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on Econometric Time Series |
| By: | Christos Ntantamis (School of Economics and Management, University of Aarhus and CREATES) |
| Abstract: | Testing for structural breaks and identifying their location is essential for econometric modeling. In this paper, a Hidden Markov Model (HMM) approach is used in order to perform these tasks. Breaks are defined as the data points where the underlying Markov Chain switches from one state to another. The estimation of the HMM is conducted using a variant of the Iterative Conditional Expectation-Generalized Mixture (ICE-GEMI) algorithm proposed by Delignon et al. (1997), that permits analysis of the conditional distributions of economic data and allows for different functional forms across regimes. The locations of the breaks are subsequently obtained by assigning states to data points according to the Maximum Posterior Mode (MPM) algorithm. The Integrated Classification Likelihood-Bayesian Information Criterion (ICL-BIC) allows for the determination of the number of regimes by taking into account the classification of the data points to their corresponding regimes. The performance of the overall procedure, denoted IMI by the initials of the component algorithms, is validated by two sets of simulations; one in which only the parameters are permitted to differ across regimes, and one that also permits differences in the functional forms. The IMI method performs well in both sets. Moreover, when it is compared to the Bai and Perron (1998) method its performance is superior in the assessing the number of breaks and their respective locations. Finally, the methodology is applied for the detection of breaks in the monetary policy of United States, the di erent functional form being variants of the Taylor (1993) rule. |
| Keywords: | Structural change, Hidden Markov Model, Regime Switching, Bayesian Segmentation, Monetary Policy |
| JEL: | C13 C22 C52 |
| Date: | 2010–08–31 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2010-52&r=ets |
| By: | Christos Ntantamis (School of Economics and Management, University of Aarhus and CREATES) |
| Abstract: | This paper introduces a Duration Hidden Markov Model to model bull and bear market regime switches in the stock market; the duration of each state of the Markov Chain is a random variable that depends on a set of exogenous variables. The model not only allows the endogenous determination of the different regimes and but also estimates the effect of the explanatory variables on the regimes' durations. The model is estimated here on NYSE returns using the short-term interest rate and the interest rate spread as exogenous variables. The bull market regime is assigned to the identified state with the higher mean and lower variance; bull market duration is found to be negatively dependent on short-term interest rates and positively on the interest rate spread, while bear market duration depends positively the short-term interest rate and negatively on the interest rate spread. |
| Keywords: | Hidden Markov Model, Variable-dependent regime duration, Regime Switching, Interest rate effect |
| JEL: | C13 C22 G1 |
| Date: | 2010–08–25 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2010-51&r=ets |
| By: | Laurent Ferrara (DGEI-DAMEP - Banque de France); Dominique Guegan (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris); Zhiping Lu (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, ECNU - East China Normal University) |
| Abstract: | Testing the fractionally integrated order of seasonal and nonseasonal unit roots is quite important for the economic and financial time series modeling. In this article, the widely used Robinson's (1994) test is applied to various well-known long memory models. Via Monte Carlo experiments, we study and compare the performances of this test using several sample sizes. |
| Keywords: | Long memory processes – test – Monte Carlo simulations |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:hal-00486655_v1&r=ets |
| By: | Dominique Guegan (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris); Patrick Rakotomarolahy (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I) |
| Abstract: | An empirical forecast accuracy comparison of the non-parametric method, known as multivariate Nearest Neighbor method, with parametric VAR modelling is conducted on the euro area GDP. Using both methods for nowcasting and forecasting the GDP, through the estimation of economic indicators plugged in the bridge equations, we get more accurate forecasts when using nearest neighbor method. We prove also the asymptotic normality of the multivariate k-nearest neighbor regression estimator for dependent time series, providing confidence intervals for point forecast in time series. |
| Keywords: | Forecast - Economic indicators - GDP - Euro area - VAR - Multivariate k nearest neighbor regression - Asymptotic normality |
| Date: | 2010–12 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00511979_v1&r=ets |
| By: | David Grreasley (University of Canterbury) |
