Journal article
Inference robustness of ARIMA models under non-normality —Special application to stock price data
Metrika, Vol.26(1), pp.43-56
12/1979
DOI: 10.1007/BF01893469
Abstract
Wold's decomposition theorem [Wold] states that every weakly stationary stochastic process can be written as a linear combination of orthogonal shocks. For practical reasons, however, it is desirable to employ models which use parameters parsimoniously. Box and Jenkins [1970] show how parsimony can be achieved by representing the linear process in terms of a small number of autoregressive and moving average terms (ARIMA-models). The Gaussian hypothesis assumes that the shocks follow a normal distribution with fixed mean and variance. In this case the process is characterized by first and second order moments. The normality assumption seems reasonable for many kinds of series. However, it was pointed out by Kendall [1953], Mandelbrot [1963, 1967], Fama [1965], Mandelbrot and Taylor [1967] that particularly for stock price data the distribution of the shocks appears leptokurtic: In this paper we investigate the sensitivity of ARIMA models to non-normality of the distribution of the shocks. We suppose that the distribution function of the shocks is a member of the symmetric exponential power family, which includes the normal as well as leptokurtic and platikurtic distributions. A Bayesian approach is adopted and the inference robustness of ARIMA models with respect to i) the estimation of parameters ii) the forecasts of future observations is discussed. © 1979 Physica-Verlag Rudolf Liebing KG.
Details
- Title: Subtitle
- Inference robustness of ARIMA models under non-normality —Special application to stock price data
- Creators
- J. Ledolter - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Metrika, Vol.26(1), pp.43-56
- DOI
- 10.1007/BF01893469
- ISSN
- 0026-1335
- eISSN
- 1435-926X
- Language
- English
- Date published
- 12/1979
- Academic Unit
- Statistics and Actuarial Science; Business Analytics
- Record Identifier
- 9984380382702771
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