Limits of Econometrics

In the social and behavioral sciences, far-reaching claims are often made for the superiority of advanced quantitative methods by those who manage to ignore the far-reaching assumptions behind the models. In section 2, we see there was considerable skepticism about disentangling causal processes by statistical modeling. Freedman (2005) examined several well-known modeling exercises, and discovered good reasons for skepticism. Some kinds of problems may yield to sophisticated statistical technique; others will not. The goal of empirical research is or should be to increase our understanding of the phenomena, rather than displaying our mastery of technique.

Testing the link specification in binary choice models. A semiparametric approach.

Doutoramento em Matemática

Diagnostic Checking, Time Series and Regression

In this thesis, a new univariate-multivariate portmanteau test is derived. The proposed test statistic can be used for diagnostic checking ARMA, VAR, FGN, GARCH, and TAR time series models as well as for checking randomness of series and goodness-of- fit VAR models with stable Paretian errors. The asymptotic distribution of the test statistic is derived as well as a chi-square approximation. However, the Monte-Carlo test is recommended unless the series is very long. Extensive simulation experiments demonstrate the usefulness of this test and its improved power performance compared to widely used previous multivariate portmanteau diagnostic check. The contributed R package portes is also introduced. This package can utilize multi-core CPUs often found in modern personal computers as well as a computer cluster or grid. The proposed package includes the most important univariate and multivariate diagnostic portmanteau tests with the new test statistic given in this thesis. It is also useful for simulating univariate/multivariate data from nonseasonal ARIMA/VARIMA process with nite or in nite variances, testing for stationarity and invertibility, and estimating parameters from stable distributions. Many illustrative applications are given. In this thesis, it has been shown that the classical ordinary least squares regression may produce smaller p-values than it should due to the lack of statistical independency in the tted model which may invalidate the statistical inferences. The Poincare plots are suggested to check for such hidden positive correlations

The Determinants of the Time to Efficiency in Options Markets : A Survival Analysis Approach.

This paper examines the determinants of the time it takes for an index options marketto be brought back to efficiency after put-call parity deviations, using intraday transactionsdata from the French CAC 40 index options over the August 2000 – July 2001 period. Weaddress this issue through survival analysis which allows us to characterize how differencesin market conditions influence the expected time before the market reaches the no-arbitragerelationship. We find that maturity, trading volume as well as trade imbalances in call andput options, and volatility are important in understanding why some arbitrage opportunitiesdisappear faster than others. After controlling for differences in the trading environnement,we find a strong and negative relationship between the existence of ETFs on the index andthe time to efficiency.Survival Analysis; Market efficiency; Index Options; Exchange TradedFunds.;

Specification Testing for Multivariate Time Series Volatility Models

Volatility models have been playing an important role in economics and finance. Using a multivariate generalized spectral approach, we propose a new class of generally applicable omnibus tests for univariate and multivariate volatility models. Both GARCH models and stochastic volatility models are covered. Our tests have a convenient asymptotic null N(0,1) distribution, and can detect a wide range of misspecifications for volatility dynamics. Distinct from the existing tests for volatility models, our tests are robust to higher order time-varying moments of unknown form (e.g., time-varying skewness and kurtosis). Our tests check a large number of lags and are therefore expected to be powerful against neglected volatility dynamics that occurs at higher order lags or display long memory properties. Despite using a large number of lags, our tests do not suffer much from loss of a large number of degrees of freedom, because our approach naturally discounts higher order lags, which is consistent with the stylized fact that economic or financial markets are more affected by the recent past events than by the remote past events. No specific estimation method is required, and parameter estimation uncertainty has no impact on the limit distribution of the test statistics. Moreover, there is no need to formulate an alternative volatility model, and only estimated standardized residuals are needed to implement our tests. We do not have to calculate tedious score functions or derivatives of volatility models with respect to estimated parameters, which are model-specific and are required in some existing popular tests for volatility models. We examine the finite sample performance of the proposed tests. An empirical application to some popular GARCH models for stock returns illustrates our approachGeneralized spectral derivative, Kernel, Multivariate generalized spectrum, Multivariate GARCH models, Nonlinear volatility dynamics, Robustness, Specification testing, Stochastic Volatility Model, Time-varying higher order moments of unknown form.

