Nonparametric Forecasting in Time Series—A Comparative Study

The problem of predicting a future value of a time series is considered in this article. If the series follows a stationary Markov process, this can be done by nonparametric estimation of the autoregression function. Two forecasting algorithms are introduced. They only differ in the nonparametric kernel-type estimator used: the Nadaraya-Watson estimator and the local linear estimator. There are three major issues in the implementation of these algorithms: selection of the autoregressor variables, smoothing parameter selection, and computing prediction intervals. These have been tackled using recent techniques borrowed from the nonparametric regression estimation literature under dependence. The performance of these nonparametric algorithms has been studied by applying them to a collection of 43 well-known time series. Their results have been compared to those obtained using classical Box-Jenkins methods. Finally, the practical behavior of the methods is also illustrated by a detailed analysis of two data sets.     

Modeling Interval Time Series with Space–Time Processes

We consider interval-valued time series, that is, series resulting from collecting real intervals as an ordered sequence through time. Since the lower and upper bounds of the observed intervals at each time point are in fact values of the same variable, they are naturally related. We propose modeling interval time series with space–time autoregressive models and, based on the process appropriate for the interval bounds, we derive the model for the intervals’ center and radius. A simulation study and an application with data of daily wind speed at different meteorological stations in Ireland illustrate that the proposed approach is appropriate and useful.     

Why Aggregate Long Memory Time Series?

This article shows that, for large samples, temporally aggregating a true long memory time series (in order to get an improved estimator) may make little or no sense, as the practitioner can get virtually the same estimates as those from the aggregated series by choosing the appropriate bandwidths on the original one, provided some fairly general conditions apply. Besides, the practitioner has a wider choice of bandwidths than she has of aggregating levels. However, these results apply only to two specific and commonly used estimators, and do not apply to the aggregation procedure undertaken to compute the realized volatility. Also, aggregating a time series in order to test true versus spurious long memory (as in Ohanissian et al., 2008) is a relevant issue, particularly regarding stochastic and/or realized volatility, as many nonlinear processes display spurious long memory where the above result does not apply.     

The Computer Analysis of Factorial Experiments: In Memoriam—Frank Yates

The responses to a recent paper by Dallal in this journal are evaluated by reference to the ideas of Frank Yates. It is concluded that much unnecessary complication has been introduced into the computer analysis of linear models by (1) the imposition of constraints on parameters, (2) neglect of marginality relations in forming hypotheses, and (3) confusion between the form of noncentrality parameters and hypotheses.     

New Developments in Statistical Computing: New Bias Evaluation Features of EXPLOR—A Program for Assessing Experimental Design Properties

Longitudinal investigations play an increasingly prominent role in biomedical research. Much of the literature on specifying and fitting linear models for serial measurements uses methods based on the standard multivariate linear model. This article proposes a more flexible approach that permits specification of the expected response as an arbitrary linear function of fixed and time-varying covariates so that mean-value functions can be derived from subject matter considerations rather than methodological constraints. Three families of models for the covariance function are discussed: multivariate, autoregressive, and random effects. Illustrations demonstrate the flexibility and utility of the proposed approach to longitudinal analysis.     

A More Powerful Average Bioequivalence Analysis for the 2 × 2 Crossover

The 2 × 2 crossover is commonly used to establish average bioequivalence of two treatments. In practice, the sample size for this design is often calculated under a supposition that the true average bioavailabilities of the two treatments are almost identical. However, the average bioequivalence analysis that is subsequently carried out does not reflect this prior belief and this leads to a loss in efficiency. We propose an alternate average bioequivalence analysis that avoids this inefficiency. The validity and substantial power advantages of our proposed method are illustrated by simulations, and two numerical examples with real data are provided.     

Nonparametric Estimation of Sojourn Time Distributions for Truncated Serial Event Data—a Weight-adjusted Approach

In follow-up studies, survival data often include subjects who have had a certain event at recruitment and may potentially experience a series of subsequent events during the follow-up period. This kind of survival data collected under a cross-sectional sampling criterion is called truncated serial event data. The outcome variables of interest in this paper are serial sojourn times between successive events. To analyze the sojourn times in truncated serial event data, we need to confront two potential sampling biases arising simultaneously from a sampling criterion and induced informative censoring. In this study, nonparametric estimation of the joint probability function of serial sojourn times is developed by using inverse probabilities of the truncation and censoring times as weight functions to accommodate these two sampling biases under various situations of truncation and censoring. Relevant statistical properties of the proposed estimators are also discussed. Simulation studies and two real data are presented to illustrate the proposed methods.     

Comments on “Canonical Correlation in Multivariate Time Series Analysis With an Application to One-Year-Ahead and Multiyear- Ahead Macroeconomic Forecasting,” by P. W. Otter

We examine the orthogonality assumption of seasonal and nonseasonal components for official quarterly unemployment figures in Germany and the United States. Although nonperiodic correlations do not seem to reject the orthogonality assumption, a periodic analysis based on correlation functions that vary with the seasons indicates the violation of orthogonality. We find that the unadjusted data can be described by periodic autoregressive models with a unit root. In simulations we replicate the empirical findings for the German data, where we use these simple models to generate artificial samples. Multiplicative seasonal adjustment leads to large periodic correlations. Additive adjustment leads to smaller ones.     

