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on Econometric Time Series |
| By: | Ole Eiler Barndorff-Nielsen (Thiele Centre, Department of Mathematical Sciences & CREATES, Aarhus University); Robert Stelzer (TUM Institute for Advanced Study & Zentrum Mathematik, Technische Universität München) |
| Abstract: | Using positive semidefinite supOU (superposition of Ornstein-Uhlenbeck type) processes to describe the volatility, we introduce a multivariate stochastic volatility model for financial data which is capable of modelling long range dependence effects. The finiteness of moments and the second order structure of the volatility, the log returns, as well as their “squares” are discussed in detail. Moreover, we give several examples in which long memory effects occur and study how the model as well as the simple Ornstein-Uhlenbeck type stochastic volatility model behave under linear transformations. In particular, the models are shown to be preserved under invertible linear transformations. Finally, we discuss how (sup)OU stochastic volatility models can be combined with a factor modelling approach. |
| Keywords: | factor modelling, Lévy bases, linear transformations, long memory, Ornstein-Uhlenbeck type process, second order moment structure, stochastic volatility |
| JEL: | C1 C5 G0 G1 |
| Date: | 2009–09–17 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2009-42&r=ets |
| By: | Matias D. Cattaneo (Department of Economics, University of Michigan); Richard K. Crump (Federal Reserve Bank of New York); Michael Jansson (Department of Economics, UC Berkeley and CREATES) |
| Abstract: | This paper presents a new data-driven bandwidth selector compatible with the small bandwidth asymptotics developed in Cattaneo, Crump, and Jansson (2009) for density- weighted average derivatives. The new bandwidth selector is of the plug-in variety, and is obtained based on a mean squared error expansion of the estimator of interest. An extensive Monte Carlo experiment shows a remarkable improvement in performance when the bandwidth- dependent robust inference procedure proposed by Cattaneo, Crump, and Jansson (2009) is coupled with this new data-driven bandwidth selector. The resulting robust data-driven confi- dence intervals compare favorably to the alternative procedures available in the literature. |
| Keywords: | Average derivatives, Bandwidth selection, Robust inference, Small bandwidth asymptotics |
| JEL: | C12 C14 C21 C24 |
| Date: | 2009–09–28 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2009-46&r=ets |
| By: | Kim Christensen (Aarhus University and CREATES); Silja Kinnebrock (Oxford-Man Institute of Quantitative Finance, Oxford University); Mark Podolskij (ETH Zürich, Switzerland and CREATES, Aarhus University) |
| Abstract: | In this paper, we show how simple pre-averaging can be applied to measure the ex-post covariance of high-frequency financial time series under market microstructure noise and non-synchronous trading. A modulated realised covariance based on pre-averaged data is proposed and studied in this setting, and we provide complete large sample asymptotics for this new estimator, including feasible central limit theorems for standard methods such as covariance, regression, and correlation analysis. We discuss several versions of the modulated realised covariance, which can be designed to possess an optimal rate of convergence or to guarantee positive semi-definite covariance matrix estimates. We also derive a pre-averaged version of the Hayashi-Yoshida estimator that can be applied directly to the noisy and nonsynchronous data without any prior alignment of prices. An empirical study illustrates how high-frequency covariances, regression coefficients, and correlations change through time. |
| Keywords: | Central limit theorem,Diffusionmodels, High-frequency data, Marketmicrostructure noise, Non-synchronous trading, Pre-averaging, Realised covariance |
| JEL: | C10 C22 C80 |
| Date: | 2009–09–01 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2009-45&r=ets |
| By: | Lasse Bork (Finance Research Group, Aarhus School of Business, University of Aarhus and CREATES); Hans Dewachter (CES, University of Leuven, RSM Rotterdam and CESIFO.); Romain Houssa (CRED and CEREFIM, University of Namur, CES, University of Leuven) |
