A fractionally integrated Wishart stochastic volatility model

There has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process, and derive the conditional Laplace transform of the FIWSV model in order to obtain a closed form expression of moments. A two-step procedure is used, namely estimating the parameter of fractional integration via the local Whittle estimator in the first step, and estimating the remaining parameters via the generalized method of moments in the second step. Monte Carlo results for the procedure show a reasonable performance in finite samples. The empirical results for the S&P 500 and FTSE 100 indexes show that the data favor the new FIWSV process rather than the one-factor and two-factor models of the Wishart autoregressive process for the covariance structure.     

Moment-based estimation of nonlinear regression models with boundary outcomes and endogeneity,with applications to nonnegative and fractional responses

In this article, we suggest simple moment-based estimators to deal with unobserved heterogeneity in a special class of nonlinear regression models that includes as main particular cases exponential models for nonnegative responses and logit and complementary loglog models for fractional responses. The proposed estimators: (i) treat observed and omitted covariates in a similar manner; (ii) can deal with boundary outcomes; (iii) accommodate endogenous explanatory variables without requiring knowledge on the reduced form model, although such information may be easily incorporated in the estimation process; (iv) do not require distributional assumptions on the unobservables, a conditional mean assumption being enough for consistent estimation of the structural parameters; and (v) under the additional assumption that the dependence between observables and unobservables is restricted to the conditional mean, produce consistent estimators of partial effects conditional only on observables.     

Optimal foldover designs

An obvious strategy for obtaining a Doptimal foldover design for p factors at two levels each in 2N runs is to fold a Doptimal main effects plan. We show that this strategy works except when N = 4t + 2 and s is even In that case there are two different classes of D-optimal main effects plans with N runs that have the same determinant. However folding them gives two different values foi the D-optimality criteiion One set of designs is D-optimal The other is not.     

A multivariate long-memory model with structural breaks

This paper introduces a multivariate long-memory model with structural breaks. In the proposed framework, the time series exhibits possibly fractional orders of integration which are allowed to be different in each subsample. The break date is endogenously determined using a procedure that minimizes the residual sum of squares (RSS). Monte Carlo experiments show that this method for detecting breaks performs well in large samples. As an illustration, we estimate a trivariate VAR including prices, employment and GDP in both the US and Mexico. For the subsample preceding the break, our findings are similar to those of earlier studies based on a standard VAR approach in both the countries, such that the variables exhibit integer degrees of integration. On the contrary, the series is found to be fractionally integrated after the break, with the fractional differencing parameters being higher than one in the case of Mexico.     

On the wavelet-based simulation of anomalous diffusion

The field of microrheology is based on experiments involving particle diffusion. Microscopic tracer beads are placed into a non-Newtonian fluid and tracked using high speed video capture and light microscopy. The modelling of the behaviour of these beads is now an active scientific area which demands multiple stochastic and statistical methods. We propose an approximate wavelet-based simulation technique for two classes of continuous time anomalous diffusion models, the fractional Ornstein–Uhlenbeck process and the fractional generalized Langevin equation. The proposed algorithm is an iterative method that provides approximate discretizations that converge quickly and in an appropriate sense to the continuous time target process. As compared to previous works, it covers cases where the natural discretization of the target process does not have closed form in the time domain. Moreover, we propose to minimize the border effect via smoothing.     

Imputation for statistical inference with coarse data

Coarse data is a general type of incomplete data that includes grouped data, censored data, and missing data. The likelihood‐based estimation approach with coarse data is challenging because the likelihood function is in integral form. The Monte Carlo EM algorithm of Wei & Tanner [Wei & Tanner (1990). Journal of the American Statistical Association, 85, 699–704] is adapted to compute the maximum likelihood estimator in the presence of coarse data. Stochastic coarse data is also covered and the computation can be implemented using the parametric fractional imputation method proposed by Kim [Kim (2011). Biometrika, 98, 119–132]. Results from a limited simulation study are presented. The proposed method is also applied to the Korean Longitudinal Study of Aging (KLoSA). The Canadian Journal of Statistics 40: 604–618; 2012 © 2012 Statistical Society of Canada     

A generalization of a Gaussian semiparametric estimator on multivariate long-range dependent processes

In this paper, we propose and study a general class of Gaussian semiparametric estimators (GSE) of the fractional differencing parameter in the context of long-range dependent multivariate time series. We establish large sample properties of the estimator without assuming Gaussianity. The class of models considered here satisfies simple conditions on the spectral density function, restricted to a small neighbourhood of the zero frequency and includes important class of vector autoregressive fractionally integrated moving average processes. We also present a simulation study to assess the finite sample properties of the proposed estimator based on a smoothed version of the GSE which supports its competitiveness.     

Fractional Lévy stable motion time-changed by gamma subordinator

Abstract

In this paper a new stochastic process is introduced by subordinating fractional Lévy stable motion (FLSM) with gamma process. This new process incorporates stochastic volatility in the parent process FLSM. Fractional order moments, tail asymptotic, codifference and persistence of signs long-range dependence of the new process are discussed. A step-by-step procedure for simulations of sample trajectories and estimation of the parameters of the introduced process are given. Our study complements and generalizes the results available on variance-gamma process and fractional Laplace motion in various directions, which are well studied processes in literature.     

Acceptance sampling plan based on an exponentially weighted moving average statistic with the yield index for autocorrelation between polynomial profiles

Acceptance sampling plans based on process yield indices provide a proven resource for the lot-sentencing problem when the required fraction defective is very low. In this study, a new sampling plan based on the exponentially weighted moving average (EWMA) model with yield index for lot sentencing for autocorrelation between polynomial profiles is proposed. The advantage of the EWMA statistic is the accumulation of quality history from previous lots. In addition, the number of profiles required for lot sentencing is more economical than in the traditional single sampling plan. Considering the acceptable quality level (AQL) at the producer's risk and the lot tolerance percent defective (LTPD) at the consumer's risk, we proposed a new search algorithm to determine the optimal plan parameters. The plan parameters are tabulated for various combinations of the smoothing constant of the EWMA statistic, AQL, LTPD, and two risks. A comparison study and two numerical examples are provided to show the applicability of the proposed sampling plan.