Vector autoregression and causality: a theoretical overview and simulation study

This paper provides a theoretical overview of Wald tests for Granger causality in levels vector autoregressions (VAR's) and Johansen-type error correction models (ECM's). The theory is based on results in Toda and Phillips (1991a) and allows for stochastic and deterministic trends as well as arbitrary degrees of cointegration. We recommend some operational procedures for conducting Granger causality tests that are based on the Gaussian maximum likelihood estimation of ECM's. These procedures are applicable in the important practical case of testing the causal effects of one variable on another group of variables and vice versa. This paper also investigates the sampling properties of these testing procedures through simulation exercises. Three sequential causality tests in ECM's are compared with conventional causality tests in levels and differences VAR's.     

Vector autoregression and causality: a theoretical overview and simulation study

This paper provides a theoretical overview of Wald tests for Granger causality in levels vector autoregressions (VAR's) and Johansen-type error correction models (ECM's). The theory is based on results in Toda and Phillips (1991a) and allows for stochastic and deterministic trends as well as arbitrary degrees of cointegration. We recommend some operational procedures for conducting Granger causality tests that are based on the Gaussian maximum likelihood estimation of ECM's. These procedures are applicable in the important practical case of testing the causal effects of one variable on another group of variables and vice versa. This paper also investigates the sampling properties of these testing procedures through simulation exercises. Three sequential causality tests in ECM's are compared with conventional causality tests in levels and differences VAR's.     

Kalman filter-based modelling and forecasting of stochastic volatility with threshold

We propose a parametric nonlinear time-series model, namely the Autoregressive-Stochastic volatility with threshold (AR-SVT) model with mean equation for forecasting level and volatility. Methodology for estimation of parameters of this model is developed by first obtaining recursive Kalman filter time-update equation and then employing the unrestricted quasi-maximum likelihood method. Furthermore, optimal one-step and two-step-ahead out-of-sample forecasts formulae along with forecast error variances are derived analytically by recursive use of conditional expectation and variance. As an illustration, volatile all-India monthly spices export during the period January 2006 to January 2012 is considered. Entire data analysis is carried out using EViews and matrix laboratory (MATLAB) software packages. The AR-SVT model is fitted and interval forecasts for 10 hold-out data points are obtained. Superiority of this model for describing and forecasting over other competing models for volatility, namely AR-Generalized autoregressive conditional heteroscedastic, AR-Exponential GARCH, AR-Threshold GARCH, and AR-Stochastic volatility models is shown for the data under consideration. Finally, for the AR-SVT model, optimal out-of-sample forecasts along with forecasts of one-step-ahead variances are obtained.     

A SARIMAX coupled modelling applied to individual load curves intraday forecasting

A dynamic coupled modelling is investigated to take temperature into account in the individual energy consumption forecasting. The objective is both to avoid the inherent complexity of exhaustive SARIMAX models and to take advantage of the usual linear relation between energy consumption and temperature for thermosensitive customers. We first recall some issues related to individual load curves forecasting. Then, we propose and study the properties of a dynamic coupled modelling taking temperature into account as an exogenous contribution and its application to the intraday prediction of energy consumption. Finally, these theoretical results are illustrated on a real individual load curve. The authors discuss the relevance of such an approach and anticipate that it could form a substantial alternative to the commonly used methods for energy consumption forecasting of individual customers.     

New concepts in deterministic growth curve forecasting

Attempts to better the Performance of classical growth curve functions have met with limited success. Construction industry projects highlighted the need to improve deterministic models rather than the stochastic methodologies which are nearly always based on the former. New concepts (changed for the first time since 1825) are formulated and used to generate multi-component deterministic models. Six highly diverse case studies, of which three are presented, were used to test one model and its autocorrelation form. Trial forecast standard errors showed a drop of 50% when compared to classical and stochastic models. Among the by-products of this work are uses of normalisation, scaling and a simple statistical procedure to estimate linear constants. A different consequence of the new concepts thew light on the problem of predicting a consumption process in marketing. The major implications of this research show the import of the new concepts and diversification of the fields of study on deterministic modelling; and also the need to reappraise the functional interface with many of the underlying processes of growth.     

