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on Econometric Time Series |
| By: | Giuseppe Cavaliere (Department of Statistical Sciences, University of Bologna); Anders Rahbek (Department of Economics, University of Copenhagen and CREATES); A.M.Robert Taylor (School of Economics and Granger Centre for Time Series Econometrics, University of Nottingham) |
| Abstract: | In a recent paper Cavaliere et al. (2012) develop bootstrap implementations of the (pseudo-) likelihood ratio [PLR] co-integration rank test and associated sequential rank determination procedure of Johansen (1996). The bootstrap samples are constructed using the restricted parameter estimates of the underlying VAR model which obtain under the reduced rank null hypothesis. They propose methods based on an i.i.d. bootstrap re-sampling scheme and establish the validity of their proposed bootstrap procedures in the context of a co-integrated VAR model with i.i.d. innovations. In this paper we investigate the properties of their bootstrap procedures, together with analogous procedures based on a wild bootstrap re-sampling scheme, when time-varying behaviour is present in either the conditional or unconditional variance of the innovations. We show that the bootstrap PLR tests are asymptotically correctly sized and, moreover, that the probability that the associated bootstrap sequential procedures select a rank smaller than the true rank converges to zero. This result is shown to hold for both the i.i.d. and wild bootstrap variants under conditional heteroskedasticity but only for the latter under unconditional heteroskedasticity. Monte Carlo evidence is reported which suggests that the bootstrap approach of Cavaliere et al. (2012) signi?cantly improves upon the ?nite sample performance of corresponding procedures based on either the asymptotic PLR test or an alternative bootstrap method (where the short run dynamics in the VAR model are estimated unrestrictedly) for a variety of conditionally and unconditionally heteroskedastic innovation processes. |
| Keywords: | Bootstrap, Co-integration, Trace statistic, Rank determination, heteroskedasticity. |
| JEL: | C30 C32 |
| Date: | 2012–08–31 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2012-36&r=ets |
| By: | Marcelo C. Medeiros (Pontifical Catholic University of Rio de Janeiro); Eduardo F. Mendes (Pontifical Catholic University of Rio de Janeiro) |
| Abstract: | We study the asymptotic properties of the Adaptive LASSO (adaLASSO) in sparse, high-dimensional, linear time-series models. We assume both the number of covariates in the model and candidate variables can increase with the number of observations and the number of candidate variables is, possibly, larger than the number of observations. We show the adaLASSO consistently chooses the relevant variables as the number of observations increases (model selection consistency), and has the oracle property, even when the errors are non-Gaussian and conditionally heteroskedastic. A simulation study shows the method performs well in very general settings. Finally, we consider two applications: in the first one the goal is to forecast quarterly US inflation one-step ahead, and in the second we are interested in the excess return of the S&P 500 index. The method used outperforms the usual benchmarks in the literature. |
| Keywords: | sparse models, shrinkage, LASSO, adaLASSO, time series, forecasting. |
| JEL: | C22 |
| Date: | 2012–09–04 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2012-37&r=ets |
| By: | Jiti Gao; Maxwell King |
| Abstract: | This paper proposes a simple and improved nonparametric unit-root test. An asymptotic distribution of the proposed test is established. Finite sample comparisons with an existing nonparametric test are discussed. Some issues about possible extensions are outlined. |
| Keywords: | Autoregression, nonparametric unit?root test, nonstationary time series, specification testing. |
| JEL: | C12 C14 C22 |
| Date: | 2012–08 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2012-16&r=ets |
| By: | Charley Xia and William Griffiths |
| Abstract: | A Monte Carlo experiment is used to examine the size and power properties of alternative Bayesian tests for unit roots. Four different prior distributions for the root that is potentially unity – a uniform prior and priors attributable to Jeffreys, Lubrano, and Berger and Yang – are used in conjunction with two testing procedures: a credible interval test and a Bayes factor test. Two extensions are also considered: a test based on model averaging with different priors and a test with a hierarchical prior for a hyperparameter. The tests are applied to both trending and non-trending series. Our results favor the use of a prior suggested by Lubrano. Outcomes from applying the tests to some Australian macroeconomic time series are presented. |
