|
on Econometric Time Series |
| By: | Shin Kanaya (Department of Economics, Oxford-Man Institute and Nuffield College); Dennis Kristensen (Department of Economics, Columbia University, and CREATES) |
| Abstract: | A two-step estimation method of stochastic volatility models is proposed: In the first step, we estimate the (unobserved) instantaneous volatility process using the estimator of Kristensen (2010, Econometric Theory 26). In the second step, standard estimation methods for fully observed diffusion processes are employed, but with the filtered volatility process replacing the latent process. Our estimation strategy is applicable to both parametric and nonparametric stochastic volatility models, and we give theoretical results for both. The resulting estimators of the drift and diffusion terms of the volatility model will carry additional biases and variances due to the first-step estimation, but under regularity conditions these vanish asymptotically and our estimators inherit the asymptotic properties of the infeasible estimators based on observations of the volatility process. A simulation study examines the finite-sample properties of the proposed estimators. |
| Keywords: | Realized spot volatility, stochastic volatility, kernel estimation, nonparametric, semiparametric |
| JEL: | C14 C32 |
| Date: | 2010–01–10 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2010-67&r=ets |
| By: | Dennis Kristensen (Dep. of Economics, Columbia University and CREATES); Anders Rahbek (Department of Economics, University of Copenhagen and CREATES) |
| Abstract: | In this paper, we consider a general class of vector error correction models which allow for asymmetric and non-linear error correction. We provide asymptotic results for (quasi-)maximum likelihood (QML) based estimators and tests. General hypothesis testing is considered, where testing for linearity is of particular interest as parameters of non-linear components vanish under the null. To solve the latter type of testing, we use the so-called sup tests, which here requires development of new (uniform) weak convergence results. These results are potentially useful in general for analysis of non-stationary non-linear time series models. Thus the paper provides a full asymptotic theory for estimators as well as standard and non-standard test statistics. The derived asymptotic results prove to be new compared to results found elsewhere in the literature due to the impact of the estimated cointegration relations. With respect to testing, this makes implementation of testing involved, and bootstrap versions of the tests are proposed in order to facilitate their usage. The asymptotic results regarding the QML estimators extend results in Kristensen and Rahbek (2010, Journal of Econometrics) where symmetric non-linear error correction considered. A simulation study shows that the fi?nite sample properties of the bootstrapped tests are satisfactory with good size and power properties for reasonable sample sizes. |
| Keywords: | Nonlinear error correction, cointegration, testing nonlinearity, nonlinear time series, sup tests, vanishing parameters, testing. |
| JEL: | C30 C32 |
| Date: | 2010–01–10 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2010-68&r=ets |
| By: | Nicolas Debarsy (CERPE - Centre de Recherches en Economie Régionale et Politique Economique - Facultés Universitaires Notre Dame de la Paix); Cem Ertur (LEO - Laboratoire d'économie d'Orleans - CNRS : UMR6221 - Université d'Orléans); James P. Lesage (Texas State University - Texas State University) |
| Abstract: | There is a great deal of literature regarding the asymptotic properties of various approaches to estimating simultaneous space-time panel models, but little attention has been paid to how the model estimates should be interpreted. The motivation for use of space-time panel models is that they can provide us with information not available from cross-sectional spatial regressions. LeSage and Pace (2009) show that cross-sectional simultaneous spatial autoregressive models can be viewed as a limiting outcome of a dynamic space-time autoregressive process. A valuable aspect of dynamic space-time panel data models is that the own- and cross-partial derivatives that relate changes in the explanatory variables to those that arise in the dependent variable are explicit. This allows us to employ parameter estimates from these models to quantify dynamic responses over time and space as well as space-time diffusion impacts. We illustrate our approach using the demand for cigarettes over a 30 year period from 1963-1992, where the motivation for spatial dependence is a bootlegging effect where buyers of cigarettes near state borders purchase in neighboring states if there is a price advantage to doing so. |
| Keywords: | Dynamic space-time panel data model; MCMC estimation; dynamic responses over time and space |
| Date: | 2010–08–25 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00525740_v1&r=ets |
| By: | Shimotsu, Katsumi |
| Abstract: | Semiparametric estimation of a bivariate fractionally cointegrated system is considered. We propose a two-step procedure that accommodates both (asymptotically) stationary (d<1/2) and nonstationary (d>=1/2) stochastic trend and/or equilibrium error. A tapered version of the local Whittle estimator of Robinson (2008) is used as the first-stage estimator, and the second-stage estimator employs the exact local Whittle approach of Shimotsu and Phillips (2005). The consistency and asymptotic distribution of the two-step estimator are derived. The estimator of the memory parameters has the same Gaussian asymptotic distribution in both the stationary and nonstationary case. The convergence rate and the asymptotic distribution of the estimator of the cointegrating vector are affected by the difference between the memory parameters. Further, the estimator has a Gaussian asymptotic distribution when the difference between the memory parameters is less than 1/2. |
| Keywords: | discrete Fourier transform, fractional cointegration, long memory, nonstationarity, semiparametric estimation, Whittle likelihood |
| JEL: | C22 |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:hit:econdp:2010-11&r=ets |
| By: | Richard Ashley |