Analysis of Poisson varying-coefficient models with autoregression

In the regression analysis of time series of event counts, it is of interest to account for serial dependence that is likely to be present among such data as well as a nonlinear interaction between the expected event counts and predictors as a function of some underlying variables. We thus develop a Poisson autoregressive varying-coefficient model, which introduces autocorrelation through a latent process and allows regression coefficients to nonparametrically vary as a function of the underlying variables. The nonparametric functions for varying regression coefficients are estimated with data-driven basis selection, thereby avoiding overfitting and adapting to curvature variation. An efficient posterior sampling scheme is devised to analyse the proposed model. The proposed methodology is illustrated using simulated data and daily homicide data in Cali, Colombia.     

韩国的金融政策与金融危机及对我国的警示

金融危机的爆发对经济发展的危害是巨大的,受这次金融风暴直接冲击的国家,其经济实力普遍倒退７至１０年。其中韩国因货币贬值五成,其经济规模已由世界排名第１２位降至第１７位,人均国民生产总值由１９９６年的１０５４８美元降至目前的６６６４美元,经济实力倒退了...     

Multilevel multivariate modelling of childhood growth, numbers of growth measurements and adult characteristics

Summary.  A general latent normal model for multilevel data with mixtures of response types is extended in the case of ordered responses to deal with variates having a large number of categories and including count data. An example is analysed by using repeated measures data on child growth and adult measures of body mass index and glucose. Applications are described that are concerned with the flexible prediction of adult measurements from collections of growth measurements and for studying the relationship between the number of measurement occasions and growth trajectories.     

Projected polynomial autoregression for prediction of stationary time series

Polynomial autoregressions are usually considered to be unrealistic models for time series. However, this paper shows that they can successfully be used when the purpose of the time series study is to provide forecasts. A projection scheme inspired from projection pursuit regression and feedforward artificial neural networks is used in order to avoid an explosion of the number of parameters when considering a large number of lags. The estimation of the parameters of the projected polynomial autoregressions is a non-linear least-squares problem. A consistency result is proved. A simulation study shows that the naive use of the common final prediction error criterion is inappropriate to identify the best projected polynomial autoregression. An explanation of this phenomenon is given and a correction to the criterion is proposed. An important feature of the polynomial predictors introduced in this paper is their simple implementation, which allows for automatic use. This is illustrated with real data for the three-month US Treasury Bill.     

Lee–Carter mortality forecasting: a parallel generalized linear modelling approach for England and Wales mortality projections

Summary. The paper presents a reinterpretation of the model underpinning the Lee–Carter methodology for forecasting mortality (and other vital) rates. A parallel methodology based on generalized linear modelling is introduced. The use of residual plots is proposed for both methods to aid the assessment of the goodness of fit. The two methods are compared in terms of structure and assumptions. They are then compared through an analysis of the gender- and age-specific mortality rates for England and Wales over the period 1950–1998 and through a consideration of the forecasts generated by the two methods. The paper also compares different approaches to the forecasting of life expectancy and considers the effectiveness of the Coale–Guo method for extrapolating mortality rates to the oldest ages.     

Investigating impacts of complex sampling on latent growth curve modelling

We investigate the impacts of complex sampling on point and standard error estimates in latent growth curve modelling of survey data. Methodological issues are illustrated with empirical evidence from the analysis of longitudinal data on life satisfaction trajectories using data from the British Household Panel Survey, a national representative survey in Great Britain. A multi-process second-order latent growth curve model with conditional linear growth is used to study variation in the two perceived life satisfaction latent factors considered. The benefits of accounting for the complex survey design are considered, including obtaining unbiased both point and standard error estimates, and therefore correctly specified confidence intervals and statistical tests. We conclude that, even for the rather elaborated longitudinal data models that were considered, estimation procedures are affected by variance-inflating impacts of complex sampling.     

Piecewise deterministic Markov processes applied to fatigue crack growth modelling

In this paper, we use a particular piecewise deterministic Markov process (PDMP) to model the evolution of a degradation mechanism that may arise in various structural components, namely, the fatigue crack growth. We first derive some probability results on the stochastic dynamics with the help of Markov renewal theory: a closed-form solution for the transition function of the PDMP is given. Then, we investigate some methods to estimate the parameters of the dynamical system, involving Bogolyubov's averaging principle and maximum likelihood estimation for the infinitesimal generator of the underlying jump Markov process. Numerical applications on a real crack data set are given.     

