Temporal Aggregation of Stationary and Non-stationary Continuous-Time Processes

Abstract.  We study the autocorrelation structure of aggregates from a continuous-time process. The underlying continuous-time process or some of its higher derivative is assumed to be a stationary continuous-time auto-regressive fractionally integrated moving-average (CARFIMA) process with Hurst parameter H . We derive closed-form expressions for the limiting autocorrelation function and the normalized spectral density of the aggregates, as the extent of aggregation increases to infinity. The limiting model of the aggregates, after appropriate number of differencing, is shown to be some functional of the standard fractional Brownian motion with the same Hurst parameter of the continuous-time process from which the aggregates are measured. These results are then used to assess the loss of forecasting efficiency due to aggregation.     

On aliasing and generalized defining relationships of factorial arrangements

The concepts of defining contrast (DC), generalized defining relationship (GDR) and aliasing structure (AS) are now well established in the terminology of regression analysis and factorial design theory. There is no complete agreement in the literature about the meaning of regular and irregular fractional factorial designs. This paper provides a workable definition of a regular fraction from a symmetrial prime-powered factorial. It characterizes the uniqueness of the GDR for fractions from the most general factorial. Results are also présentés on the uniqueness of the GDR for regular designs, on orthogonality aspects of regular and irregular designs, and on group-theoretic generation of the complete aliasing structure. Examples are provided to illustrate the developments.     

On fractional moments of quadratic expressions in normal variables1

Fractional moments, product cumulants and product moments of general quadratic expressions in singular and nonsingular normal variables are explicitly evaluated. A general method of deriving such moments is also indicated. Particular cases art; shown to agree with known results.     

A Meta Analytic Approach to Testing for Panel Cointegration

We propose new tests for panel cointegration by extending the panel unit root tests of Choi (2001 Choi , I. ( 2001 ). Unit root tests for panel data . Journal of International Money and Finance 20 ( 2 ): 249 – 272 .[Crossref], [Web of Science ®] , [Google Scholar]) and Maddala and Wu (1999 Maddala , G. , Wu , S. ( 1999 ). A comparative study of unit root tests with panel data and a new simple test . Oxford Bulletin of Economics and Statistics 61 ( S1 ): 631 – 652 .[Crossref] , [Google Scholar]) to the panel cointegration case. The tests are flexible, intuitively appealing, and relatively easy to compute. We investigate the finite sample behavior in a simulation study. Several variants of the tests compare favorably in terms of both size and power with other widely used panel cointegration tests.     

Developing a Wide Easy-to-Generate Class of Bivariate Copulas

As of late, copulas have drawn great attention in stochastic simulation, financial engineering, and risk management. Their power lies under their ability of modeling dependent random variables. Using a known theorem in probability which proves that the fractional part of the sum of a uniform and an arbitrary independent continuous random variable follows a uniform distribution, we construct a wide class of bivariate copulas in which bivariate random vector generation can be performed easily. Some important members of this new class and their properties together with two invariant correlation measures and some insights in their application are presented.     

A Bayes comparison of Weibull extension and modified Weibull models for data showing bathtub hazard rate

A number of models have been proposed in the literature to model data reflecting bathtub-shaped hazard rate functions. Mixture distributions provide the obvious choice for modelling such data sets but these contain too many parameters and hamper the accuracy of the inferential procedures particularly when the data are meagre. Recently, a few distributions have been proposed which are simply generalizations of the two-parameter Weibull model and are capable of producing bathtub behaviour of the hazard rate function. The Weibull extension and the modified Weibull models are two such families. This study focuses on comparing these two distributions for data sets exhibiting bathtub shape of the hazard rate. Bayesian tools are preferred due to their wide range of applicability in various nested and non-nested model comparison problems. Real data illustrations are provided so that a particular model can be recommended based on various tools of model comparison discussed in the paper.     

A lower bound for the centred L 2-discrepancy on combined designs under the asymmetric factorials

The foldover is a useful technique in the construction of two-level factorial designs for follow-up experiments. To search an optimal foldover plans is an important issue. In this paper, for a set of asymmetric fractional factorials such as the original designs, a lower bound for centred L ₂-discrepancy of combined designs under a general foldover plan is obtained, which can be used as a benchmark for searching optimal foldover plans. All of our results are the extended ones of Ou et al. [Lower bounds of various discrepancies on combined designs, Metrika 74 (2011), pp. 109–119] for symmetric designs to asymmetric designs. Moreover, it also provides a theoretical justification for optimal foldover plans in terms of uniformity criterion.     

Three-part model for fractional response variables with application to Chinese household health insurance coverage

A survey on health insurance was conducted in July and August of 2011 in three major cities in China. In this study, we analyze the household coverage rate, which is an important index of the quality of health insurance. The coverage rate is restricted to the unit interval [0, 1], and it may differ from other rate data in that the “two corners” are nonzero. That is, there are nonzero probabilities of zero and full coverage. Such data may also be encountered in economics, finance, medicine, and many other areas. The existing approaches may not be able to properly accommodate such data. In this study, we develop a three-part model that properly describes fractional response variables with non-ignorable zeros and ones. We investigate estimation and inference under two proportional constraints on the regression parameters. Such constraints may lead to more lucid interpretations and fewer unknown parameters and hence more accurate estimation. A simulation study is conducted to compare the performance of constrained and unconstrained models and show that estimation under constraint can be more efficient. The analysis of household health insurance coverage data suggests that household size, income, expense, and presence of chronic disease are associated with insurance coverage.