Andre Lucas

A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations

We propose a new class of observation-driven time-varying parameter models for dynamic volatilities and correlations to handle time series from heavy-tailed distributions. The model adopts generalized autoregressive score dynamics to obtain a time-varying covariance matrix of the multivariate Student t distribution. The key novelty of our proposed model concerns the weighting of lagged squared innovations for the estimation of future correlations and volatilities. When we account for heavy tails of distributions, we obtain estimates that are more robust to large innovations. We provide an empirical illustration for a panel of daily equity returns.

Testing for ARCH in the presence of additive outliers

In this paper we investigate the properties of the Lagrange Multiplier (LM) test for autoregressive conditional heteroscedasticity (ARCH) and generalized ARCH (GARCH) in the presence of additive outliers (AOs). We show analytically that both the asymptotic size and power are adversely affected if AOs are neglected: the test rejects the null hypothesis of homoscedasticity too often when it is in fact true, while the test has difficulty detecting genuine GARCH effects. Several Monte Carlo experiments show that these phenomena occur in small samples as well. We design and implement a robust test, which has better size and power properties than the conventional test in the presence of AOs. We apply the tests to a number of US macroeconomic time series, which illustrates the dangers involved when nonrobust tests for ARCH are routinely applied as diagnostic tests for misspecification.

Conditional Euro Area Sovereign Default Risk

We propose an empirical framework to assess the likelihood of joint and conditional sovereign default from observed CDS prices. Our model is based on a dynamic skewed-t distribution that captures all salient features of the data, including skewed and heavy-tailed changes in the price of CDS protection against sovereign default, as well as dynamic volatilities and correlations that ensure that uncertainty and risk dependence can increase in times of stress. We apply the framework to euro area sovereign CDS spreads during the euro area debt crisis. Our results reveal significant time-variation in distress dependence and spill-over effects for sovereign default risk. We investigate market perceptions of joint and conditional sovereign risk around announcements of Eurosystem asset purchases programs, and document a strong impact on joint risk.

Extreme returns, downside risk, and optimal asset allocation

The issue of asset allocation is important to every investor, but because of common, yet questionable, assumptions, these allocations may be significantly biased. Perhaps the most common investor assumption is normality or lognormality of asset returns. Evidence indicates, however, that return distributions often have fat tails (i.e., are leptokurtic). If so, how far from optimality are these “optimal” allocations?

Unit Root Tests Based on M Estimators

This paper considers unit root tests based on M estimators. The asymptotic theory for these tests is developed. It is shown how the asymptotic distributions of the tests depend on nuisance parameters and how tests can be constructed that are invariant to these parameters. It is also shown that a particular linear combination of a unit root test based on the ordinary least-squares (OLS) estimator and on an M estimator converges to a normal random variate. The interpretation of this result is discussed. A simulation experiment is described, illustrating the level and power of different unit root tests for several sample sizes and data generating processes. The tests based on M estimators turn out to be more powerful than the OLS-based tests if the innovations are fat-tailed.

Testing for smooth transition nonlinearity in the presence of outliers

Regime-switching models, like the smooth transition autoregressive (STAR) model, are typically applied to time series of moderate length. Hence, the nonlinear features that these models intend to describe may be reflected in only a few observations. Conversely, neglected outliers in a linear time series of moderate length may incorrectly suggest STAR (or other) type(s of) nonlinearity. In this article, the authors propose outlier robust tests for STAR-type nonlinearity. These tests are designed such that they have a better level and power behavior than standard nonrobust tests in situations with outliers. They formally derive local and global robustness properties of the new tests. Extensive Monte Carlo simulations show the practical usefulness of the robust tests. An application to several quarterly industrial production indexes illustrates that apparent nonlinearity in time series sometimes seems due to only a few outliers.

Robustness of the student t based M-estimator

This paper considers the maximum likelihood type (M) estimator based on Students t distribution for the location/scale model. The Student t M-estimator is generally thought to be robust to outliers. This paper shows that this is only true if the degrees of freedom parameter is kept fixed. By contrast, if the degrees of freedom parameter is also estimated from the data, the influence functions for the scale and degrees of freedom parameter become unbounded. Moreover, the influence function of the location parameter remains bounded, but its change-of-variance function is unboi~nded. The intuitioil behind these results is explained in the paper. The rates at which both the influence functions and the change-of-variance function diverge to infinity, are very slow. Tliis implies that outliers have to be extremely large in order to become detrimental to the performance of the Student t based M-estimator with estimated degrees of freedom. The theoretical results are illustrated in a a simulation experiment usin...

An outlier robust unit root test with an application to the extended Nelson-Plosser data

This paper considers unit root tests based on robust estimators with a high breakdown point and high efficiency. The asymptotic distribution of these tests is derived. Critical values for the test are obtained via simulation. It is found that the size of the classical OLS based Dickey-Fuller test breaks down if the time series contains additive outliers For innovative outliers the size of the robust test is less stable, while its size-adjusted power properties are better. An example is provided by applying the robust tests to the extended Nelson-Plosser data. For four series the null hypothesis of nonstationarity is rejected.

Comprehensive definitions of breakdown points for independent and dependent observations

We provide a new definition of breakdown in finite samples with an extension to asymptotic breakdown. Previous definitions center around defining a critical region for either the parameter or the objective function. If for a particular outlier constellation the critical region is entered, breakdown is said to occur. In contract to the traditional approach, we leave the definition of the critical region implicit. Our definition encompasses all previousdefinitions of breakdown in both linear and non-linear regression settings. Insome cases, it leads to a different notion of breakdown than other procedures available. An advantage is that our new definition also applied to models for dependent observations (time-series, spatial statistics) where currenty breakdown definitions typically fail. We illustrate our points using examples from linear and non-linear regression as well as time-series and spatial statistics.

SETS, arbitrage activity and stock price dynamics

This paper provides an empirical description of the relationshipbetween the trading system operated by a stockexchange and the transaction costs faced by heterogeneous investors who use the exchange. Therecent introduction ofSETS in the London Stock Exchange provides an excellent opportunity tostudy the impact of an electronic trading systemupon transaction costs and the time taken to carry out a trade. Using thecost-of-carry model of futures prices we estimate(non-linearly) the transaction costs and trade speeds faced by arbitragerswho take advantage of mispricing of FTSE100futures contracts relative to the spot prices of the stocks that make upthe FTSE100 stock index. We divide the sample periodinto pre-SETS and post-SETS sample periods and conduct a comparative studyof arbitrager behaviour under differenttrading systems. The results indicate that there has been a significantreduction in the level of transaction costs faced byarbitragers and in the degree of transaction cost heterogeneity since theintroduction of SETS. Finally, generalised impulseresponse functions show that both spot and futures prices adjust morequickly in the post-SETS period.