High dimensional stochastic regression with latent factors, endogeneity and nonlinearity

We consider a multivariate time series model which represents a high dimensional vector process as a sum of three terms: a linear regression of some observed regressors, a linear combination of some latent and serially correlated factors, and a vector white noise. We investigate the inference without imposing stationary conditions on the target multivariate time series, the regressors and the underlying factors. Furthermore we deal with the endogeneity that there exist correlations between the observed regressors and the unobserved factors. We also consider the model with nonlinear regression term which can be approximated by a linear regression function with a large number of regressors. The convergence rates for the estimators of regression coefficients, the number of factors, factor loading space and factors are established under the settings when the dimension of time series and the number of regressors may both tend to infinity together with the sample size. The proposed method is illustrated with both simulated and real data examples

Principal component analysis for second-order stationary vector time series

We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented into several lower-dimensional subseries, and those subseries are uncorrelated with each other both contemporaneously and serially. Therefore those lower-dimensional series can be analysed separately as far as the linear dynamic structure is concerned. Technically it boils down to an eigenanalysis for a positive definite matrix. When $p$ is large, an additional step is required to perform a permutation in terms of either maximum cross-correlations or FDR based on multiple tests. The asymptotic theory is established for both fixed $p$ and diverging $p$ when the sample size $n$ tends to infinity. Numerical experiments with both simulated and real data sets indicate that the proposed method is an effective initial step in analysing multiple time series data, which leads to substantial dimension reduction in modelling and forecasting high-dimensional linear dynamical structures. Unlike PCA for independent data, there is no guarantee that the required linear transformation exists. When it does not, the proposed method provides an approximate segmentation which leads to the advantages in, for example, forecasting for future values. The method can also be adapted to segment multiple volatility processes.Comment: The original title dated back to October 2014 is "Segmenting Multiple Time Series by Contemporaneous Linear Transformation: PCA for Time Series

Refined instrumental variable estimation: maximum likelihood optimization of a unified Box–Jenkins model

For many years, various methods for the identification and estimation of parameters in linear, discretetime transfer functions have been available and implemented in widely available Toolboxes for MatlabTM. This paper considers a unified Refined Instrumental Variable (RIV) approach to the estimation of discrete and continuous-time transfer functions characterized by a unified operator that can be interpreted in terms of backward shift, derivative or delta operators. The estimation is based on the formulation of a pseudo-linear regression relationship involving optimal prefilters that is derived from an appropriately unified Box–Jenkins transfer function model. The paper shows that, contrary to apparently widely held beliefs, the iterative RIV algorithm provides a reliable solution to the maximum likelihood optimization equations for this class of Box–Jenkins transfer function models and so its en bloc or recursive parameter estimates are optimal in maximum likelihood, prediction error minimization and instrumental variable terms

Economic Structural Change: Analysis and Forecasting

In modern economic model building, structural change is a key concept. Economic growth and events like the oil price shocks have impacts on the economic system such that models with fixed structure are illusions. Considerable progress has been made in the last few years concerning statistical and econometric tools. Methods for identification of structural change, models that are robust to changes and assimilate their effects, and adequate forecasting techniques have been developed. Under the auspices of IIASA a very active community of statisticians and econometricians has made a very influential effort in this area. The purpose of this volume is to document these activities, to present new methods and developments in this area, and to demonstrate applications. Particular weight is given to nonparametric and robust methods for identification of and modeling under structural change, a Bayesian approach to forecast combination, and time-varying parameter cointegration. This book has four parts: (1) Identification of structural change, (2) Model building in the presence of structural change, (3) Forecasting in the presence of structural change, and (4) Economic modeling and the use of empirical data. The book provides an up-to-date status report on the field and should stimulate applications of the methods in empirical work as well as further research

Uncertainty and Forecasting of Water Quality

This book brings together a number of critical discussions on the role of uncertainty in the development and use of mathematical models for water quality management. It covers the application of recursive estimation, time-series analysis, maximum likelihood estimation, and the Group Method of Data Handling (GMDH), to the problem of model identification. It also treats the analysis of prediction-error propagation, real-time forecasting, and the use of Monte Carlo simulation in the generation of speculative hypotheses about system behaviour