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on Econometric Time Series |
| By: | Diaa Noureldin; Neil Shephard; Kevin Sheppard |
| Abstract: | This paper introduces a new class of multivariate volatility models which is easy to estimate using covariance targeting, even with rich dynamics. We call them rotated ARCH (RARCH) models. The basic structure is to rotate the returns and then to fit them using a BEKK-type parameterization of the time-varying covariance whose long-run covariance is the identity matrix. The extension to DCC-type parameterizations is given, introducing the rotated conditional correlation (RCC) model. Inference for these mdoels is computationally attractive, and the asymptotics are standard. The techniques are illustrated using data on some SJIA stocks. |
| Keywords: | RCC, Multivariate volatiity, Covariance targeting, Common persistence, Empirical Bayes, Predictive likelihood |
| JEL: | C32 C52 C58 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:594&r=ets |
| By: | Dominique Guegan (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris); Zhiping Lu (ECNU - East China Normal University); Beijia Zhu (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon Sorbonne, ECNU - East China Normal University) |
| Abstract: | In this paper, nine memory parameter estimation procedures for the fractionally integrated I(d) process, semi-parametric and parametric, which prevail in the existing literature are reviewed ; through the simulation study under the ARFIMA (p,d,q) setting we cast a light on the finite sample performance of these estimation procedures for the non-stationary long memory time series. As a by-product of this study, we provide a bandwidth parameter selection strategy for the frequency domain estimation and an upper-and-lower scale trimming strategy for the wavelet domain estimation from a practical stand-point. The other objective of this paper is to give a useful reference to the applied reserachers and practitioners. |
| Keywords: | Long memory processes, wavelets, Monte Carlo simulations. |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00673934&r=ets |
| By: | Chaohua Dong; Jiti Gao |
| Abstract: | In this paper, expansions of functionals of Lévy processes are established under some Hilbert spaces and their orthogonal bases. From practical standpoint, both time-homogeneous and time-inhomogeneous functionals of Lévy processes are considered. Several expansions and rates of convergence are established. In order to state asymptotic distributions for statistical estimators of unknown parameters involved in a general regression model, we develop a general asymptotic theory for partial sums of functionals of Lévy processes. The results show that these estimators of the unknown parameters in different situations converge to quite different random variables. In addition, the rates of convergence depend on various factors rather than just the sample size. |
| Keywords: | Expansion, Lévy Process, Orthogonal Series, Statistical Estimation. |
| JEL: | C13 C14 C22 |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2012-2&r=ets |
| By: | Song Li; Mervyn J. Silvapulle; Param Silvapulle; Xibin Zhang |
| Abstract: | This paper investigates nonparametric estimation of density on [0,1]. The kernel estimator of density on [0,1] has been found to be sensitive to both bandwidth and kernel. This paper proposes a unified Bayesian framework for choosing both the bandwidth and kernel function. In a simulation study, the Bayesian bandwidth estimator performed better than others, and kernel estimators were sensitive to the choice of the kernel and the shapes of the population densities on [0,1]. The simulation and empirical results demonstrate that the methods proposed in this paper can improve the way the probability densities on [0,1] are presently estimated. |
| Keywords: | Asymmetric kernel, Bayes factor, boundary bias, kernel selection, marginal likelihood, recovery-rate density |
| JEL: | C11 C14 C15 |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2012-3&r=ets |
| By: | G. Pan; J. Gao; Y. Yang; M. Guo |
| Abstract: | This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The asymptotic distributions of the test statistic under the null and local alternative hypotheses are established as dimensionality and the sample size of the data are comparable. We apply this test to examine multiple MA(1) and AR(1) models, panel data models with some spatial cross-sectional structures. In addition, in a flexible applied fashion, the proposed test can capture some dependent but uncorrelated structures, for example, nonlinear MA(1) models, multiple ARCH(1) models and vandermonde matrices. Simulation results are provided for detecting these dependent structures. An empirical study of dependence between closed stock prices of several companies from New York Stock Exchange (NYSE) demonstrates that the feature of cross-sectional dependence is popular in stock markets |
