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on Econometric Time Series |
| By: | Amélie Charles (Audencia Nantes, School of Management - Audencia, School of Management); Olivier Darné (LEMNA - Laboratoire d'économie et de management de Nantes Atlantique - Université de Nantes : EA4272) |
| Abstract: | In this paper, we test the presence of stochastic trend in long series of US real GNP measured by Balke and Gordon (1989) and Romer (1989). This is analyzed from two recent robust unit root tests proposed by Cavaliere and Georgiev (2009) and Lima and Xiao (2010), for which critical values are adapted to the small sample size. The former is improved by selecting optimally GLS detrending parameter to make the test in small samples powerful. We obtain mixed results on the full sample (1869--1993). However, the post-1929 GNP and GNP per capita series reject the unit-root null hypothesis, whereas for the pre-1929 GNP data, i.e. the period where the GNP series have been reconstructed, the unit-root hypothesis is not rejected for GNP series proposed by Balke-Gordon and Romer but this hypothesis is rejected for the same series in per capita form. This difference can be explained by the data-construction procedure employed for the pre-1929 GNP series. |
| Keywords: | GNP ; robust unit root test |
| Date: | 2010–12–17 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00547737_v1&r=ets |
| By: | Worapree Maneesoonthorn; Gael M. Martin; Catherine S. Forbes; Simone Grose |
| Abstract: | The object of this paper is to produce distributional forecasts of physical volatility and its associated risk premia using a non-Gaussian, non-linear state space approach. Option and spot market information on the unobserved variance process is captured by using dual 'model-free' variance measures to define a bivariate observation equation in the state space model. The premium for diffusive variance risk is defined as linear in the latent variance (in the usual fashion) whilst the premium for jump variance risk is specified as a conditionally deterministic dynamic process, driven by a function of past measurements. The inferential approach adopted is Bayesian, implemented via a Markov chain Monte Carlo algorithm that caters for the multiple sources of non-linearity in the model and the bivariate measure. The method is applied to empirical spot and option price data for the S&P500 index over the 1999 to 2008 period, with conclusions drawn about investors' required compensation for variance risk during the recent financial turmoil. The accuracy of the probabilistic forecasts of the observable variance measures is demonstrated, and compared with that of forecasts yielded by more standard time series models. To illustrate the benefits of the approach, the posterior distribution is augmented by information on daily returns to produce Value at Risk predictions, as well as being used to yield forecasts of the prices of derivatives on volatility itself. Linking the variance risk premia to the risk aversion parameter in a representative agent model, probabilistic forecasts of relative risk aversion are also produced. |
| Keywords: | Volatility Forecasting; Non-linear State Space Models; Non-parametric Variance Measures; Bayesian Markov Chain Monte Carlo; VIX Futures; Risk Aversion. |
| JEL: | C11 C53 |
| Date: | 2010–12–20 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2010-22&r=ets |
| By: | Jian Huang (Guangdong University of Finance); Masahito Kobayashi (Faculty of Economics, Yokohama National University); Michael McAleer (Erasmus University Rotterdam, Tinbergen Institute, The Netherlands, and Institute of Economic Research, Kyoto University) |
| Abstract: | This paper analyses the constant elasticity of volatility (CEV) model suggested by Chan et al. (1992). The CEV model without mean reversion is shown to be the inverse Box-Cox transformation of integrated processes asymptotically. It is demonstrated that the maximum likelihood estimator of the power parameter has a nonstandard asymptotic distribution, which is expressed as an integral of Brownian motions, when the data generating process is not mean reverting. However, it is shown that the t-ratio follows a standard normal distribution asymptotically, so that the use of the conventional t-test in analyzing the power parameter of the CEV model is justified even if there is no mean reversion, as is often the case in empirical research. The model may applied to ultra high frequency data. |
| Keywords: | Box-Cox transformation, Brownian Motion, Constant Elasticity of Volatility, Mean Reversion, Nonstandard distribution. |
| Date: | 2010–12 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:750&r=ets |
| By: | David E. Allen (School of Accounting, Finance and Economics, Edith Cowan University); Michael McAleer (Erasmus University Rotterdam, Tinbergen Institute, The Netherlands, and Institute of Economic Research, Kyoto University); Marcel Scharth (Tinbergen Institute, The Netherlands, Department of Econometrics, VU University Amsterdam) |
| Abstract: | In this paper we show that realized variation measures constructed from high- frequency returns reveal a large degree of volatility risk in stock and index returns, where we characterize volatility risk by the extent to which forecasting errors in realized volatility are substantive. Even though returns standardized by ex post quadratic variation measures are nearly Gaussian, this unpredictability brings greater uncertainty to the empirically relevant ex ante distribution of returns. Explicitly modeling this volatility risk is fundamental. We propose a dually asymmetric realized volatility model, which incorporates the fact that realized volatility series are systematically more volatile in high volatility periods. Returns in this framework display time varying volatility, skewness and kurtosis. We provide a detailed account of the empirical advantages of the model using data on the S&P 500 index and eight other indexes and stocks. |
| Keywords: | Realized volatility, volatility of volatility, volatility risk, value-at-risk, forecasting, conditional heteroskedasticity. |
| Date: | 2010–12 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:753&r=ets |
