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on Econometric Time Series |
| By: | Monica Billio (University of Venice, GRETA Assoc. and School for Advanced Studies in Venice); Roberto Casarin (University of Venice, GRETA Assoc. and School for Advanced Studies in Venice); Francesco Ravazzolo (Norges Bank (Central Bank of Norway) and BI Norwegian Business School); Herman K. van Dijk (Econometric Institute, Erasmus University Rotterdam and VU University Amsterdam and Tinbergen Institute) |
| Abstract: | We propose new forecast combination schemes for predicting turning points of business cycles. The combination schemes deal with the forecasting performance of a given set of models and possibly providing better turning point predictions. We consider turning point predictions generated by autoregressive (AR) and Markov-Switching AR models, which are commonly used for business cycle analysis. In order to account for parameter uncertainty we consider a Bayesian approach to both estimation and prediction and compare, in terms of statistical accuracy, the individual models and the combined turning point predictions for the United States and Euro area business cycles. |
| Keywords: | Turning Points, Markov-switching, Forecast Combination, Bayesian Model Averaging |
| JEL: | C11 C15 C53 E37 |
| Date: | 2012–04–10 |
| URL: | http://d.repec.org/n?u=RePEc:bno:worpap:2012_04&r=ets |
| By: | M. Angeles Carnero Fernández (Universidad de Alicante); M. Hakan Eratalay (Dpto. Fundamentos del Análisis Económico) |
| Date: | 2012–03 |
| URL: | http://d.repec.org/n?u=RePEc:ivi:wpasad:2012-10&r=ets |
| By: | Michael McAleer (Erasmus University Rotterdam,Tinbergen Institute,Kyoto University,Complutense University of Madrid); Manabu Asai (Faculty of Economics Soka University); Massimiliano Caporin (Department of Economics and Management “Marco Fanno”University of Padova) |
| 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 was to combine the need for interpretability and efficiency faced by model users with the computational problems that may emerge when the number of assets is quite large. We contribute to this strand of the literature proposing a block-type parameterization for multivariate stochastic volatility models. The empirical analysis on stock returns on 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 includes 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: | 2012–04 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:812&r=ets |
| By: | Márcio Laurini (IBMEC Business School); Márcio Alves Diniz (Departament of Statistics - UFSCAR) |
| Abstract: | This article discusses the use of Integrated Nested Laplace Approximations (INLA) in inference procedures and construction of unit root tests in stochastic volatility models. This approach allows to obtain accurate analytical approximations for the parameters and latent volatities, representing an alternative to methods based on Markov Chain Monte Carlo. |
| Keywords: | Unit Roots, Stochastic Volatility, Integrated Nested Laplace Approximations |
| JEL: | C11 C12 C22 |
| Date: | 2012–04–04 |
| URL: | http://d.repec.org/n?u=RePEc:ibr:dpaper:2012-05&r=ets |
| By: | Massimiliano Caporin; Michael McAleer (University of Canterbury) |
| Abstract: | During the last 15 years, several Multivariate GARCH (MGARCH) models have appeared in the literature. Recent research has begun to examine MGARCH specifications in terms of their out-of-sample forecasting performance. We provide an empirical comparison of alternative MGARCH models, namely BEKK, DCC, Corrected DCC (cDCC), CCC, OGARCH Exponentially Weighted Moving Average, and covariance shrinking, using historical data for 89 US equities. We contribute to the literature in several directions. First, we consider a wide range of models, including the recent cDCC and covariance shrinking models. Second, we use a range of tests and approaches for direct and indirect model comparison, including the Model Confidence Set. Third, we examine how the robust model rankings are influenced by the crosssectional dimension of the problem. |
| Keywords: | Covariance forecasting; model confidence set; robust model ranking; MGARCH; robust model comparison |
| JEL: | C18 C81 Y10 |
| Date: | 2012–04–01 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:12/06&r=ets |
| By: | Liang Chen; Juan José Dolado; Jesús Gonzalo |
| Abstract: | Time invariance of factor loadings is a standard assumption in the analysis of large factor models. Yet, this assumption may be restrictive unless parameter shifts are mild (i.e., local to zero). In this paper we develop a new testing procedure to detect big breaks in these loadings at either known or unknown dates. It relies upon testing for parameter breaks in a regression of the first of the r¯ factors estimated by PCA on the remaining r¯ - 1 factors, where r¯ is chosen according to Bai and Ng’s (2002) information criteria. The test fares well in terms of power relative to other recently proposed tests on this issue, and can be easily implemented to avoid forecasting failures in standard factor-augmented (FAR, FAVAR) models where the number of factors is a priori imposed on the basis of theoretical considerations. |
| Keywords: | Structural break, Large factor model, Loadings, Principal components |
| JEL: | C12 C33 |
| Date: | 2011–12 |
| URL: | http://d.repec.org/n?u=RePEc:cte:werepe:we1141&r=ets |
| By: | Gary Koop (University of Strathclyde, UK; The Rimini Centre for Economic Analysis (RCEA), Italy); Dimitris Korobilis (University of Glasgow, UK; The Rimini Centre for Economic Analysis (RCEA), Italy) |
