
| URL: | http://d.repec.org/n?u=RePEc:bcb:wpaper:400&r=all |
| By: | Stéphane Goutte (LED - Université Vincennes Saint-Denis (Paris 8)); Amine Ismail (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UP7 - Université Paris Diderot - Paris 7 - CNRS); Huyên Pham (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UP7 - Université Paris Diderot - Paris 7 - CNRS, ENSAE Paris-Tech & CREST, Laboratoire de Finance et d'Assurance - ENSAE Paris-Tech & CREST) |
| Abstract: | We develop and implement a method for maximum likelihood estimation of a regime-switching stochastic volatility model. Our model uses a continuous time stochastic process for the stock dynamics with the instantaneous variance driven by a Cox-Ingersoll-Ross (CIR) process and each parameter modulated by a hidden Markov chain. We propose an extension of the EM algorithm through the Baum-Welch implementation to estimate our model and filter the hidden state of the Markov chain while using the VIX index to invert the latent volatility state. Using Monte Carlo simulations, we test the convergence of our algorithm and compare it with an approximate likelihood procedure where the volatility state is replaced by the VIX index. We found that our method is more accurate than the approximate procedure. Then, we apply Fourier methods to derive a semi-analytical expression of S&P 500 and VIX option prices, which we calibrate to market data. We show that the model is sufficiently rich to encapsulate important features of the joint dynamics of the stock and the volatility and to consistently fit option market prices. |
| Keywords: | EM algorithm,Regime-switching model, Stochastic volatility, VIX index, Baum-Welch algorithm. |
| Date: | 2015–10–06 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01212018&r=all |
| By: | Michel Fliess (LIX - Laboratoire d'informatique de l'école polytechnique [Palaiseau] - Polytechnique - X - CNRS, ALIEN); Cédric Join (INRIA Lille - Nord Europe - INRIA, CRAN - Centre de Recherche en Automatique de Nancy - CNRS - UL - Université de Lorraine, ALIEN) |
| Abstract: | Recent advances in the understanding of time series permit to clarify seasonalities and cycles, which might be rather obscure in today's literature. A theorem due to P. Cartier and Y. Perrin, which was published only recently, in 1995, and several time scales yield, perhaps for the first time, a clear-cut definition of seasonalities and cycles. Their detection and their extraction, moreover, become easy to implement. Several computer experiments with concrete data from various fields are presented and discussed. The conclusion suggests the application of this approach to the debatable Kondriatev waves. |
| Keywords: | time scales, nonstandard analysis, deseasonalization, Kondriatev waves,time series, seasonalities, cycles, decomposition, detection, extraction, trend |
| Date: | 2015–12–14 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-01208171&r=all |
| By: | Jia Chen; Degui Li; Oliver Linton; Zudi Lu |
| Abstract: | In this paper, we consider semiparametric model averaging of the nonlinear dynamic time series system where the number of exogenous regressors is ultra large and the number of autoregressors is moderately large. In order to accurately forecast the response variable, we propose two semiparametric approaches of dimension reduction among the exogenous regressors and auto-regressors (lags of the response variable). In the first approach, we introduce a Kernel Sure Independence Screening (KSIS) technique for the nonlinear time series setting which screens out the regressors whose marginal regression (or auto-regression) functions do not make significant contribution to estimating the joint multivariate regression function and thus reduces the dimension of the regressors from a possible exponential rate to a certain polynomial rate, typically smaller than the sample size; then we consider a semiparametric method of Model Averaging MArginal Regression (MAMAR) for the regressors and auto-regressors that survive the screening procedure, and propose a penalised MAMAR method to further select the regressors which have significant effects on estimating the multivariate regression function and predicting the future values of the response variable. In the second approach, we impose an approximate factor modelling structure on the ultra-high dimensional exogenous regressors and use a well-known principal component analysis to estimate the latent common factors, and then apply the penalised MAMAR method to select the estimated common factors and lags of the response variable which are significant. Through either of the two approaches, we can finally determine the optimal combination of the signicant marginal regression and auto-regression functions. Under some regularity conditions, we derive the asymptotic properties for the two semiparametric dimension-reduction approaches. Some numerical studies including simulation and an empirical application are provided to illustrate the proposed methodology. |
| Keywords: | Kernel smoother, penalised MAMAR, principal component analysis, semiparametric approximation, sure independence screening, ultra-high dimensional time series. |
| JEL: | C14 C22 C52 |
| Date: | 2015–10 |
| URL: | http://d.repec.org/n?u=RePEc:yor:yorken:15/18&r=all |