Efficient Block Designs for Dependent Observations—A Computer-Aided Search

In this article, the exchange and interchange algorithm of Zergaw (1989 Zergaw , G. ( 1989 ). A sequential method of constructing optimal block designs . Austral. J. Statist. 31 : 333 – 342 .[Crossref] , [Google Scholar]) and Martin and Eccleston (1992 Martin , R. J. , Eccleston , J. A. ( 1992 ). Recursive formulae for constructing block designs with dependent errors . Biometrika 79 : 426 – 430 .[Crossref], [Web of Science ®] , [Google Scholar]) have been modified and used for searching efficient block designs for making all possible pairwise treatment comparisons when observations are dependent. The lower bounds to the A- and D-efficiencies of the designs in a given class of the designs have been obtained for correlated observation structure and the procedure of computing lower bounds to A- and D-efficiencies has been incorporated in the algorithm. The algorithm has been translated into a computer program using Microsoft Visual C++. Using this program, a search for efficient designs for making all possible pairwise treatment comparisons has been made for v ≤ 10, b ≤ 33, k ≤ 10 such that bk ≤ 100 and v > k. The block designs considered are usual block designs (rectangular block designs) and circular block designs. Nearest neighbor (NN), autoregressive of order 1 (AR(1)) correlation structures are studied. The ranges of correlation coefficients for different correlation structures investigated are |ρ|≤0.50 for NN correlation structure in rectangular blocks, |ρ|≤0.45 for NN correlation structure in circular blocks, and |ρ|≤0.95 for AR(1) correlation structure. For these ranges, the matrix of correlation coefficients among observations within a block is positive definite. Robustness aspects of designs that are efficient for a given value of correlation have been investigated against other values of correlation coefficients. Robustness aspects of designs that are efficient for independent observations have also been studied for experimental situations with dependent observations.     

Trend,Growth Rate,and Change Point Analysis—A Data Driven Approach

A data-driven technique is proposed to estimate the trend and relative growth rate of time series data. The method is based on the local linear regression smoother and the only assumption about the form of the trend and growth rate function is that they are smooth functions of time. We also extended the method for handling sudden shifts or changes in the trend or growth rate functions by adding dummy variables for the jumps. Simulation studies are carried out to see the performance of the proposed procedure. The method is applied to study the trend and growth rate of wheat production in India from 1951–2005.     

Random Balance or Once upon a Time—

A simple confidence interval and hypothesis tests for the ratio of the proportions in two categories in a sampled population are presented. They are illustrated by examples on a consumer preference study, election poll results, and the life of coins.     

Bayesian Analysis of DSGE Models—Rejoinder

We would like to thank all the discussants for their stimulating comments. While our article to a large extent reviews current practice of Bayesian analysis of Dynamic Stochastic General Equilibrium (DSGE) models the discussants provide many ideas to improve upon the current practice, thereby outlining a research agenda for the years to come. In our rejoinder we will briefly revisit some of the issues that were raised.     

A new approach for disclosure control in the IAB establishment panel—multiple imputation for a better data access

For micro-datasets considered for release as scientific or public use files, statistical agencies have to face the dilemma of guaranteeing the confidentiality of survey respondents on the one hand and offering sufficiently detailed data on the other hand. For that reason, a variety of methods to guarantee disclosure control is discussed in the literature. In this paper, we present an application of Rubin’s (J. Off. Stat. 9, 462–468, 1993) idea to generate synthetic datasets from existing confidential survey data for public release.We use a set of variables from the 1997 wave of the German IAB Establishment Panel and evaluate the quality of the approach by comparing results from an analysis by Zwick (Ger. Econ. Rev. 6(2), 155–184, 2005) with the original data with the results we achieve for the same analysis run on the dataset after the imputation procedure. The comparison shows that valid inferences can be obtained using the synthetic datasets in this context, while confidentiality is guaranteed for the survey participants.     

A Note on Overdifferencing and the Equivalence of Seasonal Time Series Models With Monthly Means and Models With (0, 1, 1)12 Seasonal Parts When ⊖ = 1

Two general models for monthly seasonal time series are considered, one in which seasonality is modeled with monthly means and another in which seasonality is modeled with a (0, 1, 1)₁₂ ARIMA structure. The models are shown to be equivalent if the seasonal moving average parameter (?) is 1 and if the same assumptions about the 12 initial observations are made for both models. The role of the assumptions about the initial observations is analyzed, and it is argued that for practical purposes the two models can be regarded as equivalent when ? = 1. It is observed that the result extends easily to more general models involving overdifferencing.     

Stein estimation—A review

This paper presents an expository development of Stein estimation in several distribution families. Considered are both the point estimation and confidence interval cases. Specific results for linear regression models are added. Emphasis is laid on the chronological history and on recent results.     

Comment on “Issues Involved With the Seasonal Adjustment of Economic Time Series” by William R. Bell and Steven C. Hiilmer

This article investigates the existence of multiple regimes in the U.S. economy during the 1923—1991 period. A technique known as regression tree analysis is applied to search for splits in the data, if any exist, rather than choosing a splitting point a priori as has been done in previous work. Using this technique, strong evidence for the existence of nonlinear behavior of U.S. output is found over this period. Monte Carlo results are presented to assess the significance of the regime changes that are found.