| Abstract: | In this paper we develop methods for estimation and forecasting in large time-varying parameter vector autoregressive models (TVP-VARs). To overcome computational constraints with likelihood-based estimation of large systems, we rely on Kalman filter estimation with forgetting factors. We also draw on ideas from the dynamic model averaging literature and extend the TVP-VAR so that its dimension can change over time. A final extension lies in the development of a new method for estimating, in a time-varying manner, the parameter(s) of the shrinkage priors commonly-used with large VARs. These extensions are operationalized through the use of forgetting factor methods and are, thus, computationally simple. An empirical application involving forecasting inflation, real output, and interest rates demonstrates the feasibility and usefulness of our approach. |
| Keywords: | Bayesian VAR; forecasting; time-varying coefficients; state-space model |
| JEL: | C11 C52 E27 E37 |
| Date: | 2012–03 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:11_12&r=ets |
| By: | Jozef Barunik; Lukas Vacha |
| Abstract: | In this paper, we propose a forecasting model for volatility based on its decomposition to several investment horizons and jumps. As a forecasting tool, we utilize Realized GARCH framework of Hansen et al. (2011), which models jointly returns and realized measures of volatility. For the decomposition, we use jump wavelet two scale realized volatility estimator (JWTSRV) of Barunik and Vacha (2012). While the main advantage of our time-frequency estimator is that it provides us with realized volatility measure robust to noise as well as with consistent estimate of jumps, it also allows to decompose volatility into the several investment horizons. On currency futures data covering the period of recent financial crisis, we compare forecasts from Realized GARCH(1,1) model using several measures. Namely, we use the realized volatility, bipower variation, two- scale realized volatility, realized kernel and our jump wavelet two scale realized volatility. We find that in-sample as well as out-of-sample performance of the model significantly differs based on the realized measure used. When JWTSRV estimator is used, model produces significantly best forecasts. We also utilize jumps and build Realized Jump-GARCH model. Utilizing the decomposition obtained by our estimator, we finally build Realized Wavelet-Jump GARCH model, which uses estimated jumps as well as volatility at several investment horizons. Our Realized Wavelet-Jump GARCH model proves to further improve the volatility forecasts. We conclude that realized volatility measurement in the time-frequency domain and inclusion of jumps improves the volatility forecasting considerably. |
| Date: | 2012–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1204.1452&r=ets |
| By: | Peter C. B. Phillips (Yale University, University of Auckland, University of Southampton & Singapore Management University); Shu-Ping Shi (Research School of Economics, The Australian National University); Jun Yu (Sim Kee Boon Institute for Financial Economics, School of Economics and Lee Kong Chian School of Business) |
| Abstract: | Identifying and dating explosive bubbles when there is periodically collapsing behavior over time has been a major concern in the economics literature and is of great importance for practitioners. The complexity of the nonlinear structure inherent in multiple bubble phenomena within the same sample period makes econometric analysis particularly difficult. The present paper develops new recursive procedures for practical implementation and surveillance strategies that may be employed by central banks and fiscal regulators. We show how the testing procedure and dating algorithm of Phillips, Wu and Yu (2011, PWY) are affected by multiple bubbles and may fail to be consistent. The present paper proposes a generalized version of the sup ADF test of PWY to address this difficulty, derives its asymptotic distribution, introduces a new date-stamping strategy for the origination and termination of multiple bubbles, and proves consistency of this dating procedure. Simulations show that the test significantly improves discriminatory power and leads to distinct power gains when multiple bubbles occur. Empirical applications are conducted to S&P 500 stock market data over a long historical period from January 1871 to December 2010. The new approach identifies many key historical episodes of exuberance and collapse over this period, whereas the strategy of PWY and the CUSUM procedure locate far fewer episodes in the same sample range. |
| Keywords: | Date-stamping strategy; Generalized sup ADF test; Multiple bubbles, Rational bubble; Periodically collapsing bubbles; Sup ADF test |
| JEL: | C15 C22 |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:siu:wpaper:13-2012&r=ets |
| By: | Ye Chen (School of Economics and Sim Kee Boon Institute for Financial Economics, Singapore Management University); Jun Yu (Sim Kee Boon Institute for Financial Economics, School of Economics and Lee Kong Chian School of Business) |
| Abstract: | Maximum likelihood estimation of the persistence parameter in the discrete time unit root model is known for suffering from a downward bias. The bias is more pronounced in the continuous time unit root model. Recently Chambers and Kyriacou (2010) introduced a new jackknife method to remove the .rst order bias in the estimator of the persistence parameter in a discrete time unit root model. This paper proposes an improved jackknife estimator of the persistence parameter that works for both the discrete time unit root model and the continuous time unit root model. The proposed jackknife estimator is optimal in the sense that it minimizes the variance. Simulations highlight the performance of the proposed method in both contexts. They show that our optimal jackknife reduces the variance of the jackknife method of Chambers and Kyriacou by at least 10% in both cases. |
