
on Econometric Time Series 
By:  Roy Cerqueti (University of Macerata); Paolo Falbo (University of Brescia); Cristian Pelizzari (University of Brescia); Federica Ricca (Sapienza University of Rome); Andrea Scozzari (University Niccolo' Cusano, Rome) 
Abstract:  Bootstrapping time series is one of the most acknowledged tools to make forecasts and study the statistical properties of an evolutive phenomenon. The idea underlying this procedure is to replicate the phenomenon on the basis of an observed sample. One of the most important classes of bootstrap procedures is based on the assumption that the sampled phenomenon evolves according to a Markov chain. Such an assumption does not apply when the process takes values in a continuous set, as frequently happens for time series related to economic and financial variables. In this paper we apply Markov chain theory for bootstrapping continuous processes, relying on the idea of discretizing the support of the process and suggesting Markov chains of order k to model the evolution of the time series under study. The difficulty of this approach is that, even for small k, the number of rows of the transition probability matrix is too large, and this leads to a bootstrap procedure of high complexity. In many practical cases such complexity is not fully justified by the information really required to replicate a phenomenon satisfactorily. In this paper we propose a methodology to reduce the number of rows without loosing ``too much'' information on the process evolution. This requires a clustering of the rows that preserves as much as possible the ``law'' that originally generated the process. The novel aspect of our work is the use of Mixed Integer Linear Programming for formulating and solving the problem of clustering similar rows in the original transition probability matrix. Even if it is well known that this problem is computationally hard, in our application medium size reallife instances were solved efficiently. Our empirical analysis, which is done on two time series of prices from the German and the Spanish electricity markets, shows that the use of the aggregated transition probability matrix does not affect the bootstrapping procedure, since the characteristic features of the original series are maintained in the resampled ones. 
Keywords:  Continuous Markov processes,,Time series bootstrapping.,Mixed Integer Linear Programming,,Markov chains, 
Date:  2012–11 
URL:  http://d.repec.org/n?u=RePEc:mcr:wpdief:wpaper00067&r=ets 
By:  Baumöhl, Eduard; Lyócsa, Štefan 
Abstract:  The weekly returns of equities are commonly used in the empirical research to avoid the nonsynchronicity of daily data. An empirical analysis is used to show that the statistical properties of a weekly stock returns series strongly depend on the method used to construct this series. Three types of weekly returns construction are considered: (i) WednesdaytoWednesday, (ii) FridaytoFriday, and (iii) averaging daily observations within the corresponding week. Considerable distinctions are found between these procedures using data from the S&P500 and DAX stock market indices. Differences occurred in the unitroot tests, identified volatility breaks, unconditional correlations, ARMAGARCH and DCC MVGARCH models as well. Our findings provide evidence that the method employed for constructing weekly stock returns can have a decisive effect on the outcomes of empirical studies. 
Keywords:  stock markets; weekly returns; statistical properties 
JEL:  C10 G10 C80 
Date:  2012–12–26 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:43431&r=ets 
By:  Hanck, Christoph; Demetrescu, Matei; Tarcolea, Adina 
Abstract:  While the limiting null distributions of cointegration tests are invariant to a certain amount of conditional heteroskedasticity as long as global homoskedasticity conditions are fulfilled, they are certainly affected when the innovations exhibit timevarying volatility. Worse yet, distortions from single units accumulate in panels, where one must anyway pay special attention to dependence among crosssectional units, be it timedependent or not. To obtain a panel cointegration test robust to both global heteroskedasticity and crossunit dependence, we start by adapting the nonlinear instruments method proposed for the DickeyFuller test by Chang (J of Econometrics 110, 261292) to an errorcorrection testing framework. We show that IVbased testing of the null of no errorcorrection in individual equations results in asymptotic standard normality of the test statistic as long as the ttype statistics are computed with White heteroskedasticityconsistent standard errors. Remarkably, the result holds even in the presence of endogenous regressors, irrespective of the number of integrated covariates, and for any variance profile. Furthermore, a test for the null of no cointegrationin effect, a joint test against no error correction in any equation of each unitretains the nice properties of the univariate tests. In panels with fixed crosssectional dimension, both types of test statistics from individual units are shown to be asymptotically independent even in the presence of correlation or cointegration across units, leading to a panel test statistic robust to crossunit dependence and unconditional heteroskedasticity. The tests perform well in panels of usual dimensions with innovations exhibiting variance breaks and a factor structure.  
JEL:  C12 C22 C23 
Date:  2012 
URL:  http://d.repec.org/n?u=RePEc:zbw:vfsc12:62072&r=ets 