Spectral properties of the concurrent and forecasting seasonal linear filters of the X-11-ARIMA method

This study analyzes the properties of the linear filters of the X-11-ARIMA seasonal adjustment method applied for current seasonal adjustment. It provides the general formula for the combined weights that result from the ARIMA model extrapolation filters with the X-11 seasonal-adjustment filters. The three cases studied correspond to the three ARIMA models automatically tested by the X-11-ARIMA program, namely, (0, 1, 1)(0, 1, 1), (0, 2, 2)(0, 1, 1), and (2, 1. 2)(0, 1,1). The parameter values chosen reflect different degrees of flexibility of the trend-cycle and seasonal components. It is shown that the X-11-ARIMA linear filters for current seasonal adjustment are very flexible; they change with both the ARIMA extrapolation model and its parameter values, contrary to those of the X-11 program, which are fixed for a given set of options.     

Seasonal Adjustment Using Structural Time Series Models: An Application and a Comparison With the Census X-11 Method

This article makes the method of seasonal adjustment operational using suitable structural time series models (STM). This so-called STM method is applied to several relevant Dutch macro- economic quarterly and monthly time series. The results are compared with those of the Census X-11 method using several formal criteria as yardsticks. The STM method proves to compete well with the Census X-11 method in this respect.     

Diagnostic tools in generalized Weibull linear regression models

We propose some statistical tools for diagnosing the class of generalized Weibull linear regression models [A.A. Prudente and G.M. Cordeiro, Generalized Weibull linear models, Comm. Statist. Theory Methods 39 (2010), pp. 3739–3755]. This class of models is an alternative means of analysing positive, continuous and skewed data and, due to its statistical properties, is very competitive with gamma regression models. First, we show that the Weibull model induces ma-ximum likelihood estimators asymptotically more efficient than the gamma model. Standardized residuals are defined, and their statistical properties are examined empirically. Some measures are derived based on the case-deletion model, including the generalized Cook's distance and measures for identifying influential observations on partial F-tests. The results of a simulation study conducted to assess behaviour of the global influence approach are also presented. Further, we perform a local influence analysis under the case-weights, response and explanatory variables perturbation schemes. The Weibull, gamma and other Weibull-type regression models are fitted into three data sets to illustrate the proposed diagnostic tools. Statistical analyses indicate that the Weibull model fitted into these data yields better fits than other common alternative models.     

春节模型的设计与应用

 季节调整是经济数据预处理中非常重要的一个步骤。现有的主流季节调整方法X-12-ARIMA 和TRAMO/SEATS中都包含节假日因素的调整。由于不同的国家节假日一般不同,因此各国在进行经济数据的季节调整时,都需要结合本国的假日对季节调整方法进行修正。春节是中国最为重要而且持续时间最长的节日,具体日期可以出现在一月也可以在二月。本文基于X-12-ARIMA方法,同时考虑春节对经济指标的正负性影响效应、春节影响的变化速率以及春节效应的时长三个因素,设计了十二个不同类型的春节模型。本文应用Eviews软件和Demetra软件,采集不同的经济指标,对所设计的春节模型进行了应用研究,并根据异常值改善标准,对最佳的春节模型进行了选择与比较分析。     

A systematic review on model selection in high-dimensional regression

High dimensional models are getting much attention from diverse research fields involving very many parameters with a moderate size of data. Model selection is an important issue in such a high dimensional data analysis. Recent literature on theoretical understanding of high dimensional models covers a wide range of penalized methods including LASSO and SCAD. This paper presents a systematic overview of the recent development in high dimensional statistical models. We provide a brief review on the recent development of theory, methods, and guideline on applications of several penalized methods. The review includes appropriate settings to be implemented and limitations along with potential solution for each of the reviewed method. In particular, we provide a systematic review of statistical theory of the high dimensional methods by considering a unified high-dimensional modeling framework together with high level conditions. This framework includes (generalized) linear regression and quantile regression as its special cases. We hope our review helps researchers in this field to have a better understanding of the area and provides useful information to future study.     