| Keywords: | Independence test, cross-sectional dependence, empirical spectral distribution, characteristic function, Marcenko-Pastur Law |
| JEL: | C12 C21 C22 |
| Date: | 2012–01–20 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2012-1&r=ets |
| By: | Eiji Kurozumi |
| Abstract: | This paper investigates tests for multiple structural changes with non-homogeneous regressors, such as polynomial trends. We consider exponential-type, supremum-type and average-type tests as well as the corresponding weighted-type tests suggested in the literature. We show that the limiting distributions depend on regressors in general, and we need to tabulate critical values depending on them. Then, we focus on the linear trend case and obtain the critical values of the test statistics. The Mote Carlo simulations are conducted to investigate the finite sample properties of the tests proposed in the paper, and it is found that the specification of the number of breaks is an important factor for the finite sample performance of the tests. Since it is often the case that we cannot prespecify the number of breaks under the alternative but can suppose only the maximum number of breaks, the weighted-type tests are useful in practice. |
| Keywords: | Multiple Breaks, Exp-type Test, Sup-type Test, Avg-type Test, Mean-type Test |
| JEL: | C12 C22 |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:hst:ghsdps:gd11-227&r=ets |
| By: | Antipin, Jan-Erik (National Institute of Economic Research); Boumediene, Farid Jimmy (Ministry of Finance); Österholm, Pär (Sveriges Riksbank) |
| Abstract: | This paper assesses the usefulness of constant gain least squares when forecasting inflation. An out-of-sample forecast exercise is conducted, in which univariate autoregressive models for inflation in Australia, Swe-den, the United Kingdom and the United States are used. The results suggest that it is possible to improve the forecast accuracy by employing constant gain least squares instead of ordinary least squares. In particular, when using a gain of 0.05, constant gain least squares generally outper-forms the corresponding autoregressive model estimated with ordinary least squares. In fact, at longer forecast horizons, the root mean square forecast error is reliably lowered for all four countries and for all lag lengths considered in the study. |
| Keywords: | Out-of-sample forecasts; Inflation |
| JEL: | E31 E37 |
| Date: | 2012–02–01 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:nierwp:0126&r=ets |
| By: | Mantalos, Panagiotis (Department of Business, Economics, Statistics and Informatics) |
| Abstract: | In this paper, we introduce a set of critical values for unit root tests that are robust in the presence of conditional heteroscedasticity errors using the normalizing and variance-stabilizing transformation (NoVaS) in Politis (2007) and examine their properties using Monte Carlo methods. In terms of the size of the test, our analysis reveals that unit root tests with NoVaS-modified critical values have actual sizes close to the nominal size. For the power of the test, we find that unit root tests with NoVaS-modified critical values either have the same power as, or slightly better than, tests using conventional Dickey–Fuller critical values across the sample range considered. |
| Keywords: | Critical values; normalizing and variance-stabilizing transformation; unit root tests |
| JEL: | C01 C12 C15 |
| Date: | 2012–02–02 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:oruesi:2012_002&r=ets |
| By: | Wan, Lei (Maastricht University) |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:ner:maastr:urn:nbn:nl:ui:27-28190&r=ets |
| By: | Joshua C C Chan; Gary Koop |
| Abstract: | Macroeconomists working with multivariate models typically face uncertainty over which (if any) of their variables have long run steady states which are subject to breaks. Furthermore, the nature of the break process is often unknown. In this paper, we draw on methods from the Bayesian clustering literature to develop an econometric methodology which: i) finds groups of variables which have the same number of breaks; and ii) determines the nature of the break process within each group. We present an application involving a five-variate steady-state VAR. |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:acb:camaaa:2012-07&r=ets |
| By: | Michael Wolf; Dan Wunderli |