| Abstract: | The paper discusses a range of modern time series methods that have become popular in the past 20 years and considers their usefulness for cliometrics research both in theory and via a range of applications. Issues such as, spurious regression, unit roots, cointegration, persistence, causality, structural time series methods, including time varying parameter models, are introduced as are the estimation and testing implications that they involve. Applications include a discussion of the timing and potential causes of the British Industrial Revolution, income „convergence? and the long run behaviour of English Real Wages 1264 – 1913. Finally some new and potentially useful developments are discussed including the mildly explosive processes; graphical modelling and long memory. |
| Keywords: | Time series; cointegration; unit roots; persistence; causality; cliometrics; convergence; long memory; graphical modelling; British Industrial Revolution |
| JEL: | N33 O47 O56 C22 C32 |
| Date: | 2010–09–04 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:10/56&r=ets |
| By: | Harvey, A. |
| Abstract: | The asymptotic distribution of maximum likelihood estimators is derived for a class of exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models. The result carries over to models for duration and realised volatility that use an exponential link function. A key feature of the model formulation is that the dynamics are driven by the score. |
| Keywords: | Duration models; gamma distribution; general error distribution; heteroskedasticity; leverage; score; Student's t. |
| JEL: | C22 |
| Date: | 2010–08–26 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1040&r=ets |
| By: | Kruse, Robinson; Sibbertsen, Philipp |
| Abstract: | We study the empirical behaviour of semi-parametric log-periodogram estimation for long memory models when the true process exhibits a change in persistence. Simulation results confirm theoretical arguments which suggest that evidence for long memory is likely to be found. A recently proposed test by Sibbertsen and Kruse (2009) is shown to exhibit noticeable power to discriminate between long memory and a structural change in autoregressive parameters. |
| Keywords: | Long memory; changing persistence; structural break; semi-parametric estimation |
| JEL: | C12 C22 |
| Date: | 2010–08 |
| URL: | http://d.repec.org/n?u=RePEc:han:dpaper:dp-455&r=ets |
| By: | Politis, D N; McElroy, Tucker S |
| Abstract: | This paper considers the problem of distribution estimation for the studentized sample mean in the context of Long Memory and Negative Memory time series dynamics, adopting the fixed-bandwidth approach now popular in the econometrics literature. The distribution theory complements the Short Memory results of Kiefer and Vogelsang (2005). In particular, our results highlight the dependence on the employed kernel, whether or not the taper is nonzero at the boundary, and most importantly whether or not the process has short memory. We also demonstrate that small-bandwidth approaches fail when long memory or negative memory is present since the limiting distribution is either a point mass at zero or degenerate. Extensive numerical work provides approximations to the quantiles of the asymptotic distribution for a range of tapers and memory parameters; these quantiles can be used in practice for the construction of confidence intervals and hypothesis tests for the mean of the time series. |
| Keywords: | confidence intervals, critical values, dependence, gaussian, kernel spectral density, tapers, testing |
| Date: | 2009–12–01 |
| URL: | http://d.repec.org/n?u=RePEc:cdl:ucsdec:1088027&r=ets |
| By: | McMurry, Timothy L; Politis, D N |
| Abstract: | We address the problem of estimating the autocovariance matrix of a stationary process. Under short range dependence assumptions, convergence rates are established for a gradually tapered version of the sample autocovariance matrix and for its inverse. The proposed estimator is formed by leaving the main diagonals of the sample autocovariance matrix intact while gradually down-weighting o�-diagonal entries towards zero. In addition we show the same convergence rates hold for a positive de�nite version of the estimator, and we introduce a new approach for selecting the banding parameter. The new matrix estimator is shown to perform well theoretically and in simulation studies. As an application we introduce a new resampling scheme for stationary processes termed the linear process bootstrap (LPB). The LPB is shown to be asymptotically valid for the sample mean and related statistics. The e�ectiveness of the proposed methods are demonstrated in a simulation study. |
| Keywords: | autocovariance matrix, stationary process, boostrap, block bootstrap, sieve bootstrap |
| Date: | 2010–03–31 |
| URL: | http://d.repec.org/n?u=RePEc:cdl:ucsdec:1257043&r=ets |
| By: | Beare, Brendan K. |
| Abstract: | We study the dependence properties of stationary Markov chains generated by lower tail dependent Archimedean copulas. Under some simple regularity conditions, we show that regular variation of the generator function at zero implies that the associated rate of beta-mixing is geometric or faster. Sufficiently rapid variation of the generator function at zero forces the rate of alpha-mixing to be no faster than polynomial, leading to a Markovian form of long memory. |
| Keywords: | Archimedean copula, ergodicity, long memory, Markov chain, mixing, regular variation, tail dependence |
| Date: | 2010–06–07 |
| URL: | http://d.repec.org/n?u=RePEc:cdl:ucsdec:1350334&r=ets |