Variational approximation for heteroscedastic linear models and matching pursuit algorithms

Modern statistical applications involving large data sets have focused attention on statistical methodologies which are both efficient computationally and able to deal with the screening of large numbers of different candidate models. Here we consider computationally efficient variational Bayes approaches to inference in high-dimensional heteroscedastic linear regression, where both the mean and variance are described in terms of linear functions of the predictors and where the number of predictors can be larger than the sample size. We derive a closed form variational lower bound on the log marginal likelihood useful for model selection, and propose a novel fast greedy search algorithm on the model space which makes use of one-step optimization updates to the variational lower bound in the current model for screening large numbers of candidate predictor variables for inclusion/exclusion in a computationally thrifty way. We show that the model search strategy we suggest is related to widely used orthogonal matching pursuit algorithms for model search but yields a framework for potentially extending these algorithms to more complex models. The methodology is applied in simulations and in two real examples involving prediction for food constituents using NIR technology and prediction of disease progression in diabetes.     

An Empirical Comparison of Multiple Imputation Methods for Categorical Data

Multiple imputation is a common approach for dealing with missing values in statistical databases. The imputer fills in missing values with draws from predictive models estimated from the observed data, resulting in multiple, completed versions of the database. Researchers have developed a variety of default routines to implement multiple imputation; however, there has been limited research comparing the performance of these methods, particularly for categorical data. We use simulation studies to compare repeated sampling properties of three default multiple imputation methods for categorical data, including chained equations using generalized linear models, chained equations using classification and regression trees, and a fully Bayesian joint distribution based on Dirichlet process mixture models. We base the simulations on categorical data from the American Community Survey. In the circumstances of this study, the results suggest that default chained equations approaches based on generalized linear models are dominated by the default regression tree and Bayesian mixture model approaches. They also suggest competing advantages for the regression tree and Bayesian mixture model approaches, making both reasonable default engines for multiple imputation of categorical data. Supplementary material for this article is available online.     

State space mixed models for longitudinal observations with binary and binomial responses

We propose a new class of state space models for longitudinal discrete response data where the observation equation is specified in an additive form involving both deterministic and random linear predictors. These models allow us to explicitly address the effects of trend, seasonal or other time-varying covariates while preserving the power of state space models in modeling serial dependence in the data. We develop a Markov chain Monte Carlo algorithm to carry out statistical inference for models with binary and binomial responses, in which we invoke de Jong and Shephard’s (Biometrika 82(2):339–350, 1995) simulation smoother to establish an efficient sampling procedure for the state variables. To quantify and control the sensitivity of posteriors on the priors of variance parameters, we add a signal-to-noise ratio type parameter in the specification of these priors. Finally, we illustrate the applicability of the proposed state space mixed models for longitudinal binomial response data in both simulation studies and data examples.     

Unobserved-Components Models for Seasonal Adjustment Filters

Time series models are presented, for which the seasonal-component estimates delivered by linear least squares signal extraction closely approximate those of the standard option of the widely-used Census X-11 program. Earlier work is extended by consideration of a broader class of models and by examination of asymmetric filters, in addition to the symmetric filter implicit in the adjustment of historical data. Various criteria that guide the specification of unobserved- components models are discussed, and a new preferred model is presented. Some nonstandard options in X-11 are considered in the Appendix.     

Truncated location-scale non linear regression models

We present a class of truncated non linear regression models for location and scale where the truncated nature of the data is incorporated into the statistical model by assuming that the response variable follows a truncated distribution. The location parameter of the response variable is assumed to be modeled by a continuous non linear function of covariates and unknown parameters. In addition, the proposed model also allows for the scale parameter of the responses to be characterized by a continuous function of the covariates and unknown parameters. Three particular cases of the proposed models are presented by considering the response variable to follow a truncated normal, truncated skew normal, and truncated beta distribution. These truncated non linear regression models are constructed assuming fixed known truncation limits and model parameters are estimated by direct maximization of the log-likelihood using a non linear optimization algorithm. Standardized residuals and diagnostic metrics based on the cases deletion are considered to verify the adequacy of the model and to detect outliers and influential observations. Results based on simulated data are presented to assess the frequentist properties of estimates, and a real data set on soil-water retention from the Buriti Vermelho River Basin database is analyzed using the proposed methodology.     