| By: | Felix Chan (School of Economics and Finance, Curtin University of Technologyy); Michael McAleer (Erasmus University Rotterdam, Tinbergen Institute, The Netherlands, and Institute of Economic Research, Kyoto University); Marcelo C. Medeiros (Department of Economics, Pontifical Catholic University of Rio de Janeiro) |
| Abstract: | Nonlinear time series models, especially those with regime-switching and conditionally heteroskedastic errors, have become increasingly popular in the economics and finance literature. However, much of the research has concentrated on the empirical applications of various models, with little theoretical or statistical analysis associated with the structure of the processes or the associated asymptotic theory. In this paper, we first derive necessary conditions for strict stationarity and ergodicity of three different specifications of the first-order smooth transition autoregressions with heteroskedastic errors. This is important, among other reasons, to establish the conditions under which the traditional LMlinearity tests based on Taylor expansions are valid. Second, we provide sufficient conditions for consistency and asymptotic normality of the Quasi- Maximum Likelihood Estimator for a general nonlinear conditional mean model with first-order GARCH errors. |
| Keywords: | Nonlinear time series, regime-switching, smooth transition, STAR, GARCH, log-moment, moment conditions, asymptotic theory. |
| Date: | 2010–12 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:754&r=ets |
| By: | Manabu Asai; Michael McAleer (University of Canterbury) |
| Abstract: | The paper develops two Dynamic Conditional Correlation (DCC) models, namely the Wishart DCC (WDCC) model and the Matrix-Exponential Conditional Correlation (MECC) model. The paper applies the WDCC approach to the exponential GARCH (EGARCH) and GJR models to propose asymmetric DCC models. We use the standardized multivariate t-distribution to accommodate heavy-tailed errors. The paper presents an empirical example using the trivariate data of the Nikkei 225, Hang Seng and Straits Times Indices for estimating and forecasting the WDCC-EGARCH and WDCC-GJR models, and compares the performance with the asymmetric BEKK model. The empirical results show that AIC and BIC favour the WDCC-EGARCH model to the WDCC-GJR and asymmetric BEKK models. Moreover, the empirical results indicate that the WDCC-EGARCH-t model produces reasonable VaR threshold forecasts, which are very close to the nominal 1% to 3% values. |
| Keywords: | Dynamic conditional correlations; Matrix exponential model; Wishart process; EGARCH; GJR; asymmetric BEKK; heavy-tailed errors |
| Date: | 2010–12–01 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:10/76&r=ets |
| By: | Dominique Guegan (Centre d'Economie de la Sorbonne - Paris School of Economics); Philippe de Peretti (Centre d'Economie de la Sorbonne) |
| Abstract: | In this paper, we present a procedure that tests for the null of time-homogeneity of the first two moments of a time-series. Whereas the literature dedicated to structural breaks testing procedures often focuses on one kind of alternative, i.e. discrete shifts or smooth transition, our procedure is designed to deal with a broader alternative including i) discrete shifts, ii) smooth transition, iii) time-varying moments, iv) probability-driven breaks, v) GARCH or Stochastic Volatility Models for the variance. Our test uses the recently introduced maximum entropy bootstrap, designed to capture both time-dependency and time-heterogeneity. Running simulations, our procedure appears to be quite powerful. To some extent, our paper is an extension of Heracleous, Koutris and Spanos (2008). |
| Keywords: | Test, time-homogeneity, maximum entropy bootstrap. |
| JEL: | C01 C12 C15 |
| Date: | 2010–12 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:10098&r=ets |
| By: | Tetsuya Takaishi |
| Abstract: | A Bayesian estimation of a GARCH model is performed for US Dollar/Japanese Yen exchange rate by the Metropolis-Hastings algorithm with a proposal density given by the adaptive construction scheme. In the adaptive construction scheme the proposal density is assumed to take a form of a multivariate Student's t-distribution and its parameters are evaluated by using the sampled data and updated adaptively during Markov Chain Monte Carlo simulations. We find that the autocorrelation times between the data sampled by the adaptive construction scheme are considerably reduced. %a factor of 100 smaller than those by the conventional Metropolis method. We conclude that the adaptive construction scheme works efficiently for the Bayesian inference of the GARCH model. |
| Date: | 2010–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1012.5986&r=ets |
| By: | Boubacar Mainassara, Yacouba; Carbon, Michel; Francq, Christian |
| Abstract: | Numerous time series admit "weak" autoregressive-moving average (ARMA) representations, in which the errors are uncorrelated but not necessarily independent nor martingale differences. The statistical inference of this general class of models requires the estimation of generalized Fisher information matrices. We give analytic expressions and propose consistent estimators of these matrices, at any point of the parameter space. Our results are illustrated by means of Monte Carlo experiments and by analyzing the dynamics of daily returns and squared daily returns of financial series. |
| Keywords: | Asymptotic relative efficiency (ARE); Bahadur's slope; Information matrices; Lagrange Multiplier test; Nonlinear processes; Wald test; Weak ARMA models |
| JEL: | C13 C12 C22 C01 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:27685&r=ets |
| By: | Carbon, Michel; Francq, Christian |
| Abstract: | The asymptotic distribution of a vector of autocorrelations of squared residuals is derived for a wide class of asymmetric GARCH models. Portmanteau adequacy tests are deduced. %gathered These results are obtained under moment assumptions on the iid process, but fat tails are allowed for the observed process, which is particularly relevant for series of financial returns. A Monte Carlo experiment and an illustration to financial series are also presented. |
| Keywords: | ARCH models; Leverage effect; Portmanteau test; Goodness-of-fit test; Diagnostic checking |
| JEL: | C12 C22 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:27686&r=ets |