
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 outofsample forecasting exercise is also provided. 
Date:  2015–07 
URL:  http://d.repec.org/n?u=RePEc:rbp:wpaper:2015004&r=all 
By:  Kim, Jaeho 
Abstract:  This paper provides two Bayesian algorithms to efficiently estimate nonlinear/nonGaussian 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 continuousstate and discreteregime 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 regimedependent 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 regimedependent 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 nonexponential 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 logGARCHX model that avoids these problems. The model allows for feedback among the equations, admits several stationary regressors as conditioning variables in the Xpart (including leverage terms), and allows for timevarying covariances of unknown form. Strong consistency and asymptotic normality of an equationbyequation 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 logGARCHX, VARMAX, EquationbyEquation 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 twopart Gibbs sampler with FFBS method, to recover the joint distribution of missing observations in a mixedfrequency 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 regularlyspaced 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 highfrequency realtime 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 IBCBR, and recover what would historical PNADC 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 SaintDenis (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 ParisTech & CREST, Laboratoire de Finance et d'Assurance  ENSAE ParisTech & CREST) 
Abstract:  We develop and implement a method for maximum likelihood estimation of a regimeswitching stochastic volatility model. Our model uses a continuous time stochastic process for the stock dynamics with the instantaneous variance driven by a CoxIngersollRoss (CIR) process and each parameter modulated by a hidden Markov chain. We propose an extension of the EM algorithm through the BaumWelch 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 semianalytical 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,Regimeswitching model, Stochastic volatility, VIX index, BaumWelch algorithm. 
Date:  2015–10–06 
URL:  http://d.repec.org/n?u=RePEc:hal:wpaper:hal01212018&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 clearcut 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:hal01208171&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 autoregressors (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 autoregression) 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 autoregressors 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 ultrahigh dimensional exogenous regressors and use a wellknown 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 autoregression functions. Under some regularity conditions, we derive the asymptotic properties for the two semiparametric dimensionreduction 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, ultrahigh dimensional time series. 
JEL:  C14 C22 C52 
Date:  2015–10 
URL:  http://d.repec.org/n?u=RePEc:yor:yorken:15/18&r=all 