Recently, Bayesian solutions to the quantile regression problem, via the likelihood of a Skewed-Laplace distribution, have been proposed. These approaches are extended and applied to a family of dynamic conditional autoregressive quantile models. Popular Value at Risk models, used for risk management in finance, are extended to this fully nonlinear family. An adaptive Markov chain Monte Carlo scheme is designed for estimation and inference. Simulation studies illustrate favorable performance, compared to the standard numerical optimization of the usual non-parametric quantile criterion function. An empirical study employing ten major financial stock indices and Value at Risk forecasting finds significant nonlinearity in dynamic quantiles and evidence favoring the proposed model family, for lower level quantiles, compared to standard parametric volatility and risk models in the literature.
Currently, there exists relatively little research on the influence that the 1997 Asian financial crisis has had upon capital flows within the property market and the associated long-run implications of it. This paper examines the impact that the crisis has had upon the integration and dynamic links between a number of Asia-Pacific real estate markets. The results show that Asia-Pacific property markets are integrated, despite a structural shift occurring at the time of the crisis. These results are a particularly important finding for fund managers concerned with the impact of globalization on the performance of their real estate portfolios, showing that in the Asia-Pacific region diversification benefits are actually less than that suggested by an analysis incorrectly ignoring the crisis.
Beta distributions with both parameters equal to 0, 1 2 , or 1 are the usual choices for "noninformative" priors for Bayesian estimation of the binomial parameter. However, as illustrated by two examples from the Bayesian literature, care needs to be taken with parameter values below 1, both for noninformative and informative priors, as such priors concentrate their mass close to 0 and/or 1 and can suppress the importance of the observed data. These examples concern the case of no successes (or failures) and illustrate the informativeness of the Jeffreys prior usually recommended as the "consensus prior." In particular, the second example suggests that when the binomial parameter is known to be very small, an informative prior from the beta(1, b) family (b > 1) seems appropriate, while a beta(a, b) with a < 1 can be too informative. It is thus argued that sensitivity analysis of an informative prior should be based on a consensus posterior corresponding to the Bayes-Laplace prior rather than the Jeffreys prior.
Test statistics are proposed to determine the goodness of ®t of a time series model. The test statistics are based on a sequence of random variables that are independent and standard normal if the model is correct. The paper shows how to compute this sequence of random variables ef®ciently using a combination of Markov chain Monte Carlo and importance sampling. The power of the statistics to detect outliers and level shifts is studied for an autoregressive model. The methodology is illustrated using both simulated and real data.
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