Markovian Processes, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes.

In this paper, we develop finite-sample inference procedures for stationary and nonstationary autoregressive (AR) models. The method is based on special properties of Markov processes and a split-sample technique. The results on Markovian processes (intercalary independence and truncation) only require the existence of conditional densities. They are proved for possibly nonstationary and/or non-Gaussian multivariate Markov processes. In the context of a linear regression model with AR(1) errors, we show how these results can be used to simplify the distributional properties of the model by conditioning a subset of the data on the remaining observations. This transformation leads to a new model which has the form of a two-sided autoregression to which standard classical linear regression inference techniques can be applied. We show how to derive tests and confidence sets for the mean and/or autoregressive parameters of the model. We also develop a test on the order of an autoregression. We show that a combination of subsample-based inferences can improve the performance of the procedure. An application to U.S. domestic investment data illustrates the method.

A fast adaptive tunable RBF network for nonstationary systems

This paper describes a novel on-line learning approach for radial basis function (RBF) neural network. Based on an RBF network with individually tunable nodes and a fixed small model size, the weight vector is adjusted using the multi-innovation recursive least square algorithm on-line. When the residual error of the RBF network becomes large despite of the weight adaptation, an insignificant node with little contribution to the overall system is replaced by a new node. Structural parameters of the new node are optimized by proposed fast algorithms in order to significantly improve the modeling performance. The proposed scheme describes a novel, flexible, and fast way for on-line system identification problems. Simulation results show that the proposed approach can significantly outperform existing ones for nonstationary systems in particular.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Estimates of covariance functions for growth of Nelore cattle applying a parametric correlation structure to model within-animal correlations

A total of 20,065 weights recorded on 3016 Nelore animals were used to estimate covariance functions for growth from birth to 630 days of age, assuming a parametric correlation structure to model within-animal correlations. The model of analysis included fixed effects of contemporary groups and age of dam as quadratic covariable. Mean trends were taken into account by a cubic regression on orthogonal polynomials of animal age. Genetic effects of the animal and its dam and maternal permanent environmental effects were modelled by random regressions on Legendre polynomials of age at recording. Changes in direct permanent environmental effect variances were modelled by a polynomial variance function, together with a parametric correlation function to account for correlations between ages. Stationary and nonstationary models were used to model within-animal correlations between different ages. Residual variances were considered homogeneous or heterogeneous, with changes modelled by a step or polynomial function of age at recording. Based on Bayesian information criterion, a model with a cubic variance function combined with a nonstationary correlation function for permanent environmental effects, with 49 parameters to be estimated, fitted best. Modelling within-animal correlations through a parametric correlation structure can describe the variation pattern adequately. Moreover, the number of parameters to be estimated can be decreased substantially compared to a model fitting random regression on Legendre polynomial of age. © 2004 Elsevier B.V. All rights reserved.

A Nonstationary Negative Binomial Time Series with Time-Dependent Covariates: Enterococcus Counts in Boston Harbor

Boston Harbor has had a history of poor water quality, including contamination by enteric pathogens. We conduct a statistical analysis of data collected by the Massachusetts Water Resources Authority (MWRA) between 1996 and 2002 to evaluate the effects of court-mandated improvements in sewage treatment. Motivated by the ineffectiveness of standard Poisson mixture models and their zero-inflated counterparts, we propose a new negative binomial model for time series of Enterococcus counts in Boston Harbor, where nonstationarity and autocorrelation are modeled using a nonparametric smooth function of time in the predictor. Without further restrictions, this function is not identifiable in the presence of time-dependent covariates; consequently we use a basis orthogonal to the space spanned by the covariates and use penalized quasi-likelihood (PQL) for estimation. We conclude that Enterococcus counts were greatly reduced near the Nut Island Treatment Plant (NITP) outfalls following the transfer of wastewaters from NITP to the Deer Island Treatment Plant (DITP) and that the transfer of wastewaters from Boston Harbor to the offshore diffusers in Massachusetts Bay reduced the Enterococcus counts near the DITP outfalls.

Cross-Country Evidence on Output Growth Volatility: Nonstationary Variance and GARCH Models

This paper revisits the issue of conditional volatility in real GDP growth rates for Canada, Japan, the United Kingdom, and the United States. Previous studies find high persistence in the volatility. This paper shows that this finding largely reflects a nonstationary variance. Output growth in the four countries became noticeably less volatile over the past few decades. In this paper, we employ the modified ICSS algorithm to detect structural change in the unconditional variance of output growth. One structural break exists in each of the four countries. We then use generalized autoregressive conditional heteroskedasticity (GARCH) specifications modeling output growth and its volatility with and without the break in volatility. The evidence shows that the time-varying variance falls sharply in Canada, Japan, and the U.K. and disappears in the U.S., excess kurtosis vanishes in Canada, Japan, and the U.S. and drops substantially in the U.K., once we incorporate the break in the variance equation of output for the four countries. That is, the integrated GARCH (IGARCH) effect proves spurious and the GARCH model demonstrates misspecification, if researchers neglect a nonstationary unconditional variance.

Conceptual modelling to assess how the interplay of hydrological connectivity, catchment storage and tracer dynamics controls nonstationary water age estimates

Acknowledgements We would like to gratefully acknowledge the data provided by SEPA, Iain Malcolm. Mark Speed, Susan Waldron and many MSS staff helped with sample collection and lab analysis. We thank the European Research Council (project GA 335910 VEWA) for funding and are grateful for the constructive comments provided by three anonymous reviewers.

Nonstationary brand variables in category management: A cointegration perspective

Category-management models serve to assist in the development of plans for pricing and promotions of individual brands. Techniques to solve the models can have problems of accuracy and interpretability because they are susceptible to spurious regression problems due to nonstationary time-series data. Improperly stated nonstationary systems can reduce the accuracy of the forecasts and undermine the interpretation of the results. This is problematic because recent studies indicate that sales are often a nonstationary time-series. Newly developed correction techniques can account for nonstationarity by incorporating error-correction terms into the model when using a Bayesian Vector Error-Correction Model. The benefit of using such a technique is that shocks to control variates can be separated into permanent and temporary effects and allow cointegration of series for analysis purposes. Analysis of a brand data set indicates that this is important even at the brand level. Thus, additional information is generated that allows a decision maker to examine controllable variables in terms of whether they influence sales over a short or long duration. Only products that are nonstationary in sales volume can be manipulated for long-term profit gain, and promotions must be cointegrated with brand sales volume. The brand data set is used to explore the capabilities and interpretation of cointegration.

Practical methods of tracking of nonstationary time series applied to real-world data

In this paper, we discuss some practical implications for implementing adaptable network algorithms applied to non-stationary time series problems. Two real world data sets, containing electricity load demands and foreign exchange market prices, are used to test several different methods, ranging from linear models with fixed parameters, to non-linear models which adapt both parameters and model order on-line. Training with the extended Kalman filter, we demonstrate that the dynamic model-order increment procedure of the resource allocating RBF network (RAN) is highly sensitive to the parameters of the novelty criterion. We investigate the use of system noise for increasing the plasticity of the Kalman filter training algorithm, and discuss the consequences for on-line model order selection. The results of our experiments show that there are advantages to be gained in tracking real world non-stationary data through the use of more complex adaptive models.

Detecting Precipitation Climate Changes: An Approach Based on a Stochastic Daily Precipitation Model

2002 Mathematics Subject Classification: 62M10.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.