| Abstract: | Many economic and financial applications require the forecast of a random variable of interest over several periods into the future. The sequence of individual forecasts, one period at a time, is called a path-forecast, where the term path refers to the sequence of individual future realizations of the random variable. The problem of constructing a corresponding joint prediction region has been rather neglected in the literature so far: such a region is supposed to contain the entire future path with a prespecified probability. We develop bootstrap methods to construct joint prediction regions. The resulting regions are proven to be asymptotically consistent under a mild high-level assumption. We compare the finite-sample performance of our joint prediction regions to some previous proposals via Monte Carlo simulations. An empirical application to a real data set is also provided. |
| Keywords: | Generalized error rates, path-forecast, simultaneous prediction intervals |
| JEL: | C14 C32 C53 |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:064&r=ets |
| By: | Jakob Söhl |
| Abstract: | Confidence intervals and joint confidence sets are constructed for the nonparametric calibration of exponential Lévy models based on prices of European options. This is done by showing joint asymptotic normality for the estimation of the volatility, the drift, the intensity and the Lévy density at nitely many points in the spectral calibration method. Furthermore, the asymptotic normality result leads to a test on the value of the volatility in exponential Lévy models. |
| Keywords: | European option, Jump diffusion, Confidence sets, Asymptotic normality, Nonlinear inverse problem |
| JEL: | G13 C14 |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2012-012&r=ets |
| By: | Gianluca Cubadda (Faculty of Economics, University of Rome "Tor Vergata"); Barbara Guardabascio (ISTAT); Alain Hecq (Maastricht University) |
| Abstract: | Combining economic time series with the aim to obtain an indicator for business cycle analyses is an important issue for policy makers. In this area, econometric techniques usually rely on systems with either a small number of series, N, (VAR or VECM) or, at the other extreme, a very large N (factor models). In this paper we propose tools to select the relevant business cycle indicators in a "medium" N framework, a situation that is likely to be the most frequent in empirical works. An example is provided by our empirical application, in which we study jointly the short-run co-movements of 24 European countries. We show, under not too restrictive conditions, that parsimonious single-equation models can be used to split a set of N countries in three groups. The first group comprises countries that share a synchronous common cycle, a non-synchronous common cycle is present among the countries of the second group, and the third group collects countries that exhibit idiosyncratic cycles. Moreover, we offer a method for constructing a composite coincident indicator that explicitly takes into account the existence of these various forms of short-run co-movements among variables. |
| Keywords: | Co-movements, common cycles, composite business cycle indicators, Euro area. |
| JEL: | C32 |
| Date: | 2012–02–27 |
| URL: | http://d.repec.org/n?u=RePEc:rtv:ceisrp:224&r=ets |
| By: | Ioannis Kasparis; Peter C.B. Phillips; Tassos Magdalinos |
| Abstract: | In regressions involving integrable functions we examine the limit properties of IV estimators that utilise integrable transformations of lagged regressors as instruments. The regressors can be either I(0) or I(1) processes. We show that this kind of nonlinearity in the regression function can significantly affect the relevance of the instruments. In particular, such instruments become weak when the signal of the regressor is strong, as it is in the I(1) case. Instruments based on integrable functions of lagged I(1) regressors display long range dependence and so remain relevant even at long lags, continuing to contribute to variance reduction in IV estimation. However, simulations show that OLS is generally superior to IV estimation in terms of MSE, even in the presence of endogeneity. Estimation precision is also reduced when the regressor is nonstationary. |
| Keywords: | Instrumental variables, Integrable function, Integrated process, Invariance principle, Local time, Mixed normality, Stationarity, Nonlinear cointegration, Unit roots, Weak Instruments. |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:ucy:cypeua:02-2012&r=ets |
| By: | Xiaohong Chen (Institute for Fiscal Studies and Yale University); Zhipeng Liao; Yixiao Sun |
