Nobuhiko Terui

Combined forecasts from linear and nonlinear time series models

Combined forecasts from a linear and a nonlinear model are investigated for time series with possibly nonlinear characteristics. The forecasts are combined by a constant coefficient regression method as well as a time varying method. The time varying method allows for a locally (non)linear model. The methods are applied to data from two kinds of disciplines: the Canadian lynx and sunspot series from the natural sciences, and Nelson-Plossers U.S. series from economics. It is shown that the combined forecasts perform well, especially with time varying coefficients. This result holds for out of sample performance for the sunspot and Canadian lynx number series, but it does not uniformly hold for economic time series.

The Effect of Media Advertising on Brand Consideration and Choice

The nature of the effect of media advertising on brand choice is investigated in two product categories in analyses that combine household scanner panel data with media exposure information. Alternative model specifications are tested in which advertising is assumed to directly affect brand utility, model error variance, and brand consideration. We find strong support for advertising effects on choice through an indirect route of consideration set formation that does not directly affect brand utility. Implications for media buying and advertising effects are explored.

Testing Gaussianity and Linearity of Japanese Stock Returns

In this article, we first investigate the Gaussianity of Japanese stock return time series (214 daily, 18 weekly) by the Gaussianity test proposed by Kariya, Tsay, Terui and Li (1994) comprehensively and consistently. And it is observed that all the series are not Gaussian when the 6th order moment structures are taken into account. Up to the 4th order moments there are some series which are compatible with the Gaussianity. Secondly, we apply five well-known nonlinearity tests for stationary time series to the data set and examine the specific nonlinearity of the series. Some series strongly exhibit the specific types of nonlinearity. Typically the Nikkei daily index shows the TAR (Threshold Autoregressive) type nonlinearity. Comparing daily return series with weekly series, it is also shown that a central limit effect is working on the weekly stock returns, where daily information is accumulated over a week, in the sense that weekly returns are relatively closer to Gaussian.

Tests for Multinormality with Application to Time Series

Making use of a characterization of multivariate normality by Hermitian polynomials, we propose a multivariate normality test. The approach is then applied to time series analysis by constructing a test for Gaussianity of a stationary univariate series. Simulation study shows that the proposed test has reasonable power and outperforms other tests available in the literature when the innovation series of the time series is symmetric, but non-Gaussian.

Forecasting dynamic market share relationships

In market share analysis, it is fully recognized that we have often inadmissibly predicted market share, which means that some of predictors take the values outside the range [0, 1] and the total sum of predicted shares is not always one, so‐called “logical inconsistency”. Based on the Bayesian VAR model, proposes a dynamic market share model with logical consistency. The proposed method makes it possible to forecast not only the values of market share themselves, but also various dynamic market share relations across different brands or companies. The daily scanner data from the Nikkei POS information system are analyzed by the proposed method.

Ancillarity and the Limited Information Maximum-Likelihood Estimation of a Structural Equation in a Simultaneous Equation System

The concepts of the curved exponential family of distributions and ancillarity are applied to estimation problems of a single structural equation in a simultaneous equation model, and the effect of conditioning on ancillary statistics on the limited information maximum-likelihood (LIML) estimator is investigated. The asymptotic conditional covariance matrix of the LIML estimator conditioned on the second-order asymptotic maximal ancillary statistic is shown to be efficiently estimated by Liu and Breens formula. The effect of conditioning on a second-order asymptotic ancillary statistic, i.e., the smallest characteristic root associated with the LIML estimation, is analyzed by means of an asymptotic expansion of the distribution as well as the exact distribution. The smallest root helps to give an intuitively appealing measure of precision of the LIML estimator.

An F-type small sample simultaneous test for nested linear regression models

A small sample simultaneous testing method is proposed for nested linear regression model. The methodology is based on the generalized likelihood ratio test which is the large sample simultaneous testing method for general nested models. The proposed test is also used for model identification.

Measuring delayed and long‐term effects of pricing decisions on market share

Market‐share analysis focuses on the competitive interrelations between products or brands. Marketing activity may affect the performance of a companys own product and that of its competitors not only within a single time horizon but also over several extended periods. Starting from a static market‐share analysis model, the dynamic relationships of market shares between competitive brands are described by multiplicative competitive interaction (MCI) time‐series models, in which the problem of logical consistency for estimated shares is resolved. A Bayesian shrinkage estimator solution is applied to the further problem of model‐induced collinearity in cross‐differential MCI models. Dynamic elasticity is defined and used to measure the delayed and long‐term effects of marketing mix variables on market shares. The dynamic relationships of future market shares are predicted by means of predictive density. Strategic simulations are conducted under several scenarios for marketing planning. It is argued that the new dynamic model proposed here, applied to daily national or store tracking data, provides useful insights into dynamic competitive relationships in the marketplace, to the benefit of corporate planners, marketing directors, brand managers and retail strategists.

Personalized market response analysis for a wide variety of products from sparse transaction data

Advanced database marketing is designed to ascertain individual customers’ market responses with a discount or display of widely various products from transaction data. However, transaction data recorded in a supermarket or electric commerce are fundamentally sparse because most customers purchase only a few products from all products in shops. Existing methods are not applicable to elucidate the personalized response because of a lack of sample size of purchased data. This paper proposes a personalized market response estimation method for a wide set of customers and products from these sparse data. The method compresses a sparse transaction data with information related to response to marketing variables into a reduced-dimensional space for feasible parameter estimation. Then, they are decompressed into original space using augmented latent variables to obtain individual response parameters. Results show that the method can find suitable marketing promotions for individual customers to every analyzed product.

Forecasting model with asymmetric market response and its application to pricing of consumer package goods: Research Articles

The original article to which this Erratum refers was published in Applied Stochastic Models in Business and Industry 2005;21 (3):241–249