Total least squares solution for compositional data using linear models

The restrictive properties of compositional data, that is multivariate data with positive parts that carry only relative information in their components, call for special care to be taken while performing standard statistical methods, for example, regression analysis. Among the special methods suitable for handling this problem is the total least squares procedure (TLS, orthogonal regression, regression with errors in variables, calibration problem), performed after an appropriate log-ratio transformation. The difficulty or even impossibility of deeper statistical analysis (confidence regions, hypotheses testing) using the standard TLS techniques can be overcome by calibration solution based on linear regression. This approach can be combined with standard statistical inference, for example, confidence and prediction regions and bounds, hypotheses testing, etc., suitable for interpretation of results. Here, we deal with the simplest TLS problem where we assume a linear relationship between two errorless measurements of the same object (substance, quantity). We propose an iterative algorithm for estimating the calibration line and also give confidence ellipses for the location of unknown errorless results of measurement. Moreover, illustrative examples from the fields of geology, geochemistry and medicine are included. It is shown that the iterative algorithm converges to the same values as those obtained using the standard TLS techniques. Fitted lines and confidence regions are presented for both original and transformed compositional data. The paper contains basic principles of linear models and addresses many related problems.     

A comparison of indicators for evaluating x-11-arima seasonal adjustment

Summary The evaluation of the performance of seasonal adjustment procedures is an issue of practical importance in view of the unobservable nature of the components. Looking at just one indicator when judging the overall quality of a procedure may be misleading, even though this is common practice when many series are involved. The main purpose of this paper is to compare the information content of different synthetic indicators with reference to the X-11-ARIMA procedure. Sixty-six different types of monthly seasonal series are generated and the seasonal component then extracted by carrying out X-11-ARIMA with standard options. The correlation between the pseudo-true error for each series and various synthetic indicators allows us to compare the latter's reliability, under both the hypotheses of minimum and maximum variance of the pseudo-true seasonal component. We show that the overall quality indexQ-the indicator most commonly adopted by users of the X-11-ARIMA-is always outperformed by the simpler diagnostics based on the stability of the estimates. In particular, the “sliding-spans” indicator, proposed by Findley et al. (1990) and included in the diagnostics of the new X-12 procedure, shows a much stronger correlation with the pseudo-true error in the seasonal adjustment. We also show that the total forecasting errors in the one-year-ahead extrapolation of the seasonal component have a good informative power and perform almost as well as the “sliding-spans” indicator.     

Semiparametric model average prediction in panel data analysis

Forecasting in economic data analysis is dominated by linear prediction methods where the predicted values are calculated from a fitted linear regression model. With multiple predictor variables, multivariate nonparametric models were proposed in the literature. However, empirical studies indicate the prediction performance of multi-dimensional nonparametric models may be unsatisfactory. We propose a new semiparametric model average prediction (SMAP) approach to analyse panel data and investigate its prediction performance with numerical examples. Estimation of individual covariate effect only requires univariate smoothing and thus may be more stable than previous multivariate smoothing approaches. The estimation of optimal weight parameters incorporates the longitudinal correlation and the asymptotic properties of the estimated results are carefully studied in this paper.     

Generalized partially linear varying-coefficient models

Generalized varying-coefficient models are useful extensions of generalized linear models. They arise naturally when investigating how regression coefficients change over different groups characterized by certain covariates such as age. In this paper, we extend these models to generalized partially linear varying-coefficient models, in which some coefficients are constants and the others are functions of certain covariates. Procedures for estimating the linear and non-parametric parts are developed and their associated statistical properties are studied. The methods proposed are illustrated using some simulations and real data analysis.     

