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on Econometric Time Series |
| By: | Nicolas Huth (MAS - Mathématiques Appliquées aux Systèmes - EA 4037 - Ecole Centrale Paris); Frédéric Abergel (MAS - Mathématiques Appliquées aux Systèmes - EA 4037 - Ecole Centrale Paris) |
| Abstract: | Many statistical arbitrage strategies, such as pair trading or basket trading, are based on several assets. Optimal execution routines should also take into account correlation between stocks when proceeding clients orders. However, not so much effort has been devoted to correlation modelling and only few empirical results are known about high frequency correlation. We develop a theoretical framework based on correlated point processes in order to capture the Epps effect in section 1. We show in section 2 that this model converges to correlated Brownian motions when moving to large time scales. A way of introducing non-Gaussian correlations is also discussed in section 2. We conclude by addressing the limits of this model and further research on high frequency correlation. |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-00621244&r=ets |
| By: | Maria Elvira Mancino (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze); Simona Sanfelici (Dipartimento di Economia, Universita' di Parma) |
| Abstract: | We propose a new methodology based on Fourier analysis to estimate the fourth power of volatility function (spot quarticity) and, as a byproduct, the integrated function. We prove consistency of the proposed estimator of integrated quarticity. Further we analyze its efficiency in the presence of microstructure noise, both from a theoretical and empirical viewpoint. Extensions to higher powers of volatility and to the multivariate case are also discussed. |
| Keywords: | volatility, covariance, quarticity, microstructure, Fourier analysis |
| Date: | 2011–09 |
| URL: | http://d.repec.org/n?u=RePEc:flo:wpaper:2011-06&r=ets |
| By: | Giulio Cifarelli (Dipartimento Scienze Economiche) |
| Abstract: | The interaction between rational hedgers and informed oil traders is parameterized and tested empirically with the help of a complex non linear smooth transition regime shift CCC-GARCH procedure. In spite of their gyrations, futures price changes are usually self-correcting. Well informed producers and consumers will ensure that crude oil prices – and thus the prices of the corresponding futures contracts – fluctuate within a long run equilibrium range determined by market fundamentals. During the 2008 oil price upswing, however, shifts in positions in the futures markets by well informed optimizing agents, that usually dampen price changes, result in destabilizing positive feedback trading. Futures price changes that can be classified as speculative are due to hedgers’ reaction to movements in the variability of the return of their covered cash position. |
| Keywords: | oil price dynamics; dynamic hedging; logistic smooth transition; multivariate GARCH. |
| JEL: | G11 G12 G18 Q40 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:frz:wpaper:wp2011_13.rdf&r=ets |
| By: | Tomás del Barrio Castro; Paulo M.M. Rodrigues; A. M. Robert Taylor |
| Abstract: | In this paper we investigate the impact of non-stationary cycles on the asymptotic and finite sample properties of standard unit root tests. Results are presented for the augmented Dickey-Fuller normalised bias and t-ratio-based tests (Dickey and Fuller, 1979, and Said and Dickey, 1984), the variance ratio unit root test of Breitung (2002) and the M class of unit-root tests introduced by Stock (1999) and Perron and Ng (1996). The limiting distributions of these statistics are derived in the presence of non-stationary cycles. We show that while the ADF statistics remain pivotal (provided the test regression is properly augmented), this is not the case for the other statistics considered and show numerically that the size properties of the tests based on these statistics are too unreliable to be used in practice. We also show that the t-ratios associated with lags of the dependent variable of order greater than two in the ADF regression are asymptotically normally distributed. This is an important result as it implies that extant sequential methods (see Hall, 1994 and Ng and Perron, 1995) used to determine the order of augmentation in the ADF regression remain valid in the presence of non-stationary cycles. |
| JEL: | C20 C22 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:ptu:wpaper:w201124&r=ets |
| By: | Tomás del Barrio Castro; Denise R. Osborn; A.M. Robert Taylor |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:man:sespap:1121&r=ets |
| By: | Bai, Jushan; Wang, Peng |
| Abstract: | Motivated by the great moderation in major U.S. macroeconomic time series, we formulate the regime switching problem through a conditional Markov chain. We model the long-run volatility change as a recurrent structure change, while short-run changes in the mean growth rate as regime switches. Both structure and regime are unobserved. The structure is assumed to be Markovian. Conditioning on the structure, the regime is also Markovian, whose transition matrix is structure-dependent. This formulation imposes interpretable restrictions on the Hamilton Markov switching model. Empirical studies show that this restricted model well identifies both short-run regime switches and long-run structure changes in the U.S. macroeconomic data. |
| Keywords: | Markov regime switching; Conditional Markov chain |
| JEL: | C32 C22 C01 |
| Date: | 2011–08 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:33369&r=ets |
| By: | Yuriy Gorodnichenko; Anna Mikusheva; Serena Ng |
| Abstract: | This paper considers a moments based non-linear estimator that is root-T consistent and uniformly asymptotically normal irrespective of the degree of persistence of the forcing process. These properties hold for linear autoregressive models, linear predictive regressions, as well as certain non-linear dynamic models. Asymptotic normality is obtained because the moments are chosen so that the objective function is uniformly bounded in probability and that a central limit theorem can be applied. Critical values from the normal distribution can be used irrespective of the treatment of the deterministic terms. Simulations show that the estimates are precise, and the t-test has good size in the parameter region where the least squares estimates usually yield distorted inference. |
| JEL: | C22 C32 E27 E37 |
| Date: | 2011–09 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:17424&r=ets |