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Gouriéroux and Zakoïan (2013) propose to use noncausal models to parsimoniously capture nonlinear features often observed in financial time series and in particular bubble phenomena. In order to distinguish causal autoregressive processes from purely noncausal or mixed causal-noncausal ones, one has to depart from the Gaussianity assumption on the error distribution. Financial (and to a large extent macroeconomic) data are characterized by large and sudden changes that cannot be capturedby the Normal distribution, which explains why leptokurtic error distributions are often considered in empirical finance. By means of Monte Carlo simulations, this paper investigates the identication of mixed causal-noncausal models in finite samples for different values of the excess kurtosis of the error process. We compare the performance of the MLE, assuming a t-distribution, with that of theLAD estimator that we propose in this paper. Similar to Davis, Knight and Liu (1992) we find that for infinite variance autoregressive processes both the MLE and LAD estimator converge faster. We further specify the general asymptotic normality results obtained in Andrews, Breidt and Davis (2006)for the case of t-distributed and Laplacian distributed error terms. We first illustrate our analysis by estimating mixed causal-noncausal autoregressions to model the demand for solar panels in Belgium over the last decade. Then we look at the presence of potential noncausal components in daily realizedvolatility measures for 21 equity indexes. The presence of a noncausal component is confirmed in both empirical illustrations.

It is increasingly important in financial economics to estimate volatilities of asset returns. However, most of the available methods are not directly applicable when the number of assets involved is large, due to the lack of accuracy in estimating high-dimensional matrices. Therefore it is pertinent to reduce the effective size of volatility matrices in order to produce adequate estimates and forecasts. Furthermore, since high-frequency financial data for different assets are typically not recorded at the same time points, conventional dimension-reduction techniques are not directly applicable. To overcome those difficulties we explore a novel approach that combines high-frequency volatility matrix estimation together with low-frequency dynamic models. The proposed methodology consists of three steps: (i) estimate daily realized covolatility matrices directly based on high-frequency data, (ii) fit a matrix factor model to the estimated daily covolatility matrices, and (iii) fit a vector autoregressive model to the estimated volatility factors.We establish the asymptotic theory for the proposed methodology in the framework that allows sample size, number of assets, and number of days go to infinity together. Our theory shows that the relevant eigenvalues and eigenvectors can be consistently estimated. We illustrate the methodology with the high-frequency price data on several hundreds of stocks traded in Shenzhen and Shanghai Stock Exchanges over a period of 177 days in 2003. Our approach pools together the strengths of modeling and estimation at both intra-daily (high-frequency) and inter-daily (low-frequency) levels.

We provide an empirical framework for assessing the distributional properties of daily speculative returns within the context of the continuous-time modeling paradigm traditionally used in asset pricing finance. Our approach builds directly on recently developed realized variation measures and non-parametric jump detection statistics constructed from high-frequency intraday data. A sequence of relatively simple-to-implement moment-based tests involving various transforms of the daily returns speak directly to the import of different features of the underlying continuous-time processes that might have generated the data. As such, the tests may serve as a useful diagnostic tool in the specification of empirically more realistic asset pricing models. Our results are also directly related to the popular mixture-of-distributions hypothesis and the role of the corresponding latent information arrival process. On applying our sequential test procedure to the thirty individual stocks in the Dow Jones Industrial Average index, the data suggest that it is important to allow for both time-varying diffusive volatility, jumps, and leverage effects in order to satisfactorily describe the daily stock price dynamics. At a broader level, the empirical results also illustrate how the realized variation measures and high-frequency sampling schemes may be used in eliciting important distributional features and asset pricing implications more generally.

We provide an empirical framework for assessing the distributional properties of daily specu-lative returns within the context of the continuous-time modeling paradigm traditionally usedin asset pricing finance. Our approach builds directly on recently developed realized variationmeasures and non-parametric jump detection statistics constructed from high-frequency intra-day data. A sequence of relatively simple-to-implement moment-based tests involving varioustransforms of the daily returns speak directly to the import of different features of the under-lying continuous-time processes that might have generated the data. As such, the tests mayserve as a useful diagnostic tool in the specification of empirically more realistic asset pricingmodels. Our results are also directly related to the popular mixture-of-distributions hypoth-esis and the role of the corresponding latent information arrival process. On applying oursequential test procedure to the thirty individual stocks in the Dow Jones Industrial Averageindex, the data suggest that it is important to allow for both time-varying diffusive volatility,jumps, and leverage effects in order to satisfactorily describe the daily stock price dynamics.At a broader level, the empirical results also illustrate how the realized variation measures andhigh-frequency sampling schemes may be used in eliciting important distributional features andasset pricing implications more generally.