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on Econometric Time Series |
| By: | Wei Wei (Aarhus University and CREATES); Denis Pelletier (North Carolina State University) |
| Abstract: | Market microstructure theories suggest that the durations between transactions carry information about volatility. This paper puts forward a model featuring stochastic volatility, stochastic conditional duration, and jumps to analyze high frequency returns and durations. Durations affect price jumps in two ways: as exogenous sampling intervals, and through the interaction with volatility. We adopt a bivariate Ornstein-Ulenbeck process to model intraday volatility and conditional duration. We develop a MCMC algorithm for the inference on irregularly spaced multivariate processes with jumps. The algorithm provides smoothed estimates of the latent variables such as spot volatility, conditional duration, jump times, and jump sizes. We apply this model to IBM data and find that volatility and conditional duration are interdependent. We also find that jumps play an important role in return variation, but joint modeling of volatility and conditional duration reduces significantly the need for jumps. |
| Keywords: | Durations, Stochastic Volatility, Price jumps, High-frequency data, Bayesian inference |
| JEL: | C1 C5 G1 |
| Date: | 2015–08–06 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2015-34&r=ets |
| By: | Jie Ding; Mohammad Noshad; Vahid Tarokh |
| Abstract: | A new criterion is introduced for determining the order of an autoregressive model fit to time series data. The proposed technique is shown to give a consistent and asymptotically efficient order estimation. It has the benefits of the two well-known model selection techniques, the Akaike information criterion and the Bayesian information criterion. When the true order of the autoregression is relatively large compared with the sample size, the Akaike information criterion is known to be efficient, and the new criterion behaves in a similar manner. When the true order is finite and small compared with the sample size, the Bayesian information criterion is known to be consistent, and so is the new criterion. Thus the new criterion builds a bridge between the two classical criteria automatically. In practice, where the observed time series is given without any prior information about the autoregression, the proposed order selection criterion is more flexible and robust compared with classical approaches. Numerical results are presented demonstrating the robustness of the proposed technique when applied to various datasets. |
| Date: | 2015–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1508.02473&r=ets |
| By: | Beaudry, Paul; Fève, Patrick; Guay, Alain; Portier, Franck |
| Abstract: | When a structural model has a nonfundamental VAR representation, standard SVAR techniques cannot be used to properly identify the effects of structural shocks. This problem is known to potentially arise when one of the structural shocks represents news about the future. However, as we shall show, in many cases the nonfundamental representation of a time series may be very close to its fundamental representation implying that standard SVAR techniques may provide a very good approximation of the effects of structural shocks even when the nonfundamentalness is formally present. This leads to the question: When is nonfundamentalness a real problem? In this paper we derive and illustrate a diagnostic based on a R2 which provides a simple means of detecting whether nonfundamentalness is likely to be a quantitatively important problem in an applied settings. We use the identification of technological news shocks in US data as our running example. |
| Keywords: | business cycles; news; nonfundamentalness; svar |
| JEL: | E3 |
| Date: | 2015–08 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:10763&r=ets |
| By: | Barend Abeln; Jan P.A.M. Jacobs |
| Abstract: | Seasonality in macroeconomic time series can obscure movements of other components in a series that are operationally more important for economic and econometric analyses. Indeed, in practice one often prefers to work with seasonally adjusted data to assess the current state of the economy and its future course. Recently, two most widely used seasonal adjustment methods, Census X-12-ARIMA and TRAMO-SEATS, merged into X-13ARIMA-SEATS to become a new industry standard. In this paper, we compare and contrast X-13ARIMA-SEATS with a seasonal adjustment program called CAMPLET, an acronym of its tuning parameters. CAMPLET consists of a simple adaptive procedure which separates the seasonal component and the non-seasonal component from an observed time series. Once this process has been carried out there will be no need to revise these components at a later stage when more observations become available, in contrast with other seasonal adjustment methods. The paper briefly reviews of X-13ARIMA-SEATS and describes the main features of CAMPLET. We evaluate the outcomes of both methods in a controlled simulation framework using a variety of processes. Finally, we apply the X-13ARIMA-SEATS and CAMPLET methods to three time series: U.S. non-farm payroll employment, operational income of Ahold, and real GDP in the Netherlands. |
