2,638 research outputs found
Bivariate binomial autoregressive models
This paper introduces new classes of bivariate time series models being useful to fit count data time series with a finite range of counts. Motivation comes mainly from the comparison of schemes for monitoring tourism demand, stock data, production and environmental processes. All models are based on the bivariate binomial distribution of Type II. First, a new family of bivariate integer-valued GARCH models is proposed. Then, a new bivariate thinning operation is introduced and explained in detail. The new thinning operation has a number of advantages including the fact that marginally it behaves as the usual binomial thinning operation and also that allows for both positive and negative cross-correlations. Based upon this new thinning operation, a bivariate extension of the binomial autoregressive model of order one is introduced. Basic probabilistic and statistical properties of the model are discussed. Parameter estimation and forecasting are also covered. The performance of these models is illustrated through an empirical application to a set of rainy days time series collected from 2000 up to 2010 in the German cities of Bremen and Cuxhaven.publishe
Modelling High Frequency Financial Count Data
This thesis comprises two papers concerning modelling of financial count data. The papers advance the integer-valued moving average model (INMA), a special case of integer-valued autoregressive moving average (INARMA) model class, and apply the models to the number of stock transactions in intra-day data. Paper [1] advances the INMA model to model the number of transactions in stocks in intra-day data. The conditional mean and variance properties are discussed and model extensions to include, e.g., explanatory variables are offered. Least squares and generalized method of moment estimators are presented. In a small Monte Carlo study a feasible least squares estimator comes out as the best choice. Empirically we find support for the use of long-lag moving average models in a Swedish stock series. There is evidence of asymmetric effects of news about prices on the number of transactions. Paper [2] introduces a bivariate integer-valued moving average model (BINMA) and applies the BINMA model to the number of stock transactions in intra-day data. The BINMA model allows for both positive and negative correlations between the count data series. The study shows that the correlation between series in the BINMA model is always smaller than 1 in an absolute sense. The conditional mean, variance and covariance are given. Model extensions to include explanatory variables are suggested. Using the BINMA model for AstraZeneca and Ericsson B it is found that there is positive correlation between the stock transactions series. Empirically, we find support for the use of long-lag bivariate moving average models for the two series.Count data; Intra-day; High frequency; Time series; Estimation; Long memory; Finance
Gibbs Sampling, Exponential Families and Orthogonal Polynomials
We give families of examples where sharp rates of convergence to stationarity
of the widely used Gibbs sampler are available. The examples involve standard
exponential families and their conjugate priors. In each case, the transition
operator is explicitly diagonalizable with classical orthogonal polynomials as
eigenfunctions.Comment: This paper commented in: [arXiv:0808.3855], [arXiv:0808.3856],
[arXiv:0808.3859], [arXiv:0808.3861]. Rejoinder in [arXiv:0808.3864].
Published in at http://dx.doi.org/10.1214/07-STS252 the Statistical Science
(http://www.imstat.org/sts/) by the Institute of Mathematical Statistics
(http://www.imstat.org
Multifractal detrending moving average cross-correlation analysis
There are a number of situations in which several signals are simultaneously
recorded in complex systems, which exhibit long-term power-law
cross-correlations. The multifractal detrended cross-correlation analysis
(MF-DCCA) approaches can be used to quantify such cross-correlations, such as
the MF-DCCA based on detrended fluctuation analysis (MF-X-DFA) method. We
develop in this work a class of MF-DCCA algorithms based on the detrending
moving average analysis, called MF-X-DMA. The performances of the MF-X-DMA
algorithms are compared with the MF-X-DFA method by extensive numerical
experiments on pairs of time series generated from bivariate fractional
Brownian motions, two-component autoregressive fractionally integrated moving
average processes and binomial measures, which have theoretical expressions of
the multifractal nature. In all cases, the scaling exponents extracted
from the MF-X-DMA and MF-X-DFA algorithms are very close to the theoretical
values. For bivariate fractional Brownian motions, the scaling exponent of the
cross-correlation is independent of the cross-correlation coefficient between
two time series and the MF-X-DFA and centered MF-X-DMA algorithms have
comparative performance, which outperform the forward and backward MF-X-DMA
algorithms. We apply these algorithms to the return time series of two stock
market indexes and to their volatilities. For the returns, the centered
MF-X-DMA algorithm gives the best estimates of since its
is closest to 0.5 as expected, and the MF-X-DFA algorithm has the
second best performance. For the volatilities, the forward and backward
MF-X-DMA algorithms give similar results, while the centered MF-X-DMA and the
MF-X-DFA algorithms fails to extract rational multifractal nature.Comment: 15 pages, 4 figures, 2 matlab codes for MF-X-DMA and MF-X-DF
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