Advances in Portmanteau Diagnostic Tests

Portmanteau test serves an important role in model diagnostics for Box-Jenkins Modelling procedures. A large number of Portmanteau test based on the autocorrelation function are proposed for a general purpose goodness-of-fit test. Since the asymptotic distributions for the statistics has a complicated form which makes it hard to obtain the p-value directly, the gamma approximation is introduced to obtain the p-value. But the approximation will inevitably introduce approximation errors and needs a large number of observations to yield a good approximation. To avoid some pitfalls in the approximation, the Lin-Mcleod Test is further proposed to obtain a numeric solution to this problem based on Monte Carlo Simulation. In this thesis, we first identify the problem of nuisance parameters for Autoregressive Fractionally Integrated Moving Average Model (ARFIMA model) in the Lin-McLeod Test; the size would be distorted, leading to an inaccurate level of type I error. We solve the problem through a modification of Lin-McLeod Test: Wild Monte Carlo Test, borrowing the idea of Wild Dependent Bootstrapping. In order to validate the algorithm, we derive the asymptotic distribution for the bootstrapped statistics in ARFIMA cases. By perturbing the estimated residuals, the Wild Monte Carlo Test outperforms a wide spread of Portmanteau test for this type of model. It solves the problem of the size underestimation and improves the test power for ARFIMA cases. Later, we consider the general variance Portmanteau test on Autoregressive Moving Average Model with Generalized Autoregressive Conditional Heteroskedasticity Error (ARMA − GARCH Model), as a special case of weak ARMA model . When we have the null hypothesis of an ARMA − GARCH process, the asymptotic distribution of general variance are derived. With the complicated structure of the asymptotic distribution, the Lin-McLeod Test can serve a better solution to obtain the p-value rather than the gamma approximation. However, the test will still suffer from the size distortion due to the nuisance parameter issues. In this chapter, we mainly derive the asymptotic distribution for general variance Portmanteau tests on the ARMA − GARCH models and propose to use the Wild Monte Carlo Test to reduce the effect of nuisance parameters. The simulation and practical examples show the power of the newly test compared to the results of Francq et al. (2005). Additionally, we shall consider the data generating process as the ARMA with infinite variance errors. In order to valid the general variance Portmanteau test and Fisher-Gallagher Test under this setup, we use the idea of the autocorrelation of the trimmed time series to construct the modified Portmanteau test and derive the asymptotic distribution for these two kinds of Portmanteau tests on trimmed time series. Still, when we use the Lin-McLeod Test to obtain the p-value, Wild Monte Carlo Test can correct the nuisance parameter distortion for the size and improve the model performance. Finally, we revisit the cross correlation test for two independent time series. A mistake in Hong (1996) simulation is pointed out and the corrected size for the test is provided later. Then we identify a spurious correlation for the time series with GARCH type errors

Measurements, Models, Systems and Design

531 s.

The Determinants of the Time to Efficiency in Options Markets: A Survival Analysis Approach.

This paper examines the determinants of the time it takes for an index options market to be brought back to efficiency after put-call parity deviations, using intraday transactions data from the French CAC 40 index options over the August 2000 - July 2001 period. We address this issue through survival analysis which allows us to characterize how differences in market conditions influence the expected time before the market reaches the no-arbitrage relationship. We find that moneyness, maturity, trading volume as well as trade imbalances in call and put options, and volatility are important in understanding why some arbitrage opportunities disappear faster than others. After controlling for differences in the trading environnement, we find evidence of a negative relationship between the existence of ETFs on the index and the time to efficiency.Survival analysis; Market efficiency; Survival analysis; exchange traded funds; Index options;