Publication: Perspectiva histórica de los modelos ARIMA y su utilidad en el análisis económico
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1991
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Centro de Estudios Constitucionales (España)
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Este trabajo comienza enumerando las contribuciones a la teoría de procesos estocásticos estacionarios que aparecieron entre 1912 y 1942 y comentando, al mismo tiempo,
los principales procedimientos existentes en las décadas de los cincuenta y sesenta
para predecir y extraer señales de series económicas que, en general, se consideraba que
no eran estacionarias. Esta brecha existente entre la aplicación práctica y el análisis teórico
fue cubierta por Box y Jenkins (1970) con los modelos ARJMA. Estos modelos
incorporan un tipo específico de procesos evolutivos que se caracteriza por la presencia
de raíces autorregresivas unitarias sobre una estructura ARIMA, la cual constituye una
forma general de aproximar procesos estacionarios.
En la literatura econométrica, la naturaleza evolutiva de las variables económicas se
capta también, generalmente, mediante el uso de raíces unitarias en los modelos econométricos
y/o en los modelos que generan las variables exógenas. Por ello, tal como se
ha ido discutiendo por diferentes autores, los modelos ARIMA no son cajas negras,
sino formas finales de modelos econométricos. Por tanto, los modelos ARIMA se pueden
utilizar de forma consistente, pero ineficiente, para describir y estimar el comportamiento
a largo y corto plazo de las series económicas, y tales resultados pueden ser
muy útiles en la elaboración de los informes que las instituciones privadas y públicas
realizan periódicamente.
This paper starts enumerating some of the contributions to the theory of Stationary Stochastic Processes during the first half of this century and commenting the main procedures used in the fifties and sixties for forecasting and signal extraction based on the fact that a great number o( the observed economic time series are nonstationary. The gap between the theory and practice was filled by Box and Jenkins (1970) with the ARJMA models, which incorporate a specific type of processes characterized by the presence of unit autoregressive roots on top of a general approximation — ARMA models— for a linear stationary process. In the econometric literature the evolving nature of the economic variables is also generally captured by the same procedure of including unit roots into the model and for in the processes generating the exogenous variables, Therefore, as it has been widely discussed in the literature, the ARIMA models are not black-boxes but a sort of final forms of the econometric models. Thus, the ARIMA schemes can be employed as a consistent, but certainly inefficient, way of characterizing and estimating the long and short-term behaviour of economic time series, and these results can be used in the economic reports that private and public institutions need to procedure periodically.
This paper starts enumerating some of the contributions to the theory of Stationary Stochastic Processes during the first half of this century and commenting the main procedures used in the fifties and sixties for forecasting and signal extraction based on the fact that a great number o( the observed economic time series are nonstationary. The gap between the theory and practice was filled by Box and Jenkins (1970) with the ARJMA models, which incorporate a specific type of processes characterized by the presence of unit autoregressive roots on top of a general approximation — ARMA models— for a linear stationary process. In the econometric literature the evolving nature of the economic variables is also generally captured by the same procedure of including unit roots into the model and for in the processes generating the exogenous variables, Therefore, as it has been widely discussed in the literature, the ARIMA models are not black-boxes but a sort of final forms of the econometric models. Thus, the ARIMA schemes can be employed as a consistent, but certainly inefficient, way of characterizing and estimating the long and short-term behaviour of economic time series, and these results can be used in the economic reports that private and public institutions need to procedure periodically.
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Revista de Historia Económica, Año IX, Otoño 1991, n. 3, p. 541-552