| Keywords: | seasonal adjustment, real-time, seasonal pattern, simulations, employment, operational income, real GDP |
| JEL: | C22 E24 E32 E37 |
| Date: | 2015–07 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2015-25&r=ets |
| By: | Joshua C.C. Chan; Eric Eisenstat |
| Abstract: | We develop importance sampling methods for computing two popular Bayesian model comparison criteria, namely, the marginal likelihood and deviance information criterion (DIC) for TVP-VARs with stochastic volatility. The proposed estimators are based on the integrated likelihood, which are substantially more reliable than alternatives. Specifically, integrated likelihood evaluation is achieved by integrating out the time-varying parameters analytically, while the log-volatilities are integrated out numerically via importance sampling. Using US and Australian data, we find overwhelming support for the TVPVAR with stochastic volatility compared to a conventional constant coefficients VAR with homoscedastic innovations. Most of the gains, however, appear to have come from allowing for stochastic volatility rather than time variation in the VAR coefficients or contemporaneous relationships. Indeed, according to both criteria, a constant coefficients VAR with stochastic volatility receives similar support as the more general model with time-varying parameters. |
| Keywords: | Bayesian, state space, marginal likelihood, deviance information criterion, great moderation |
| JEL: | C11 C52 E32 E52 |
| Date: | 2015–08 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2015-32&r=ets |
| By: | Amélie Charles (Audencia Recherche - Audencia); Olivier Darné (LEMNA - Laboratoire d'économie et de management de Nantes Atlantique - UN - Université de Nantes); Fabien Tripier (CEPII - Centre d'Etudes Prospectives et d'Informations Internationales - Centre d'analyse stratégique, CLERSE - Centre lillois d'études et de recherches sociologiques et économiques - CNRS - Université Lille 1 - Sciences et technologies) |
| Abstract: | The performance of unit root tests on simulated series is compared, using the business-cycle model of Chang et al. (2007) to generate data. Overall, Monte Carlo simulations show that the e¢ cient unit root tests of Ng and Perron (2001) are more powerful than the standard unit root tests. These e¢ cient tests are frequnetly able (i) to reject the unit-root hypothesis on simulated series, using the best speci…-cation of the business-cycle model found by Chang et al. (2007), in which hours worked are stationary with adjustment costs, and (ii) to reduce the gap between the theoretical impulse response functions and those estimated with a Structural VAR model. The results of Monte Carlo simulations show that the hump-shaped behaviour of data can explain the divergence between unit root tests. |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-01101618&r=ets |
| By: | Guillaume Chevillon (ESSEC Business School - Essec Business School) |
| Abstract: | Standard tests for the rank of cointegration of a vector autoregressive process present distributions that are affected by the presence of deterministic trends. We consider the recent approach of Demetrescu et al. (2009) who recommend testing a composite null. We assess this methodology in the presence of trends (linear or broken) whose magnitude is small enough not to be detectable at conventional significance levels. We model them using local asymptotics and derive the properties of the test statistics. We show that whether the trend is orthogonal to the cointegrating vector has a major impact on the distributions but that the test combination approach remains valid. We apply of the methodology to the study of cointegration properties between global temperatures and the radiative forcing of human gas emissions. We find new evidence of Granger Causality. |
| Date: | 2013–11 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00914830&r=ets |
| By: | Bernard Candelpergher (JAD - Laboratoire Jean Alexandre Dieudonné - UNS - Université Nice Sophia Antipolis - CNRS); Michel Miniconi (JAD - Laboratoire Jean Alexandre Dieudonné - CNRS - UNS - Université Nice Sophia Antipolis); Florian Pelgrin (HEC - Faculté des Hautes Etudes Commerciales - Université de Lausanne) |
| Abstract: | Contemporaneous aggregation of individual AR(1) random processes might lead to different properties of the limit aggregated time series, in particular, long memory (Granger, 1980). We provide a new characterization of the series of autoregressive coefficients, which is defined from the Wold representation of the limit of the aggregate stochastic process, in the presence of long-memory features. Especially the infinite autoregressive stochastic process defined by the almost sure representation of the aggregate process has a unit root in the presence of the long-memory property. Finally we discuss some examples using some well-known probability density functions of the autoregressive random parameter in the aggregation literature. JEL Classification Code: C2, C13. |
