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on Econometric Time Series |
| By: | K. Triantafyllopoulos |
| Abstract: | A new multivariate stochastic volatility estimation procedure for financial time series is proposed. A Wishart autoregressive process is considered for the volatility precision covariance matrix, for the estimation of which a two step procedure is adopted. The first step is the conditional inference on the autoregressive parameters and the second step is the unconditional inference, based on a Newton-Raphson iterative algorithm. The proposed methodology, which is mostly Bayesian, is suitable for medium dimensional data and it bridges the gap between closed-form estimation and simulation-based estimation algorithms. An example, consisting of foreign exchange rates data, illustrates the proposed methodology. |
| Date: | 2013–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1311.0530&r=ets |
| By: | Song-Yon Kim; Mun-Chol Kim |
| Abstract: | In this paper nonlinear time series models are used to describe volatility in financial time series data. To describe volatility two of the nonlinear time series are combined into TAR (Threshold Auto-Regressive Model) with AARCH (Asymmetric Auto- Regressive Conditional Heteroskedasticity) error term and its parameter estimation is studied. |
| Date: | 2013–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1311.1154&r=ets |
| By: | Stefano De Marco; Peter Friz |
| Abstract: | Motivated by marginals-mimicking results for It\^o processes via SDEs and by their applications to volatility modeling in finance, we discuss the weak convergence of the law of a hypoelliptic diffusions conditioned to belong to a target affine subspace at final time, namely $\mathcal{L}(Z_t|Y_t = y)$ if $X_{\cdot}=(Y_\cdot,Z_{\cdot})$. To do so, we revisit Varadhan-type estimates in a small-noise regime, studying the density of the lower-dimensional component $Y$. The application to stochastic volatility models include the small-time and, for certain models, the large-strike asymptotics of the Gyongy-Dupire's local volatility function, the final product being asymptotic formulae that can (i) motivate parameterizations of the local volatility surface and (ii) be used to extrapolate local volatilities in a given model. |
| Date: | 2013–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1311.1545&r=ets |
| By: | Marcel Aloy (AMSE - Aix-Marseille School of Economics - Aix-Marseille Univ. - Centre national de la recherche scientifique (CNRS) - École des Hautes Études en Sciences Sociales [EHESS] - Ecole Centrale Marseille (ECM)); Gilles De Truchis (AMSE - Aix-Marseille School of Economics - Aix-Marseille Univ. - Centre national de la recherche scientifique (CNRS) - École des Hautes Études en Sciences Sociales [EHESS] - Ecole Centrale Marseille (ECM)) |
| Abstract: | Estimation methods of bivariate fractional cointegration models are numerous. In most cases they have non-equivalent asymptotic and finite sample properties, implying diffculties in determining an optimal estimation strategy. In this paper, we address this issue by means of simulations and provide useful guidance to practitioners. Our Monte Carlo study reveals the superiority of techniques that estimate jointly all parameters of interest, over those operating in two steps. In some cases, it also shows that estimators originally designed for the stationary cointegration, have good finite sample properties in non-stationary regions of the parameter space. |
| Keywords: | fractional cointegration; Monte Carlo simulation; Whittle estimation; frequency analysis |
| Date: | 2013–10 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-00879522&r=ets |
| By: | Zhu, Ke; Li, Wai-Keung |
| Abstract: | This paper proposes a Cramer-von Mises (CM) test statistic to check the adequacy of weak ARMA models. Without posing a martingale difference assumption on the error terms, the asymptotic null distribution of the CM test is obtained by using the Hillbert space approach. Moreover, this CM test is consistent, and has nontrivial power against the local alternative of order $n^{-1/2}$. Due to the unknown dependence of error terms and the estimation effects, a new block-wise random weighting method is constructed to bootstrap the critical values of the test statistic. The new method is easy to implement and its validity is justified. The theory is illustrated by a small simulation study and an application to S\&P 500 stock index. |
| Keywords: | Block-wise random weighting method; Diagnostic checking; Least squares estimation; Spectral test; Weak ARMA models; Wild bootstrap. |
| JEL: | C1 C12 |
| Date: | 2013–11–06 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:51224&r=ets |
| By: | Schleer, Frauke |
| Abstract: | This paper focuses on finding starting-values for maximum likelihood estimation of Vector STAR models. Based on a Monte Carlo exercise, different procedures are evaluated. Their performance is assessed w.r.t. model fit and computational effort. I employ i) grid search algorithms, and ii) heuristic optimization procedures, namely, differential evolution, threshold accepting, and simulated annealing. In the equation-by-equation starting-value search approach the procedures achieve equally good results. Unless the errors are cross-correlated, equation-by-equation search followed by a derivative-based algorithm can handle such an optimization problem sufficiently well. This result holds also for higher-dimensional VSTAR models with a slight edge for the heuristic methods. Being faced with more complex Vector STAR models for which a multivariate search approach is required, simulated annealing and differential evolution outperform threshold accepting and the grid with a zoom. -- |
| Keywords: | Vector STAR model,starting-values,optimization heuristics,grid search,estimation,non-linearieties |
| JEL: | C32 C61 C63 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:zewdip:13076&r=ets |