| Keywords: | Bias reduction, Variance reduction, Vasicek model, Long-span Asymptotics, Autoregression |
| JEL: | C11 C15 |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:siu:wpaper:15-2012&r=ets |
| By: | Yong Li (Sun Yat-Sen University); Jun Yu (Sim Kee Boon Institute for Financial Economics, School of Economics and Lee Kong Chian School of Business) |
| Abstract: | A new posterior odds analysis is proposed to test for a unit root in volatility dynamics in the context of stochastic volatility models. Our analysis extends the Bayesian unit root test of So and Li (1999, Journal of Business and Economic Statistics) in the two important ways. First, a numerically more stable algorithm is introduced to compute Bayes factors, taking into account the special structure of the competing models. Owing to its numerical stability, the algorithm overcomes the problem of the diverging “size” in the marginal likelihood approach. Second, to improve the “power” of the unit root test, a mixed prior specification with random weights is employed. It is shown that the posterior odds ratio is the by-product of Bayesian estimation and can be easily computed by MCMC methods. A simulation study examines the “size” and “power” performances of the new method. An empirical study, based on time series data covering the subprime crisis, reveals some interesting results. |
| Keywords: | Bayes factor; Mixed Prior; Markov Chain Monte Carlo; Posterior odds ratio; Stochastic volatility models; Unit root testing. |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:siu:wpaper:14-2012&r=ets |
| By: | Xiaohu Wang (School of Economics and Sim Kee Boon Institute for Financial Economics, Singapore Management University); Jun Yu (Sim Kee Boon Institute for Financial Economics, School of Economics and Lee Kong Chian School of Business) |
| Abstract: | This paper develops a double asymptotic limit theory for the persistent parameter (k) in explosive continuous time models driven by Lévy processes with a large number of time span (N) and a small number of sampling interval (h). The simultaneous double asymptotic theory is derived using a technique in the same spirit as in Phillips and Magdalinos (2007) for the mildly explosive discrete time model. Both the intercept term and the initial condition appear in the limiting distribution. In the special case of explosive continuous time models driven by the Brownian motion, we develop the limit theory that allows for the joint limits where N ! 1 and h ! 0 simultaneously, the sequential limits where N ! 1 is followed by h ! 0, and the sequential limits where h ! 0 is followed by N ! 1. All three asymptotic distributions are the same. |
| Keywords: | Explosive, Continuous Time, Lévy Process, Invariance Principle, Double Asymptotics |
| JEL: | C13 C22 G13 |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:siu:wpaper:16-2012&r=ets |
| By: | Peter C. B. Phillips (Yale University, University of Auckland, University of Southampton & Singapore Management University); Shu-Ping Shi (Research School of Economics, The Australian National University); Jun Yu (Sim Kee Boon Institute for Financial Economics, School of Economics and Lee Kong Chian School of Business) |
| Abstract: | Right-tailed unit root tests have proved promising for detecting exuberance in economic and financial activities. Like left-tailed tests, the limit theory and test performance are sensitive to the null hypothesis and the model specification used in parameter estimation. This paper aims to provide some empirical guidelines for the practical implementation of right-tailed unit root tests, focussing on the sup ADF test of Phillips, Wu and Yu (2011), which implements a right-tailed ADF test repeatedly on a sequence of forward sample recursions. We analyze and compare the limit theory of the sup ADF test under different hypotheses and model specifications. The size and power properties of the test under various scenarios are examined in simulations and some recommendations for empirical practice are given. Empirical applications to the Nasdaq and to Australian and New Zealand housing data illustrate these specification issues and reveal their practical importance in testing. |
| Keywords: | Unit root test; Mildly explosive process; Recursive regression; Size and power. |
| JEL: | C15 C22 |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:siu:wpaper:17-2012&r=ets |
| By: | Beare, Brendan K.; Seo, Juwon |
| Abstract: | Economic and financial time series frequently exhibit time irreversible dynamics. For instance, there is considerable evidence of asymmetric fluctuations in many macroeconomic and financial variables, and certain game theoretic models of price determination predict asymmetric cycles in price series. In this paper we make two primary contributions to the econometric literature on time reversibility. First, we propose a new test of time reversibility, applicable to stationary Markov chains. Compared to existing tests, our test has the advantage of being consistent against arbitrary violations of reversibility. Second, we explain how a circulation density function may be used to characterize the nature of time irreversibility when it is present. We propose a copula-based estimator of the circulation density, and verify that it is well behaved asymptotically under suitable regularity conditions. We illustrate the use of our time reversibility test and circulation density estimator by applying them to five years of Canadian gasoline price markup data. |
| Keywords: | Econometrics and Quantitative Economics, Markov chains, time irreversible dynamics, economic time series |
| Date: | 2012–04–08 |
| URL: | http://d.repec.org/n?u=RePEc:cdl:ucsdec:qt31f8500p&r=ets |