Abslrocr -Suppose that a rational function Z ( s ) is defined by a Laurent .series, the coefficients of which are known. Several criteria are given in terms of these coefficients (the Markov parameters of Z(s)) to ensure that Re Z ( j w ) > 0 for all red w. The criteria are defined by using a Cauchy index formulation of the ratio of two rational functions, and they are of three types-involving ...

If there is an unobserved component in corporate default intensities, then part of the fluctuation in corporate bond prices can be attributed to the variation in beliefs about this latent factor over time. Using sequential Markov Chain Monte Carlo techniques, we show evidence of a latent frailty process in the default intensities in U.S. corporate defaults. The factor is robust to the inclusion...

The relationship between stock return volatility and trading volume is analysed by using the modified mixture model (MMM) framework proposed by Andersen (1996). This theory postulates that price changes and volumes are driven by a common latent information process, which is commonly interpreted as the volatility. Using GMM estimation Andersen finds that the persistence in this latent process fa...

We define an optimal basis system into which cosmological observables can be decomposed. The basis system can be optimized for a specific cosmological model or for an ensemble of models, even if based on drastically different physical assumptions. The projection coefficients derived from this basis system, the so-called features, provide a common parametrization to study and compare different c...

In 2010, the National Basketball Association (NBA) began to install a camera system to track the positions of the players and the ball as a function of time. For the ball and for each of the 10 players on the court, the system records an (x,y) position 25 times per second. Ultimately, this wealth of data should enable us to answer a number of questions regarding basketball strategy that would h...

Due to the effective role of Markov models in customer relationship management (CRM), there is a lack of comprehensive literature review which contains all related literatures. In this paper the focus is on academic databases to find all the articles that had been published in 2011 and earlier. One hundred articles were identified and reviewed to find direct relevance for applying Markov models...

We describe a Bayesian method for detecting structural changes in a long-range dependent process. In particular, we focus on changes in the long-range dependence parameter, d, and changes in the process level, μ. Markov chain Monte Carlo methods are used to estimate the posterior probability and size of a change at time t, along with other model parameters. A time-dependent Kalman filter approa...

In our recent paper, we showed that in exponential family, contrastive divergence (CD) with fixed learning rate will give asymptotically consistent estimates [11]. In this paper, we establish consistency and convergence rate of CD with annealed learning rate ηt. Specifically, suppose CD-m generates the sequence of parameters {θt}t≥0 using an i.i.d. data sample X1 ∼ pθ∗ of size n, then δn(X n 1 ...

Since ARCH and GARCH models are presented, more and more authors are interested in the study of volatilities in financial markets with GARCH models. Method for estimating the coefficients of GARCH models is mainly the maximum likelihood estimation. Now we consider another method—MCMC method to substitute for maximum likelihood estimation method. Then we compare three GARCH models based on it. M...

Concurrent research documents sizeable changes in the volatility of U.S. macroeconomic time series; e.g., see Kim and Nelson (1999), McConnell and Pérez-Quirós (2000), Stock and Watson (2002), and Sensier and van Dijk (2004). Most of the evidence from this literature suggests a sizeable reduction in volatility for many series; many of them used to construct business cycle indicators. With the e...