| Abstract: | The volatility clustering frequently observed in financial/economic time series is often ascribed to GARCH and/or stochastic volatility models. This paper demonstrates the usefulness of re- conceptualizing the usual definition of conditional heteroscedasticity as the (h = 1) special case of h-step-ahead conditional heteroscedasticity, where the conditional volatility in period t depends on observable variables up through period t - h. Here it is shown that, for h > 1, h-step-ahead conditional heteroscedasticity arises – necessarily and endogenously – from nonlinear serial dependence in a time series; whereas one-step-ahead conditional heteroscedasticity (i.e., h= 1) requires multiple and heterogeneously-skedastic innovation terms. Consequently, the best response to observed volatility clustering may often be to model the nonlinear serial dependence which is likely causing it, rather than ‘tacking on’ an ad hoc volatility model. Even where such nonlinear modeling is infeasible – or where volatility is quantified using, say, a model-free implied volatility measure rather than squared returns – these results suggest a re-consideration of the usefulness of lag-one terms in volatility models. An application to observed daily stock returns is given. |
| Keywords: | nonlinearity; nonlinear serial dependence; conditional heteroscedasticity;ARCH models; GARCH models. |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:vpi:wpaper:e07-23&r=ets |
| By: | Croux, C.; Gelper, S.; Mahieu, K. (Tilburg University, Center for Economic Research) |
| Abstract: | This article presents a control chart for time series data, based on the one-step- ahead forecast errors of the Holt-Winters forecasting method. We use robust techniques to prevent that outliers affect the estimation of the control limits of the chart. Moreover, robustness is important to maintain the reliability of the control chart after the occurrence of alarm observations. The properties of the new control chart are examined in a simulation study and on a real data example. |
| Keywords: | Control chart;Holt-Winters;Non-stationary time series;Out- lier detection;Robustness;Statistical process control. |
| JEL: | C44 C53 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2010107&r=ets |
| By: | Croux, C.; Fried, R.; Gijbels, I.; Mahieu, K. (Tilburg University, Center for Economic Research) |
| Abstract: | This paper proposes a robust forecasting method for non-stationary time series. The time series is modelled using non-parametric heteroscedastic regression, and fitted by a localized MM-estimator, combining high robustness and large efficiency. The proposed method is shown to produce reliable forecasts in the presence of outliers, non-linearity, and heteroscedasticity. In the absence of outliers, the forecasts are only slightly less precise than those based on a localized Least Squares estimator. An additional advantage of the MM-estimator is that it provides a robust estimate of the local variability of the time series. |
| Keywords: | Heteroscedasticity;Non-parametric regression;Prediction;Outliers;Robustness |
| JEL: | C14 C53 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2010105&r=ets |
| By: | Caporin, M.; McAleer, M.J. |
| Abstract: | This paper focuses on the selection and comparison of alternative non-nested volatility models. We review the traditional in-sample methods commonly applied in the volatility framework, namely diagnostic checking procedures, information criteria, and conditions for the existence of moments and asymptotic theory, as well as the out-of-sample model selection approaches, such as mean squared error and Model Confidence Set approaches. The paper develops some innovative loss functions which are based on Value-at-Risk forecasts. Finally, we present an empirical application based on simple univariate volatility models, namely GARCH, GJR, EGARCH, and Stochastic Volatility that are widely used to capture asymmetry and leverage. |
| Keywords: | volatility model selection;volatility model comparison;non-nested models;model confidence set;Value-at-Risk forecasts;asymmetry, leverage |
| Date: | 2010–10–12 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:eureir:1765020940&r=ets |
| By: | Marina Theodosiou (Central Bank of Cyprus) |
| Abstract: | In the current paper, we investigate the bias introduced through the calendar time sampling of the price process of financial assets. We analyze results from a Monte Carlo simulation which point to the conclusion that the multitude of jumps reported in the literature might be, to a large extent, an artifact of the bias introduced through the previous tick sampling scheme, used for the time homogenization the price series. We advocate the use of Akima cubic splines as an alternative to the popular previous tick method. Monte Carlo simulation results confirm the suitability of Akima cubic splines in high frequency applications and the advantages of these over other calendar time sampling schemes, such as the linear interpolation and the previous tick method. Empirical results from the FX market complement the analysis. |
| Keywords: | Sampling schemes, previous tick method, quadratic variation, jumps, stochastic volatility,realized measures, high-frequency data |
| JEL: | C12 C14 G10 |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:cyb:wpaper:2010-7&r=ets |
| By: | Castle, Jennifer L.; Fawcett, Nicholas W.; Hendry, David F. |
| Abstract: | When location shifts occur, cointegration-based equilibrium-correction models (EqCMs) face forecasting problems. We consider alleviating such forecast failure by updating, intercept corrections, differencing, and estimating the future progress of an 'internal' break. Updating leads to a loss of cointegration when an EqCM suffers an equilibrium-mean shift, but helps when collinearities are changed by an 'external' break with the EqCM staying constant. Both mechanistic corrections help compared to retaining a pre-break estimated model, but an estimated model of the break process could outperform. We apply the approaches to EqCMs for UK M1, compared with updating a learning function as the break evolves. |
| JEL: | C1 C53 |
| Date: | 2010–10 |
| URL: | http://d.repec.org/n?u=RePEc:ner:oxford:http://economics.ouls.ox.ac.uk/14904/&r=ets |
| By: | Andrzej Jarosz |
| Abstract: | I apply the method of planar diagrammatic expansion to solve the problem of finding the mean spectral density of the non-Hermitian time-lagged covariance estimator for a system of i.i.d. Gaussian random variables. I confirm the result in a much simpler way using a recent conjecture about non-Hermitian random matrix models with rotationally-symmetric spectra. I conjecture and test numerically a form of finite-size corrections to the mean spectral density featuring the complementary error function. |
| Date: | 2010–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1010.2981&r=ets |
| By: | Nikolai Dokuchaev |
| Abstract: | This short note suggests a heuristic method for detecting the dependence of random time series that can be used in the case when this dependence is relatively weak and such that the traditional methods are not effective. The method requires to compare some special functionals on the sample characteristic functions with the same functionals computed for the benchmark time series with a known degree of correlation. Some experiments for financial time series are presented. |
| Date: | 2010–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1010.2576&r=ets |