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on Econometric Time Series |
| By: | David E. Allen; Michael McAleer (University of Canterbury); Marcel Scharth |
| Abstract: | In this paper we document that realized variation measures constructed from high- frequency returns reveal a large degree of volatility risk in stock and index returns, where we characterize volatility risk by the extent to which forecasting errors in realized volatility are substantive. Even though returns standardized by ex post quadratic variation measures are nearly gaussian, this unpredictability brings considerably more uncertainty to the empirically relevant ex ante distribution of returns. Carefully modeling this volatility risk is fundamental. We propose a dually asymmetric realized volatility (DARV) model, which incorporates the important fact that realized volatility series are systematically more volatile in high volatility periods. Returns in this framework display time varying volatility, skewness and kurtosis. We provide a detailed account of the empirical advantages of the model using data on the S&P 500 index and eight other indexes and stocks. |
| Keywords: | Realized volatility; volatility of volatility; volatility risk; value-at-risk; forecasting; conditional heteroskedasticity |
| Date: | 2010–05–01 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:10/26&r=ets |
| By: | Michael McAleer (University of Canterbury); Les Oxley (University of Canterbury) |
| Abstract: | Time series data affect many aspects of our lives. This paper highlights ten things we should all know about time series, namely: a good working knowledge of econometrics and statistics, an awareness of measurement errors, testing for zero frequency, seasonal and periodic unit roots, analysing fractionally integrated and long memory processes, estimating VARFIMA models, using and interpreting cointegrating models carefully, choosing sensibly among univariate conditional, stochastic and realized volatility models, not confusing thresholds, asymmetry and leverage, not underestimating the complexity of multivariate volatility models, and thinking carefully about forecasting models and expertise. |
| Keywords: | Unit roots; fractional integration; long memory; VARFIMA; cointegration; volatility; thresholds; asymmetry; leverage; forecasting models and expertise |
| JEL: | C22 C32 |
| Date: | 2010–06–01 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:10/42&r=ets |
| By: | [no author] |
| Abstract: | This thesis addresses the problem of how to identify and model sources of common fluctuations of economic variables. It is an interesting question not only for researchers but also for policy makers and other authorities. The literature presents two approaches. The first one is based on an assumption that the important structural shocks can be captured by a small set of macroeconomic variables. The most popular models used in this context are structural vector autoregression models (SVAR). The second approach follows from a belief that there exists a small number of factors that affect many economic processes. Therefore, it involves analysis of large data sets, with both time and cross- sectional dimensions large enough to describe the factor structure. We dedicate the first part of the thesis to the problem of identification and estimation of structural shocks in small SVAR models. We follow the ideas of Rigobon (2003) and Lanne and Lütkepohl (2008), which show that the statistical property of the data may provide enough information to identify the structure of the model. The papers argue that a shift in the error covariance matrix allows for the estimation of the structural parameters of interest. The literature concentrates on models in which the shift is a result of a structural brake or a mixed distribution of errors. |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:ner:euiflo:urn:hdl:1814/14190&r=ets |
| By: | Boubacar Mainassara, Yacouba |
| Abstract: | This article considers the problem of orders selections of vector autoregressive moving-average (VARMA) models and the sub-class of vector autoregressive (VAR) models under the assumption that the errors are uncorrelated but not necessarily independent. We relax the standard independence assumption to extend the range of application of the VARMA models, and allow to cover linear representations of general nonlinear processes. We propose a modified criterion to the corrected AIC (Akaïke information criterion) version (AICc) introduced by Tsai and Hurvich (1989). This modified criterion is an approximately unbiased estimator of the Kullback-Leibler discrepancy, originally used to derive AIC-based criteria. Moreover, this criterion requires the estimation of the matrice involved in the asymptotic variance of the quasi-maximum likelihood (QML) estimator of the models, which provide an additional information about models. Monte carlo experiments show that the proposed modified criterion estimates the models orders more accurately than the standard AIC and AICc in large samples and often in small samples. |
| Keywords: | AIC; discrepancy; Kullback-Leibler information; QMLE/LSE; order selection; structural representation; weak VARMA models. |
| JEL: | C52 C22 C01 |
| Date: | 2010–06–21 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:23412&r=ets |
| By: | Phillips, Kerk L.; Spencer, David E. |
| Abstract: | Constructing bootstrap confidence intervals for impulse response functions (IRFs) from structural vector autoregression (SVAR) models has become standard practice in empirical macroeconomic research. The accuracy of such confidence intervals can deteriorate severely, however, if the bootstrap IRFs are biased. In this paper, we document an apparently common source of bias in the estimation of the VAR error covariance matrix. The bias is easily corrected with a straightforward scale adjustment. This bias is often unrecognized because it only affects the bootstrap estimates of the error variance, not the original OLS estimates. Nevertheless, as we illustrate here, analytically, with sampling experiments, and in an example from the literature, the bootstrap error variance bias can have significant distorting effects on bootstrap IRF confidence intervals even if the original IRF estimate relies on unbiased parameter estimates. |
| Keywords: | impulse response function; structural VAR; bias; bootstrap |
| JEL: | C32 E32 E37 |
| Date: | 2010–02 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:23503&r=ets |
| By: | Niang, Abdou-Aziz; Pichery, Marie-Claude; Edjo, Marcellin |
| Abstract: | This paper presents an essay on empirical testing procedure for economic convergence. Referring to the unit root test proposed by Moon and Perron (2004), we proposed a modified Evans (1996)testing procedure of the convergence hypothesis. The advantage of this modified procedure is that it makes possible to take into account cross-sectional dependences that affect GDP per capita. It also allows to take into account structural instabilities in these aggregates. The application of the procedure on OECD member countries and CFA zone member countries leads to accept the hypothesis of economic convergence for these two groups of countries, and it shows that the convergence rate is significantly lower in the OECD sample. However, the results of the tests applied to the Global sample composed by all countries in these two samples conclude a rejection of the convergence hypothesis. |
| Keywords: | β-convergence; Unit root; Panel data; Factor model; Cross-sectional dependence; Structural change |
| JEL: | C23 C22 O40 R11 |
| Date: | 2010–04–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:23452&r=ets |