| Keywords: | N/A |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:mlb:wpaper:1152&r=ets |
| By: | Tomasz Wozniaka |
| Abstract: | Recent economic developments have shown the importance of spillover and contagion effects in financial markets. Such effects are not limited to relations between the levels of financial variables but also impact on their volatility. I investigate Granger causality in conditional mean and conditional variances of time series. For this purpose a VARMA-GARCH model is used. I derive parametric restrictions for the hypothesis of noncausality in conditional variances between two groups of variables, when there are other variables in the system as well. These novel conditions are convenient for the analysis of potentially large systems of economic variables. Such systems should be considered in order to avoid the problem of omitted variable bias. Further, I propose a Bayesian Lindley-type testing procedure in order to evaluate hypotheses of noncausality. It avoids the singularity problem that may appear in the Wald test. Also, it relaxes the assumption of the existence of higher-order moments of the residuals required for the derivation of asymptotic results of the classical tests. In the empirical example, I find that the dollar-to-Euro exchange rate does not second-order cause the pound-to-Euro exchange rate, in the system of variables containing also the Swiss frank-to-Euro exchange rate, which confirms the meteor shower hypothesis of Engle, Ito & Lin (1990). |
| Keywords: | Granger causality, second-order noncausality, VARMA-GARCH models, Bayesian testing |
| JEL: | C11 C12 C32 C53 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:eui:euiwps:eco2012/19&r=ets |
| By: | Tomasz Wozniak |
| Abstract: | Spillover and contagion effects have gained significant interest in the recent years of financial crisis. Attention has not only been directed to relations between returns of financial variables, but to spillovers in risk as well. I use the family of Constant Conditional Correlation GARCH models to model the risk associated with financial time series and to make inferences about Granger causal relations between second conditional moments. The restrictions for second-order Granger noncausality between two vectors of variables are derived. To assess the credibility of the noncausality hypotheses, I employ posterior odds ratios. This Bayesian method constitutes an alternative for classical tests that makes such testing possible, regardless of the form of the restrictions on the parameters of the model. Moreover, it relaxes the assumptions about the existence of higher-order moments of the processes required in classical tests. In the empirical example, I find that the pound-to-Euro exchange rate second-order causes the US dollar-to-Euro exchange rate, which confirms the meteor shower hypothesis of Engle, Ito & Lin (1990). |
| Keywords: | Second-Order Causality, Volatility Spillovers, Posterior Odds, GARCH Models |
| JEL: | C11 C12 C32 C53 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:eui:euiwps:eco2012/20&r=ets |
| By: | Dechert, Andreas |
| Abstract: | Modeling fractional cointegration relationships has become a major topic in applied time series analysis as it steps back from the traditional rigid I(1)/I(0) methodology. Hence, the number of proposed tests and approaches has grown over the last decade. The aim of this paper is to study the nonparametric variance ratio approach suggested by Nielsen for the case of fractional cointegration in presence of linear trend and trend breaks. The consideration of trend breaks is very important in order to avoid spurious fractional integration, so this possibility should be regarded by practitioners. This paper proposes to calculate p-values by means of gamma distributions and gives response regressions parameters for the asymptotic moments of them. In Monte Carlo simulations this work compares the power of the approach against a Johansen type rank test suggested, which is robust against trend breaks but not fractional (co-)integration. As the approach also obtains an estimator for the cointegration space, the paper compares it with OLS estimates in simulations. As an empirical example the validity of the market expectation hypothesis is tested for monthly Treasury bill rates ranging from 1958-2011, which might have a trend break around September 1979 due to change of American monetary policy. |
| Keywords: | fractional integration; fractional cointegration; long memory; variance ratio; nonparametric; trend breaks; market expectation hypothesis |
| JEL: | C32 E43 C14 |
| Date: | 2012–09–04 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:41044&r=ets |