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on Econometric Time Series |
| By: | Guglielmo Maria Caporale; Luis A. Gil-Alana |
| Abstract: | This paper examines the degree of persistence in the volatility of financial time series using a Long Memory Stochastic Volatility (LMSV) model. Specifically, it employs a Gaussian semiparametric (or local Whittle) estimator of the memory parameter, based on the frequency domain, proposed by Robinson (1995a), and shown by Arteche (2004) to be consistent and asymptotically normal in the context of signal plus noise models. Daily data on the NASDAQ index are analysed. The results suggest that volatility has a component of long- memory behaviour, the order of integration ranging between 0.3 and 0.5, the series being therefore stationary and mean-reverting. |
| Keywords: | Fractional integration, long memory, stochastic volatility, asset returns |
| JEL: | C13 C22 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:diw:diwwpp:dp1006&r=ets |
| By: | Yingyao Hu, Matthew Shum and Wei Tan |
| Abstract: | We present a method for estimating Markov dynamic models with unobserved state variables which can be serially correlated over time. We focus on the case where all the model variables have discrete support. Our estimator is simple to compute because it is noniterative, and involves only elementary matrix manipulations. Our estimation method is nonparametric, in that no parametric assumptions on the distributions of the unobserved state variables or the laws of motions of the state variables are required. Monte Carlo simulations show that the estimator performs well in practice, and we illustrate its use with a dataset of doctors' prescription of pharmaceutical drugs. |
| Date: | 2010–05 |
| URL: | http://d.repec.org/n?u=RePEc:jhu:papers:558&r=ets |
| By: | Yamaguchi, Keiko |
| Abstract: | We propose an estimator of change point in the long memory parameter d of an ARFIMA(p, d, q) process using the sup Wald test. We derive the consistency and the rate of convergence of the parameter. The convergence rate of our change point estimator depends on the magnitude of a shift. Furthermore, we obtain the limiting distribution of our change point estimator without depending on the distribution of the process. Therefore, we can construct the confidence interval of the change point. Simulations show the validity of the asymptotic theory of our estimator if the sample size is large enough. We apply our change point estimator to the yearly Nile river minimum time series. |
| Keywords: | Break in persistence, long memory, change point |
| JEL: | C22 |
| Date: | 2010–05 |
| URL: | http://d.repec.org/n?u=RePEc:hit:econdp:2010-07&r=ets |
| By: | D.S.G. Pollock (University of Leicester) |
| Abstract: | Discrete-time ARMA processes can be placed in a one-to-one correspondence with a set of continuous-time processes that are bounded in frequency by the Nyquist value of ð radians per sample period. It is well known that, if data are sampled from a continuous process of which the maximum frequency exceeds the Nyquist value, then there will be a problem of aliasing. However, if the sampling is too rapid, then other problems will arise that will cause the ARMA estimates to be severely biased. The paper reveals the nature of these problems and it shows how they may be overcome. |
| Keywords: | Stochastic Differential Equations, Band-Limited Stochastic Processes, Oversampling |
| Date: | 2010–05–25 |
| URL: | http://d.repec.org/n?u=RePEc:wse:wpaper:44&r=ets |
| By: | Massimiliano Caporin; Michael McAleer (University of Canterbury) |
| Abstract: | In the last 15 years, several Multivariate GARCH (MGARCH) models have appeared in the literature. The two most widely known and used are the Scalar BEKK model of Engle and Kroner (1995) and Ding and Engle (2001), and the DCC model of Engle (2002). Some recent research has begun to examine MGARCH specifications in terms of their out-of-sample forecasting performance. In this paper, we provide an empirical comparison of a set of MGARCH models, namely BEKK, DCC, Corrected DCC (cDCC) of Aeilli (2008), CCC of Bollerslev (1990), Exponentially Weighted Moving Average, and covariance shrinking of Ledoit and Wolf (2004), using the historical data of 89 US equities. Our methods follow some of the approach described in Patton and Sheppard (2009), and contribute to the literature in several directions. First, we consider a wide range of models, including the recent cDCC model and covariance shrinking. Second, we use a range of tests and approaches for direct and indirect model comparison, including the Weighted Likelihood Ratio test of Amisano and Giacomini (2007). Third, we examine how the model rankings are influenced by the cross-sectional dimension of the problem. |
