Journal of the Iranian Statistical Society

Modeling Chile Fishing Data Using Environmental Exogenous Variables with GARCH-X Model

Document Type : Original Article

Authors

1 Faculty of Economic Sciences, Central University of Ecuador, Quito, Ecuador.Department of Mathematics, Federico Santa María Technical University, Valparaíso, Chile.

2 Faculty of Engineering and Sciences, Adolfo Ibáñez University, Viña del Mar, Chile.

Abstract

Fishing industry has always been an economic motor in many countries around the world, but the fisheries production faces a lot of uncertainty and instability due to the complex factors involved in its operations. In this article, we consider the problem of modeling Chile fishing data using environmental exogenous variables with generalized autoregressive conditional heteroskedasticity (GARCH-X) type models. We carried out this by proposing an ARMA type model for the mean with GARCH-X noise. First, the ARMA, GARCH and GARCH-X models are briefly introduced and the data is described. The exogenous variables are selected from a group of environmental and climatic indicators by correlational analysis. Then, ARMA GARCH and ARMA GARCH-X models with exogenous variables are fitted and compared by information criteria and classical error measures, and stability of its parameters are checked. The statistical tests and comparisons evidenced that a model with inclusion of external variables in mean and variance with the ARMA GARCH-X specification performed better and adjusted the observed values more rigorously. Finally, some conclusions and possible refinations of the applied techniques are given.

Keywords

Bollerslev, T. (1986), Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307-327.
Bollerslev, T., andWooldridge, J. M. (1992), Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances. Econometric reviews, 11(2), 143-172.
Box, G., and Jenkins, G. (1976), Time Series Analysis: Forecasting and Control. Holden-Day, San Francisco.
Brenner, R. J., Harjes, R. H., and Kroner, K. F. (1996), Another look at models of the short-term interest rate. Journal of Financial and Quantitative Analysis, 31(1), 85-107.
de la Puente, S., and López de la Lama, R. (2019), Pesquería industrial en América Latina: retos y lecciones aprendidas de Chile, México y Perú. In Ruiz, M., Oyanedel, R., and Monteferri, B., editors, Mar, costas y pesquerías: una mirada comparativa desde Chile, México y Perú. Sociedad Peruana de Derecho Ambiental-SPDA.
Ghalanos, A. (2020), rugarch: Univariate GARCH models. R package version 1.4-4.
Hansen, B. E. (1992), Testing for parameter instability in linear models. Journal of Policy Modeling, 14(4), 517-533.
Hyndman, R. J., and Koehler, A. B. (2006), Another look at measures of forecast accuracy. International Journal of Forecasting, 22(4), 679-688.
Koutroumanidis, T., Iliadis, L., and Sylaios, G. K. (2006), Time-series modeling of fishery landings using ARIMA models and Fuzzy Expected Intervals software. Environmental Modelling & Software, 21(12), 1711-1721.
Lai, E. K. M., Cheng, Y.W., and MacAleer, M. (2005), Predicting monthly catch for some western Australia coastal finfish species with seasonal ARIMA-GARCH models. In ModellingWestern Australian Fisheries with Techniques of Time Series Analysis: Examining Data from a Di erent Perspective, chapter 9. Department of Fisheries Research Division,
Western Australian Marine Research Laboratories.
Ling, S., and McAleer, M. (2003), Asymptotic theory for a vector ARMA-GARCH model. Econometric theory, 19(2), 280-310.
Nyblom, J. (1989), Testing for the constancy of parameters over time. Journal of the American Statistical Association, 84(405), 223-230.
Park, H.-H., and Yoon, G.-D. (1996), Analysis and prediction of anchovy fisheries in Korea ARIMA model and spectrum analysis. Korean Journal of Fisheries and Aquatic Sciences, 29(2), 143-149.
SERNAPESCA (1963-2021), Anuarios Estadísticos de Pesca. Servicio Nacional de Pesca, Ministerio de Economía, Fomento y Turismo, Chile.
Stergiou, K. (1989), Modelling and forecasting the fishery for pilchard (Sardina pilchardus) in Greek waters using ARIMA time-series models. ICES Journal of Marine Science, 46(1), 16-23.
Stergiou, K. (1991), Short-term fisheries forecasting: comparison of smoothing, ARIMA and regression techniques. Journal of Applied Ichthyology, 7(4), 193-204.
Tsay, R. S. (1987), Conditional heteroscedastic time series models. Journal of the American Statistical Association, 82(398), 590-604.
Tsitsika, E. V., Maravelias, C. D., and Haralabous, J. (2007), Modeling and forecasting pelagic fish production using univariate and multivariate ARIMA models. Fisheries Science, 73(5), 979-988.
Valdés, J., Ortlieb, L., Gutierrez, D., Marinovic, L., Vargas, G., and Sifeddine, A. (2008), 250 years of sardine and anchovy scale deposition record in Mejillones Bay, northern Chile. Progress in Oceanography, 79(2-4), 198-207.
Vivas, E., Allende-Cid, H., Salas, R., and Bravo, L. (2019), Polynomial and wavelet-type transfer function models to improve fisheries’ landing forecasting with exogenous variables. Entropy, 21(11), 1082-1099.
Yáñez, E., Plaza, F., Gutiérrez-Estrada, J. C., Rodríguez, N., Barbieri, M. Á., Pulido- Calvo, I., and Bórquez, C. (2010), Anchovy (engraulis ringens) and sardine (sardinops sagax) abundance forecast o  northern Chile: a multivariate ecosystemic neural
network approach. Progress in Oceanography, 87(1-4), 242-250.
Yáñez, E., Plaza, F., Silva, C., Sánchez, F., Barbieri, M. Á., and Aranis, A. (2016), Pelagic resources landings in central-southern Chile under the A2 climate change scenarios. Ocean Dynamics, 66(10), 1333-1351.
Journal of the Iranian Statistical Society
Volume 21, Issue 1
June 2022
Pages 19-35
  • Receive Date: 28 June 2022
  • Revise Date: 17 November 2022
  • Accept Date: 21 December 2022