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on Econometric Time Series |
| By: | Rasmus Pedersen (Department of Economics - University of Copenhagen - KU - University of Copenhagen); Olivier Wintenberger (LSTA - Laboratoire de Statistique Théorique et Appliquée - UPMC - Université Pierre et Marie Curie - Paris 6 - CNRS - Centre National de la Recherche Scientifique, University of Copenhagen - Department of Mathematical Sciences - KU - University of Copenhagen) |
| Abstract: | Conditions for geometric ergodicity of multivariate autoregressive conditional heteroskedasticity (ARCH) processes, with the so-called BEKK (Baba, Engle, Kraft, and Kroner) parametrization, are considered. We show for a class of BEKK-ARCH processes that the invariant distribution is regularly varying. In order to account for the possibility of different tail indices of the marginals, we consider the notion of vector scaling regular variation, in the spirit of Perfekt (1997, Advances in Applied Probability, 29, pp. 138-164). The characterization of the tail behavior of the processes is used for deriving the asymptotic properties of the sample covariance matrices. |
| Keywords: | Stochastic recurrence equations,Markov processes,regular variation,multivariate ARCH,asymptotic properties,geometric ergodicity |
| Date: | 2017–02–02 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01436267&r=ets |
| By: | Fabrizio Cipollini (Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti", Università di Firenze); Robert F. Engle (Department of Finance, Stern School of Business, New York University); Giampiero M. Gallo (Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti", Università di Firenze) |
| Abstract: | We discuss several multivariate extensions of the Multiplicative Error Model by Engle (2002) to take into account dynamic interdependence and contemporaneously correlated innovations (vector MEM or vMEM). We suggest copula functions to link Gamma marginals of the innovations, in a specification where past values and conditional expectations of the variables can be simultaneously estimated. Results with realized volatility, volumes and number of trades of the JNJ stock show that significantly superior realized volatility forecasts are delivered with a fully interdependent vMEM relative to a single equation. Alternatives involving log–Normal or semiparametric formulations produce substantially equivalent results. |
| Keywords: | GARCH; MEM; Realized Volatility; Trading Volume; Trading Activity; Trades; Copula; Volatility Forecasting |
| JEL: | C32 C51 C58 C89 |
| Date: | 2017–04 |
| URL: | http://d.repec.org/n?u=RePEc:fir:econom:wp2017_02&r=ets |
| By: | Asai, M.; Chang, C-L.; McAleer, M.J. |
| Abstract: | The paper develops a novel realized matrix-exponential stochastic volatility model of multivariate returns and realized covariances that incorporates asymmetry and long memory (hereafter the RMESV-ALM model). The matrix exponential transformation guarantees the positivedefiniteness of the dynamic covariance matrix. The contribution of the paper ties in with Robert Basmann’s seminal work in terms of the estimation of highly non-linear model specifications (“Causality tests and observationally equivalent representations of econometric models”, Journal of Econometrics, 1988, 39(1-2), 69–104), especially for developing tests for leverage and spillover effects in the covariance dynamics. Efficient importance sampling is used to maximize the likelihood function of RMESV-ALM, and the finite sample properties of the quasi-maximum likelihood estimator of the parameters are analysed. Using high frequency data for three US financial assets, the new model is estimated and evaluated. The forecasting performance of the new model is compared with a novel dynamic realized matrix-exponential conditional covariance model. The volatility and co-volatility spillovers are examined via the news impact curves and the impulse response functions from returns to volatility and co-volatility. |
| Keywords: | Matrix-exponential transformation, Realized stochastic covariances, Realized conditional, covariances, Asymmetry, Long memory, Spillovers, Dynamic covariance matrix, Finite, sample properties, Forecasting performance. |
| JEL: | C22 C32 C58 G32 |
| Date: | 2016–09–01 |
| URL: | http://d.repec.org/n?u=RePEc:ems:eureir:98648&r=ets |
| By: | Christopher G. Gibbs (School of Economics, UNSW Business School, UNSW); Andrey L. Vasnev (University of Sydney) |
| Abstract: | In applied forecasting, there is a trade-off between in-sample fit and out-of-sample forecast accuracy. Parsimonious model specifications typically outperform richer model specifications. Consequently, there is often predictable information in forecast errors that is difficult to exploit. However, we show how this predictable information can be exploited in forecast combinations. In this case, optimal combination weights should minimize conditional mean squared error, or a conditional loss function, rather than the unconditional variance as in the commonly used framework of Bates and Granger (1969). We prove that our conditionally optimal weights lead to better forecast performance. The conditionally optimal weights support other forward-looking approaches to combining forecasts, where the forecast weights depend on the expected model performance. We show that forward-looking |
| Keywords: | Forecast combination, conditionally optimal weights, forecast combination puzzle, inflation, Phillips curve |
| JEL: | C18 C53 E31 |
| Date: | 2017–02 |
| URL: | http://d.repec.org/n?u=RePEc:swe:wpaper:2017-10&r=ets |
| By: | Javed Iqbal (State Bank of Pakistan); Muhammad Nadim Hanif (State Bank of Pakistan) |
| Abstract: | We compare performance of modified HP filter, wavelet analysis and empirical mode decomposition. Our simulation study results suggest that modified HP filter performs better for an overall time series. However, in the middle (of time series) wavelet analysis performs best. Wavelet analysis based filtering has highest ‘end points bias (EPB)’. However, it performs better when we extrapolate the subject time series to lower the EPB. Study based on observed data of real income, investment and consumption shows that the autoregressive properties and multivariate analytics of cyclical components depend upon filtering technique. |
| Keywords: | Business Cycle, Smoothing Macro Time Series, Modified HP Filter, Wavelet Analysis, End Point Bias in HP Filter, Simulation, Cross Country Study. |
| JEL: | E32 C18 |
| Date: | 2017–03 |
| URL: | http://d.repec.org/n?u=RePEc:sbp:wpaper:87&r=ets |
| By: | Muhammad Nadim Hanif (State Bank of Pakistan); Javed Iqbal (State Bank of Pakistan); M. Ali Choudhary (State Bank of Pakistan) |
| Abstract: | Business cycle estimation is core of macroeconomics research. Hodrick-Prescott (1997) filter, (or HP filter), is the most popular tool to extract cycle from a macroeconomic time series. There are certain issues with HP filter including fixed value of ? across the series/countries and end points bias (EPB). Modified HP filter (MHP) of McDermott (1997) attempted to address the first issue. Bloechl (2014) introduced a loss function minimization approach to address the EPB issue but keeping lambda fixed (as in HP filter). In this study we marry the endogenous lambda approach of McDermott (1997) with loss function minimization approach of Bloechl (2014) to analyze EPB in HP filter, while intuitively changing the weighting scheme used in the latter. We contribute by suggesting an endogenous weighting scheme along with endogenous smoothing parameter to resolve EPB issue of HP filter. We call this fully modified HP (FMHP) filter. Our FMHP filter outperforms a variety of conventional filters in a power comparison (simulation) study as well as in observed real data (univariate and multivariate) analytics for a large set of countries. |
| Keywords: | Business Cycle, Time Series, Fully Modified HP Filter, End Point Bias in HP Filter, Simulation, Cross Country Study. |
| JEL: | E32 C18 |
| Date: | 2017–04 |
| URL: | http://d.repec.org/n?u=RePEc:sbp:wpaper:88&r=ets |