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Log‐symmetric regression models: information criteria and application to movie business and industry data with economic implications

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  • Marcelo Ventura
  • Helton Saulo
  • Victor Leiva
  • Sandro Monsueto

Abstract

This work deals with log‐symmetric regression models, which are particularly useful when the response variable is continuous, strictly positive, and following an asymmetric distribution, with the possibility of modeling atypical observations by means of robust estimation. In these regression models, the distribution of the random errors is a member of the log‐symmetric family, which is composed by the log‐contaminated‐normal, log‐hyperbolic, log‐normal, log‐power‐exponential, log‐slash and log‐Student‐t distributions, among others. One way to select the best family member in log‐symmetric regression models is using information criteria. In this paper, we formulate log‐symmetric regression models and conduct a Monte Carlo simulation study to investigate the accuracy of popular information criteria, as Akaike, Bayesian, and Hannan‐Quinn, and their respective corrected versions to choose adequate log‐symmetric regressions models. As a business application, a movie data set assembled by authors is analyzed to compare and obtain the best possible log‐symmetric regression model for box offices. The results provide relevant information for model selection criteria in log‐symmetric regressions and for the movie industry. Economic implications of our study are discussed after the numerical illustrations.

Suggested Citation

  • Marcelo Ventura & Helton Saulo & Victor Leiva & Sandro Monsueto, 2019. "Log‐symmetric regression models: information criteria and application to movie business and industry data with economic implications," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(4), pages 963-977, July.
    • Handle: RePEc:wly:apsmbi:v:35:y:2019:i:4:p:963-977
    DOI: 10.1002/asmb.2433
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    References listed on IDEAS

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    1. Helton Saulo & Jeremias Leão, 2017. "On log-symmetric duration models applied to high frequency financial data," Economics Bulletin, AccessEcon, vol. 37(2), pages 1089-1097.
    2. Gadelha, Sérgio Ricardo de Brito & Divino, José Angelo & Almeida, Vinicius & Maranhão, André, 2017. "Alíquotas Tributárias Efetivas Médias para a Economia Brasileira: Uma Abordagem Macroeconômica," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 71(2), July.
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    Cited by:

    1. Jorge I. Figueroa-Zúñiga & Cristian L. Bayes & Víctor Leiva & Shuangzhe Liu, 2022. "Robust beta regression modeling with errors-in-variables: a Bayesian approach and numerical applications," Statistical Papers, Springer, vol. 63(3), pages 919-942, June.
    2. Yonghui Liu & Guohua Mao & Víctor Leiva & Shuangzhe Liu & Alejandra Tapia, 2020. "Diagnostic Analytics for an Autoregressive Model under the Skew-Normal Distribution," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    3. Luis Sánchez & Víctor Leiva & Manuel Galea & Helton Saulo, 2020. "Birnbaum-Saunders Quantile Regression Models with Application to Spatial Data," Mathematics, MDPI, vol. 8(6), pages 1-17, June.
    4. Luis Sánchez & Víctor Leiva & Helton Saulo & Carolina Marchant & José M. Sarabia, 2021. "A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications," Mathematics, MDPI, vol. 9(21), pages 1-21, November.
    5. Víctor Leiva & Helton Saulo & Rubens Souza & Robert G. Aykroyd & Roberto Vila, 2021. "A new BISARMA time series model for forecasting mortality using weather and particulate matter data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(2), pages 346-364, March.
    6. Xiao Jiang & Saralees Nadarajah & Thomas Hitchen, 2024. "A Review of Generalized Hyperbolic Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 64(1), pages 595-624, July.

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