| Abstract: | This paper presents a dynamic factor model in which the extracted factors and shocks are given a clear economic interpretation. The eco- nomic interpretation of the factors is obtained by means of a set of over- identifying loading restrictions, while the structural shocks are estimated following standard practices in the SVAR literature. Estimators based on the EM algorithm are developped. We apply this framework to a large panel of US monthly macroeconomic series. In particular, we identify nine macroeconomic factors and discuss the economic impact of monetary pol- icy stocks. The results are theoretically plausible and in line with other findings in the literature. |
| Keywords: | Monetary policy, Business Cycles, Factor Models, EM Algorithm |
| JEL: | E3 E43 C51 E52 C33 |
| Date: | 2009–09–01 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2009-43&r=ets |
| By: | Mark Podolskij (ETH Zürich and CREATES); Mathias Vetter (Ruhr-University of Bochum) |
| Abstract: | This paper presents a short survey on limit theorems for certain functionals of semimartingales, which are observed at high frequency. Our aim is to explain the main ideas of the theory to a broader audience. We introduce the concept of stable convergence, which is crucial for our purpose. We show some laws of large numbers (for the continuous and the discontinuous case) that are the most interesting from a practical point of view, and demonstrate the associated stable central limit theorems. Moreover, we state a simple sketch of the proofs and give some examples. |
| Keywords: | central limit theorem, high frequency observations, semimartingale, stable convergence |
| JEL: | C10 C13 C14 |
| Date: | 2009–10–05 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2009-47&r=ets |
| By: | Eiji Kurozumi; Shinya Tanaka |
| Abstract: | This paper proposes a new stationarity test based on the KPSS test with less size distortion. We extend the boundary rule proposed by Sul, Phillips and Choi (2005) to the autoregressive spectral density estimator and parametrically estimate the long-run variance. We also derive the finite sample bias of the numerator of the test statistic up to the 1/T order and propose a correction to the bias term in the numerator. Finite sample simulations show that the correction term effectively reduces the bias in the numerator and that the finite sample size of our test is close to the nominal one as long as the long-run parameter in the model satisfies the boundary condition. |
| Keywords: | Stationary test, size distortion, boundary rule, bias correction |
| JEL: | C12 C22 |
| Date: | 2009–09 |
| URL: | http://d.repec.org/n?u=RePEc:hst:ghsdps:gd09-085&r=ets |
| By: | Per Frederiksen (Nordea Markets); Frank S. Nielsen (Aarhus University and CREATES); Morten Ørregaard Nielsen (Queen's University and CREATES) |
| Abstract: | We propose a semiparametric local polynomial Whittle with noise estimator of the memory parameter in long memory time series perturbed by a noise term which may be serially correlated. The estimator approximates the log-spectrum of the short-memory component of the signal as well as that of the perturbation by two separate polynomials. Including these polynomials we obtain a reduction in the order of magnitude of the bias, but also inflate the asymptotic variance of the long memory estimator by a multiplicative constant. We show that the estimator is consistent for d in (0,1), asymptotically normal for d in (0,3/4), and if the spectral density is sufficiently smooth near frequency zero, the rate of convergence can become arbitrarily close to the parametric rate, sqrt(n). A Monte Carlo study reveals that the proposed estimator performs well in the presence of a serially correlated perturbation term. Furthermore, an empirical investigation of the 30 DJIA stocks shows that this estimator indicates stronger persistence in volatility than the standard local Whittle (with noise) estimator. |
| Keywords: | Bias reduction, local Whittle, long memory, perturbed fractional process, semiparametric estimation, stochastic volatility |
| JEL: | C22 |
| Date: | 2009–09 |
| URL: | http://d.repec.org/n?u=RePEc:qed:wpaper:1218&r=ets |
| By: | Chuan Goh |