| Abstract: | <p>The method of sieves has been widely used in estimating semiparametric and nonparametric models. In this paper, we first provide a general theory on the asymptotic normality of plug-in sieve M estimators of possibly irregular functionals of semi/nonparametric time series models. Next, we establish a surprising result that the asymptotic variances of plug-in sieve M estimators of irregular (i.e., slower than root-T estimable) functionals do not depend on temporal dependence. Nevertheless, ignoring the temporal dependence in small samples may not lead to accurate inference. We then propose an easy-to-compute and more accurate inference procedure based on a "pre-asymptotic" sieve variance estimator that captures temporal dependence. We construct a "pre-asymptotic" Wald statistic using an orthonormal series long run variance (OS-LRV) estimator. For sieve M estimators of both regular (i.e., root-T estimable) and irregular functionals, a scaled "pre-asymptotic" Wald statistic is asymptotically F distributed when the series number of terms in the OS-LRV estimator is held fixed. Simulations indicate that our scaled "pre-asymptotic" Wald test with F critical values has more accurate size in finite samples than the usual Wald test with chi-square critical values.</p> |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:06/12&r=ets |
| By: | Peter Carr; Travis Fisher; Johannes Ruf |
| Abstract: | We discuss the class of "Quadratic Normal Volatility" models, which have drawn much attention in the financial industry due to their analytic tractability and flexibility. We characterize these models as the ones that can be obtained from stopped Brownian motion by a simple transformation and a change of measure that only depends on the terminal value of the stopped Brownian motion. This explains the existence of explicit analytic formulas for option prices within Quadratic Normal Volatility models in the academic literature. |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1202.6187&r=ets |
| By: | Pesaran, M. H. |
| Abstract: | This paper considers testing the hypothesis that errors in a panel data model are weakly cross sectionally dependent, using the exponent of cross-sectional dependence <img src="http://www.econ.cam.ac.uk/faculty/pesaran/wp12/image3.png" width="11" height="13" />, introduced recently in Bailey, Kapetanios and Pesaran (2012). It is shown that the implicit null of the <em>CD</em> test depends on the relative expansion rates of <em>N</em> and <em>T</em>. When <em>T</em> = <em>O</em> <img src="http://www.econ.cam.ac.uk/faculty/pesaran/wp12/image4.png" width="29" height="15" />, for some <img src="http://www.econ.cam.ac.uk/faculty/pesaran/wp12/image5.png" width="82" height="14" />, then the implicit null of the CD test is given by <img src="http://www.econ.cam.ac.uk/faculty/pesaran/wp12/image7.png" width="118" height="15" />, which gives <img src="http://www.econ.cam.ac.uk/faculty/pesaran/wp12/image6.png" alt="image6" width="87" height="14" />, when <em>N</em> and <em>T</em> tend to infinity at the same rate such that <em>T</em>/<em>N</em> <img src="http://www.econ.cam.ac.uk/faculty/pesaran/wp12/image8.png" width="38" height="15" />, with <img src="http://www.econ.cam.ac.uk/faculty/pesaran/wp12/image9.png" width="12" height="15" /> being a finite positive constant. It is argued that in the case of large <em>N</em> panels, the null of weak dependence is more appropriate than the null of independence which could be quite restrictive for large panels. Using Monte Carlo experiments, it is shown that the CD test has the correct size for values of <img src="http://www.econ.cam.ac.uk/faculty/pesaran/wp12/image3.png" width="11" height="13" /> in the range [0, 1/4], for all combinations of <em>N</em> and <em>T</em>, and irrespective of whether the panel contains lagged values of the dependent variables, so long as there are no major asymmetries in the error distribution. |
| Keywords: | Exponent of cross-sectional dependence, Diagnostic tests, Panel data models, Dynamic heterogenous panels |
| JEL: | C12 C13 C33 |
| Date: | 2012–02–28 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1208&r=ets |
| By: | Gimeno, Ricardo; Gonzalez, Clara I. |
| Abstract: | Extreme Value Theory is increasingly used in the modelling of financial time series. The non-normality of stock returns leads to the search for alternative distributions that allows skewness and leptokurtic behavior. One of the most used distributions is the Pareto Distribution because it allows non-normal behaviour, which requires the estimation of a tail index. This paper provides a new method for estimating the tail index. We propose an automatic procedure based on the computation of successive normality tests over the whole of the distribution in order to estimate a Gaussian Distribution for the central returns and two Pareto distributions for the tails. We find that the method proposed is an automatic procedure that can be computed without need of an external agent to take the decision, so it is clearly objective. |
| Keywords: | Tail Index; Hill estimator; Normality Test |
| JEL: | C10 C15 G19 G00 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:37023&r=ets |