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on Econometrics |
| By: | Jozef Barunik; Lukas Vacha |
| Abstract: | This paper proposes generalization of the popular realized volatility framework by allowing its measurement in the time-frequency domain and bringing robustness to both noise as well as jumps. Based on the generalization of Fan and Wang (2007) approach using smooth wavelets and Maximum Overlap Discrete Wavelet Transform, we present new, general theory for wavelet decomposition of integrated variance. Using wavelets, we not only gain decomposition of the realized variance into several investment horizons, but we are also able to estimate the jumps consistently. Basing our estimator in the two-scale realized variance framework of Zhang et al. (2005), we are able to utilize all available data and get unbiased estimator in the presence of noise as well. The theory is also tested in a large numerical study of the small sample performance of the estimators and compared to other popular realized variation estimators under different simulation settings with changing noise as well as jump level. The results reveal that our wavelet-based estimator is able to estimate and forecast the realized measures with the greatest precision. Another notable contribution lies in the application of the presented theory. Our time-frequency estimators not only produce more efficient estimates, but also decompose the realized variation into arbitrarily chosen investment horizons. The results thus provide a better understanding of the dynamics of stock markets. |
| Date: | 2012–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1202.1854&r=ecm |
| By: | Ma{\l}gorzata Snarska |
| Abstract: | We show how random matrix theory can be applied to develop new algorithms to extract dynamic factors from macroeconomic time series. In particular, we consider a limit where the number of random variables N and the number of consecutive time measurements T are large but the ratio N / T is fixed. In this regime the underlying random matrices are asymptotically equivalent to Free Random Variables (FRV).Application of these methods for macroeconomic indicators for Poland economy is also presented. |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1201.6544&r=ecm |
| By: | Jeroen V.K. Rombouts (HEC Montréal, CIRANO, CIRPEE and Université catholique de Louvain, CORE); Lars Stentoft (HEC Montréal, CIRANO, CIRPEÉ, and CREATES); Francesco Violante (Maastricht University and Université catholique de Louvain, CORE) |
| Abstract: | We assess the predictive accuracy of a large number of multivariate volatility models in terms of pricing options on the Dow Jones Industrial Average. We measure the value of model sophistication in terms of dollar losses by considering a set 248 multivariate models that differ in their specification of the conditional variance, conditional correlation, and innovation distribution. All models belong to the dynamic conditional correlation class which is particularly suited because it allows to consistently estimate the risk neutral dynamics with a manageable computational effort in relatively large scale problems. It turns out that the most important gain in pricing accuracy comes from increasing the sophistication in the marginal variance processes (i.e. nonlinearity, asymmetry and component structure). Enriching the model with more complex correlation models, and relaxing a Gaussian innovation for a Laplace innovation assumption improves the pricing in a smaller way. Apart from investigating directly the value of model sophistication in terms of dollar losses, we also use the model confidence set approach to statistically infer the set of models that delivers the best pricing performance. |
| Keywords: | Option pricing, Economic Loss, Forecasting, Multivariate GARCH, Model Confidence Set |
| JEL: | C10 C32 C51 C52 C53 G10 |
| Date: | 2012–01–27 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2012-04&r=ecm |
| By: | Giacomo Livan; Luca Rebecchi |
| Abstract: | We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson correlation matrices to the realm of complex eigenvalues. We employ some recent random matrix theory results on the average eigenvalue density of this type of matrices to distinguish between noise and non trivial correlation structures, and we focus on financial data as a case study. Namely, we employ daily prices of stocks belonging to the American and British stock exchanges, and look for the emergence of correlations between two such markets in the eigenvalue spectrum of their non symmetric correlation matrix. We find several non trivial results, also when considering time-lagged correlations over short lags, and we corroborate our findings by additionally studying the asymmetric correlation matrix of the principal components of our datasets. |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1201.6535&r=ecm |