| Date: | 2015–08–07 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01166527&r=ets |
| By: | Anne Péguin-Feissolle (AMSE - Aix-Marseille School of Economics - EHESS - École des hautes études en sciences sociales - Centre national de la recherche scientifique (CNRS) - Ecole Centrale Marseille (ECM) - AMU - Aix-Marseille Université); Bilel Sanhaji (AMSE - Aix-Marseille School of Economics - EHESS - École des hautes études en sciences sociales - Centre national de la recherche scientifique (CNRS) - Ecole Centrale Marseille (ECM) - AMU - Aix-Marseille Université) |
| Abstract: | We introduce two multivariate constant conditional correlation tests that require little knowledge of the functional relationship determining the conditional correlations. The first test is based on artificial neural networks and the second one is based on a Taylor expansion of each unknown conditional correlation. These new tests can be seen as general misspecification tests of a large set of multivariate GARCH-type models. We investigate the size and the power of these tests through Monte Carlo experiments. Moreover, we study their robustness to non-normality by simulating some models such as the GARCH−t and Beta−t−EGARCH models. We give some illustrative empirical examples based on financial data. |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-01133751&r=ets |
| By: | Shin Kanaya (Institute for Fiscal Studies); Dennis Kristensen (Institute for Fiscal Studies and cemmap and UCL) |
| Abstract: | A two-step estimation method of stochastic volatility models is proposed: In the first step, we nonparametrically estimate the (unobserved) instantaneous volatility process. In the second step, standard estimation methods for fully observed diffusion processes are employed, but with the filtered/estimated volatility process replacing the latent process. Our estimation strategy is applicable to both parametric and nonparametric stochastic volatility models, and can handle both jumps and market microstructure noise. The resulting estimators of the stochastic volatility model will carry additional biases and variances due to the first-step estimation, but under regularity conditions we show that these vanish asymptotically and our estimators inherit the asymptotic properties of the infeasible estimators based on observations of the volatility process. A simulation study examines the finite-sample properties of the proposed estimators. |
| Keywords: | Realized spot volatility, stochastic volatility, kernel estimation, nonparametric, semi-parametric |
| JEL: | C14 C32 C58 |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:09/15&r=ets |
| By: | Raffaella Giacomini (Institute for Fiscal Studies and cemmap and UCL); Toru Kitagawa (Institute for Fiscal Studies and cemmap and UCL) |
| Abstract: | We propose a method for conducting inference on impulse responses in structural vector autoregressions (SVARs) when the impulse response is not point identiï¬ed because the number of equality restrictions one can credibly impose is not sufficient for point identiï¬cation and/or one imposes sign restrictions. We proceed in three steps. We ï¬rst deï¬ne the object of interest as the identiï¬ed set for a given impulse response at a given horizon and discuss how inference is simple when the identiï¬ed set is convex, as one can limit attention to the set’s upper and lower bounds. We then provide easily veriï¬able conditions on the type of equality and sign restrictions that guarantee convexity. These cover most cases of practical interest, with exceptions including sign restrictions on multiple shocks and equality restrictions that make the impulse response locally, but not globally, identiï¬ed. Second, we show how to conduct inference on the identiï¬ed set. We adopt a robust Bayes approach that considers the class of all possible priors for the non-identiï¬ed aspects of the model and delivers a class of associated posteriors. We summarize the posterior class by reporting the "posterior mean bounds", which can be interpreted as an estimator of the identiï¬ed set. We also consider a "robustiï¬ed credible region" which is a measure of the posterior uncertainty about the identiï¬ed set. The two intervals can be obtained using a computationally convenient numerical procedure. Third, we show that the posterior bounds converge asymptotically to the identiï¬ed set if the set is convex. If the identiï¬ed set is not convex, our posterior bounds can be interpreted as an estimator of the convex hull of the identiï¬ed set. Finally, a useful diagnostic tool delivered by our procedure is the posterior belief about the plausibility of the imposed identifying restrictions. |
| Date: | 2014–11 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:45/14&r=ets |