QUANTILE DOUBLE AUTOREGRESSION

Many financial time series have varying structures at different quantile levels, and also exhibit the phenomenon of conditional heteroskedasticity at the same time. However, there is presently no time series model that accommodates both of these features. This paper fills the gap by proposing a novel conditional heteroskedastic model called “quantile double autoregression”. The strict stationarity of the new model is derived, and self-weighted conditional quantile estimation is suggested. Two promising properties of the original double autoregressive model are shown to be preserved. Based on the quantile autocorrelation function and self-weighting concept, three portmanteau tests are constructed to check the adequacy of the fitted conditional quantiles. The finite sample performance of the proposed inferential tools is examined by simulation studies, and the need for use of the new model is further demonstrated by analyzing the S&P500 Index.

CHARACTERIZATION OF THE TAIL BEHAVIOR OF A CLASS OF BEKK PROCESSES: A STOCHASTIC RECURRENCE EQUATION APPROACH

We consider conditions for strict stationarity and ergodicity of a class of multivariate BEKK processes $(X_t : t=1,2,\ldots )$ and study the tail behavior of the associated stationary distributions. Specifically, we consider a class of BEKK-ARCH processes where the innovations are assumed to be Gaussian and a finite number of lagged $X_t$ ’s may load into the conditional covariance matrix of $X_t$ . By exploiting that the processes have multivariate stochastic recurrence equation representations, we show the existence of strictly stationary solutions under mild conditions, where only a fractional moment of $X_t$ may be finite. Moreover, we show that each component of the BEKK processes is regularly varying with some tail index. In general, the tail index differs along the components, which contrasts with most of the existing literature on the tail behavior of multivariate GARCH processes. Lastly, in an empirical illustration of our theoretical results, we quantify the model-implied tail index of the daily returns on two cryptocurrencies.

JOINT TIME-SERIES AND CROSS-SECTION LIMIT THEORY UNDER MIXINGALE ASSUMPTIONS

In this paper, we complement joint time-series and cross-section convergence results derived in a companion paper Hahn, Kuersteiner, and Mazzocco (2016, Central Limit Theory for Combined Cross-Section and Time Series) by allowing for serial correlation in the time-series sample. The implications of our analysis are limiting distributions that have a well-known form of long-run variances for the time-series limit. We obtain these results at the cost of imposing strict stationarity for the time-series model and conditional independence between the time-series and cross-section samples. Our results can be applied to estimators that combine time-series and cross-section data in the presence of aggregate uncertainty in models with rationally forward-looking agents.

Review of Matheron’s Kriging Method and its Application at the Estimation of Mineral Deposits

The Geostatistics provides effective tools for the solution of many problems of engineering in which the location in the space of the variable under study is considered, based on definitions of mathematics that provide the necessary foundation for its application. In particular, the Geostatistics are applied in the spatial estimation of the recoverable reserves of mineral deposits. The geostatistical methods that are used in the estimation of mineral deposits are implemented in industrial software and consider the evaluation of the complex geological structure, but these softwares only display the obtained results with an input data and do not exhibit the concepts thatthey use during the process or the methodology of its application. This happens particularly with the Kriging method, which is based on the assumption of strict stationarity, taking into account changes in the mean and local variations, therefore unreliable. In this study is established to review the Kriging method, its application in the estimation of the recoverable reserves of mining deposits and the relevance of the developed model established particularly in mines ofPeru, which use this method as part of the mining exploration for the evaluation of the feasibility of exploitation.

STATISTICAL INFERENCE FOR MEASUREMENT EQUATION SELECTION IN THE LOG-REALGARCH MODEL

This article investigates the statistical inference problem of whether a measurement equation is self-consistent in the logarithmic realized GARCH model (log-RealGARCH). First, we provide the sufficient and necessary conditions for the strict stationarity of both the log-RealGARCH model and the log-GARCH-X model. Under these conditions, strong consistency and asymptotic normality of the quasi-maximum likelihood estimators of these two models are obtained. Then, based on the asymptotic results, we propose a Hausman-type self-consistency test for diagnosing the suitability of the measurement equation in the log-RealGARCH model. Finally, the results of simulations and an empirical study are found to accord with the theoretical results.