| Abstract: | This paper proposes a test for the correct specification of a dynamic time-series model that is taken to be stationary about a deterministic linear trend function with no more than a finite number of discontinuities in the vector of trend coefficients. The test avoids the consideration of explicit alternatives to the null of trend stability. The proposal also does not involve the detailed modelling of the data-generating process of the stochastic component, which is simply assumed to satisfy a certain strong invariance principle for stationary causal processes taking a general form. As such, the resulting inference procedure is effectively an omnibus specification test for segmented linear trend stationarity. The test is of Wald-type, and is based on an asymptotically linear estimator of the vector of total-variation norms of the trend parameters whose influence function coincides with the efficient influence function. Simulations illustrate the utility of this procedure to detect discrete breaks or continuous variation in the trend parameter as well as alternatives where the trend coefficients change randomly each period. This paper also includes an application examining the adequacy of a linear trend-stationary specification with infrequent trend breaks for the historical evolution of U.S. real output. |
| Keywords: | Structural change, trend-stationary processes, nonparametric regression, efficient influence function |
| JEL: | C12 C14 C22 |
| Date: | 2009–09–30 |
| URL: | http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-373&r=ets |
| By: | Westerlund, Joakim (Department of Economics, School of Business, Economics and Law, Göteborg University) |
| Abstract: | This paper proposes two new unit root tests that are appropriate in the presence of an unknown number of structural breaks. One is based on a single time series and the other is based on a panel of multiple series. For the estimation of the number of breaks and their locations, a simple procedure based on outlier detection is proposed. The limiting distributions of the tests are derived and evaluated in small samples using simulation experiments. The implementation of the tests is illustrated using as an example purchasing power parity.<p> |
| Keywords: | Unit root test; Structural break; Outlier detection; Common factor; Purchasing power parity |
| JEL: | C12 C15 C22 F31 |
| Date: | 2009–09–29 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:gunwpe:0384&r=ets |
| By: | Westerlund, Joakim (Department of Economics, School of Business, Economics and Law, Göteborg University); Larsson, Rolf (Uppsala University) |
| Abstract: | This paper proposes a new unit root test in the context of a random autoregressive coefficient panel data model, in which the null of a unit root corresponds to the joint restriction that the autoregressive coefficient has unit mean and zero variance. The asymptotic distribution of the test statistic is derived and simulation results are provided to suggest that it performs very well in small samples.<p> |
| Keywords: | Panel unit root test; Random coefficient autoregressive model |
| JEL: | C13 C33 |
| Date: | 2009–10–01 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:gunwpe:0383&r=ets |
| By: | Jorg Breitung (University of Bonn); Gianluca Cubadda (Faculty of Economics, University of Rome "Tor Vergata") |
| Abstract: | This paper considers cointegration tests for dynamic systems where the number of variables is large relative to the sample size. Typical examples include tests for unit roots in panels, where the units are linked by complicated dynamic relationships. It is well known that conventional cointegration tests based on a parametric (vector autoregressive) representation of the system break down if the number of variables approaches the number of time periods. To sidestep this difficulty we propose nonparametric cointegration tests based on eigenvalue problems that are asymptotically free of nuisance parameters. Furthermore, a nonparametric panel unit root test is suggested. It turns out that if the number of variables is large, the nonparametric tests outperform their parametric (likelihood-ratio based) counterparts by a clear margin. |
| Date: | 2009–09–30 |
| URL: | http://d.repec.org/n?u=RePEc:rtv:ceisrp:148&r=ets |
| By: | Cerqueti, Roy; Costantini, Mauro; Lupi, Claudio |
| Abstract: | This paper provides a theoretical functional representation of the density function related to the Dickey- Fuller random variable. The approach is extended to cover the multivariate case in two special frameworks: the independence and the perfect correlation of the series. |
| Keywords: | Dickey-Fuller distribution, unit root |
| JEL: | C12 C16 C22 |
| Date: | 2009–09–28 |
| URL: | http://d.repec.org/n?u=RePEc:mol:ecsdps:esdp09055&r=ets |