| Keywords: | Covariance forecasting; model confidence set; model ranking; MGARCH; model comparison |
| JEL: | C32 C53 C52 |
| Date: | 2010–05–01 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:10/34&r=ets |
| By: | Michael McAleer (University of Canterbury); Massimiliano Caporin |
| Abstract: | DAMGARCH is a new model that extends the VARMA-GARCH model of Ling and McAleer (2003) by introducing multiple thresholds and time-dependent structure in the asymmetry of the conditional variances. Analytical expressions for the news impact surface implied by the new model are also presented. DAMGARCH models the shocks affecting the conditional variances on the basis of an underlying multivariate distribution. It is possible to model explicitly asset-specific shocks and common innovations by partitioning the multivariate density support. This paper presents the model structure, describes the implementation issues, and provides the conditions for the existence of a unique stationary solution, and for consistency and asymptotic normality of the quasi-maximum likelihood estimators. The paper also presents an empirical example to highlight the usefulness of the new model. |
| Keywords: | multivariate asymmetry; conditional variance; stationarity conditions; asymptotic theory; multivariate news impact curve |
| JEL: | C32 C51 C52 |
| Date: | 2010–04–01 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:10/32&r=ets |
| By: | Pesaran, M.H.; Chudik, A. |
| Abstract: | This paper extends the analysis of infinite dimensional vector autoregressive models (IVAR) proposed in Chudik and Pesaran (2010) to the case where one of the variables or the cross section units in the IVAR model is dominant or pervasive. This extension is not straightforward and involves several technical dificulties. The dominant unit influences the rest of the variables in the IVAR model both directly and indirectly, and its effects do not vanish even as the dimension of the model (N) tends to infinity. The dominant unit acts as a dynamic factor in the regressions of the non-dominant units and yields an infinite order distributed lag relationship between the two types of units. Despite this it is shown that the effects of the dominant unit as well as those of the neighborhood units can be consistently estimated by running augmented least squares regressions that include distributed lag functions of the dominant unit. The asymptotic distribution of the estimators is derived and their small sample properties investigated by means of Monte Carlo experiments. |
| Keywords: | IVAR Models, Dominant Units, Large Panels, Weak and Strong Cross Section Dependence, Factor Model |
| JEL: | C10 C33 C51 |
| Date: | 2010–05–29 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1024&r=ets |
| By: | Ardia, David; Hoogerheide, Lennart F. |
| Abstract: | This chapter proposes an up-to-date review of estimation strategies available for the Bayesian inference of GARCH-type models. The emphasis is put on a novel efficient procedure named AdMitIS. The methodology automatically constructs a mixture of Student-t distributions as an approximation to the posterior density of the model parameters. This density is then used in importance sampling for model estimation, model selection and model combination. The procedure is fully automatic which avoids difficult and time consuming tuning of MCMC strategies. The AdMitIS methodology is illustrated with an empirical application to S&P index log-returns where non-nested GARCH-type models are estimated and combined to predict the distribution of next-day ahead log-returns. |
| Keywords: | GARCH; Bayesian inference; MCMC; marginal likelihood; Bayesian model averaging; adaptive mixture of Student-t distributions; importance sampling. |
| JEL: | C51 C22 C15 C11 |
| Date: | 2010–02–08 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:22919&r=ets |
| By: | Janczura, Joanna; Weron, Rafal |
| Abstract: | In this paper we propose a novel goodness-of-fit testing scheme for regime-switching models. We consider models with an observable, as well as, a latent state process. The test is based on the Kolmogorov-Smirnov supremum-distance statistic and the concept of the weighted empirical distribution function. We apply the proposed scheme to test whether a 2-state Markov regime-switching model fits electricity spot price data. |
| Keywords: | Regime-switching; Goodness-of-fit; Weighted empirical distribution function; Kolmogorov-Smirnov test |
| JEL: | C52 C12 Q40 |
| Date: | 2010–05–24 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:22871&r=ets |