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Time Series Models With Asymmetric Laplace Innovations A. Alexandre Trindade

Summary: Time Series Models With Asymmetric Laplace Innovations
A. Alexandre Trindade
Yun Zhu
Beth Andrews
May 18, 2009
We propose autoregressive moving average (ARMA) and generalized autoregres-
sive conditional heteroscedastic (GARCH) models driven by Asymmetric Laplace (AL)
noise. The AL distribution plays, in the geometric-stable class, the analogous role
played by the normal in the alpha-stable class, and has shown promise in the modeling
of certain types of financial and engineering data. In the case of an ARMA model we
derive the marginal distribution of the process, as well as its bivariate distribution when
separated by a finite number of lags. The calculation of exact confidence bands for min-
imum mean-squared error linear predictors is shown to be straightforward. Conditional
maximum likelihood-based inference is advocated, and corresponding asymptotic results
are discussed. The models are particularly suited for processes that are skewed, peaked,
and leptokurtic, but which appear to have some higher order moments. A case study of
a fund of real estate returns reveals that AL noise models tend to deliver a superior fit
with substantially less parameters than normal noise counterparts, and provide both a
competitive fit and a greater degree of numerical stability with respect to other skewed


Source: Andrews, Beth - Department of Statistics, Northwestern University


Collections: Mathematics