Generalized bent-cable methodology for changepoint data: a Bayesian approach

The choice of the model framework in a regression setting depends on the nature of the data. The focus of this study is on changepoint data, exhibiting three phases: incoming and outgoing, both of which are linear, joined by a curved transition. Bent-cable regression is an appealing statistical tool to characterize such trajectories, quantifying the nature of the transition between the two linear phases by modeling the transition as a quadratic phase with unknown width. We demonstrate that a quadratic function may not be appropriate to adequately describe many changepoint data. We then propose a generalization of the bent-cable model by relaxing the assumption of the quadratic bend. The properties of the generalized model are discussed and a Bayesian approach for inference is proposed. The generalized model is demonstrated with applications to three data sets taken from environmental science and economics. We also consider a comparison among the quadratic bent-cable, generalized bent-cable and piecewise linear models in terms of goodness of fit in analyzing both real-world and simulated data. This study suggests that the proposed generalization of the bent-cable model can be valuable in adequately describing changepoint data that exhibit either an abrupt or gradual transition over time.     

On some robust estimation procedures for quantiles based on data

This paper introduces some robust estimation procedures to estimate quantiles of a continuous random variable based on data, without any other assumptions of probability distribution. We construct a reasonable linear regression model to connect the relationship between a suitable symmetric data transformation and the approximate standard normal statistics. Statistical properties of this linear regression model and its applications are studied, including estimators of quantiles, quartile mean, quartile deviation, correlation coefficient of quantiles and standard errors of these estimators. We give some empirical examples to illustrate the statistical properties and apply our estimators to grouping data.     

Multivariate Seasonal Adjustment,Economic Identities,and Seasonal Taxonomy

This article extends the methodology for multivariate seasonal adjustment by exploring the statistical modeling of seasonality jointly across multiple time series, using latent dynamic factor models fitted using maximum likelihood estimation. Signal extraction methods for the series then allow us to calculate a model-based seasonal adjustment. We emphasize several facets of our analysis: (i) we quantify the efficiency gain in multivariate signal extraction versus univariate approaches; (ii) we address the problem of the preservation of economic identities; (iii) we describe a foray into seasonal taxonomy via the device of seasonal co-integration rank. These contributions are developed through two empirical studies of aggregate U.S. retail trade series and U.S. regional housing starts. Our analysis identifies different seasonal subcomponents that are able to capture the transition from prerecession to postrecession seasonal patterns. We also address the topic of indirect seasonal adjustment by analyzing the regional aggregate series. Supplementary materials for this article are available online.     

Statistical Inference in Orthogonal Regression for Three-Part Compositional Data Using a Linear Model with Type-II Constraints

Orthogonal regression is a proper tool to analyze relations between two variables when three-part compositional data, i.e., three-part observations carrying relative information (like proportions or percentages), are under examination. When linear statistical models with type-II constraints (constraints involving other parameters besides the ones of the unknown model) are employed for estimating the parameters of the regression line, approximate variances and covariances of the estimated line coefficients can be determined. Moreover, the additional assumption of normality enables to construct confidence domains and perform hypotheses testing. The theoretical results are applied to a real-world example.     

Mean and quantile boosting for partially linear additive models

Additive models are often applied in statistical learning which allow linear and nonlinear predictors to coexist. In this article we adapt existing boosting methods for both mean regression and quantile regression in additive models which can simultaneously identify nonlinear, linear and zero predictors. We use gradient boosting in which simple linear regression and univariate penalized spline are used as base learners. Twin boosting is applied to achieve better variable selection accuracy. Simulation studies as well as real data applications illustrate the strength of our proposed methods.     

On generalized degrees of freedom with application in linear mixed models selection

The concept of degrees of freedom plays an important role in statistical modeling and is commonly used for measuring model complexity. The number of unknown parameters, which is typically used as the degrees of freedom in linear regression models, may fail to work in some modeling procedures, in particular for linear mixed effects models. In this article, we propose a new definition of generalized degrees of freedom in linear mixed effects models. It is derived from using the sum of the sensitivity of the expected fitted values with respect to their underlying true means. We explore and compare data perturbation and the residual bootstrap to empirically estimate model complexity. We also show that this empirical generalized degrees of freedom measure satisfies some desirable properties and is useful for the selection of linear mixed effects models.