Simulation of a stationary autoregression: A characterization of the normal distribution

Simulating a stationary AR(p), X_t = ∑^p_i=1α_iX_t−i + Z_t, when the innovations {Z_t} are assumed to be i.i.d. is straightforward. Starting the process in the stationary state, however, requires generation of (X₁,X₂,…,X_p) from the stationary p-dimensional distribution. When Z_t is normal this may be achieved by generating X_i as a linear function of X₁,X₂,…,X_i−1 and an independent normal variate for i = 2,3,…, p. It is shown that the ability to initialize a stationary AR(p) in this way characterizes the normal distribution.     

A robust nonparametric estimation of the autoregression function under an ergodic hypothesis

The authors propose a family of robust nonparametric estimators for regression or autoregression functions based on kernel methods. They show the strong uniform consistency of these estimators under a general ergodicity condition when the data are unbounded and range over suitably increasing sequences of compact sets. They give some implications of these results for stating the prediction in Markovian processes with finite order and show, through simulation, the efficiency of the predictors they propose.     

Adaptive estimators for parameters of the autoregression function of a Markov chain

Suppose we observe an ergodic Markov chain on the real line, with a parametric model for the autoregression function, i.e. the conditional mean of the transition distribution. If one specifies, in addition, a parametric model for the conditional variance, one can define a simple estimator for the parameter, the maximum quasi-likelihood estimator. It is robust against misspecification of the conditional variance, but not efficient. We construct an estimator which is adaptive in the sense that it is efficient if the conditional variance is misspecified, and asymptotically as good as the maximum quasi-likelihood estimator if the conditional variance is correctly specified. The adaptive estimator is a weighted nonlinear least-squares estimator, with weights given by predictors for the conditional variance.     

The Cornish-Fisher expansion for a class of statistics in first order autoregression

ABSTRACT

This article is concerned with the derivation and study of the Cornish-Fisher expansion for a wide class of estimators of the parameter in the first order autoregressive process. Second and third order Cornish-Fisher approximations to the quantile of the distribution of the corresponding asymptotically normal standardized statistic are stated explicitly and their accuracy is examined, both theoretically and numerically, by comparing them with the exact value of the quantile obtained by Monte Carlo simulation.     

Assessing switchability for biosimilar products: modelling approaches applied to children's growth

The present paper describes two statistical modelling approaches that have been developed to demonstrate switchability from the original recombinant human growth hormone (rhGH) formulation (Genotropin^®) to a biosimilar product (Omnitrope^®) in children suffering from growth hormone deficiency. Demonstrating switchability between rhGH products is challenging because the process of growth varies with the age of the child and across children. The first modelling approach aims at predicting individual height measured at several time‐points after switching to the biosimilar. The second modelling approach provides an estimate of the deviation from the overall growth rate after switching to the biosimilar, which can be regarded as an estimate of switchability. The results after applying these approaches to data from a randomized clinical trial are presented. The accuracy and precision of the predictions made using the first approach and the small deviation from switchability estimated with the second approach provide sufficient evidence to conclude that switching from Genotropin^® to Omnitrope^® has a very small effect on growth, which is neither statistically significant nor clinically relevant. Copyright © 2015 John Wiley & Sons, Ltd.     

Nonparametric tests of independence of two autoregressive time series based on autoregression rank scores

We propose a nonparametric test of independence of two autoregressive time series. The test statistic is based on lagged cross-correlation coefficients computed from autoregression rank scores, and extends the traditional correlogram-based method of Haugh (1976). It is easily computable, asymptotically distribution-free, and, contrary to its traditional parametric competitor, it does not require any estimation of the unknown autoregression parameters. The test is applied in a study of the relations between outdoor temperature and the daily mortality related to cardio-vascular problems in Brussels, during the period 1980–1989.     

Theory and techniques of demographic forecasting

This paper focuses on theories and techniques for forecasting fertility and mortality. Period and cohort analyses of fertility and mortality in Germany over the past century are first discussed. Alternative techniques for forecasting future trends in these variables in the Federal Republic of Germany are then outlined. The economic and social policy consequences of different mortality and fertility assumptions are also briefly noted.     

Threshold autoregression analysis for finite-range time series of counts with an application on measles data

This article studies the threshold autoregression analysis for the self-exciting threshold binomial autoregressive processes. Parameters' point estimation and interval estimation problems are considered via the empirical likelihood method. A new algorithm to estimate the threshold value of the threshold model is also given. Simulation study is conducted for the evaluation of the developed approach. An application on measles data is provided to show the applicability of the method.