Times series models with a specified symmetric non-normal marginal distribution
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Author
Dewald, Lee Samuel
Date
1985Advisor
Lewis, Peter A.W.
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Show full item recordAbstract
Time series models with autoregressive , moving average and mixed
autoregressive-moving average correlation structure and with symmetric,
heavy-tailed, non-normal marginal distributions, called Jl -Laplace, are
considered
.
First, a flexible mixed model NLARMA(p,q) with Laplace (double
exponential) marginals is investigated. The correlation structure for
several special cases is derived. The innovation sequence for the
second-order autoregressive case, NLAR(2), is derived. Parameter
estimation in the NLAR( 1 ) models is discussed in terms of moments, least
squares and maximum likelihood.
Second, a family of continuous random coefficient models with
2,-Laplace distributions are examined. The Sl-Laplace distribution is
described along with a useful transformation. The correlation structure
for special cases is derived. For a special case when i is one, the
BELAR(l) model with Laplace marginals, the maximum likelihood estimator
of serial correlation is derived. Least squares estimates are also
derived using the concept of a linear residual. These estimators of
correlation, along with other estimators of location and scale are
compared in a small simulation study.
Thirdly, the NLAR( 1 ) and the BELAR(I) processes are compared using
higher order residual analyses based on the uncorrelated , but dependent
linear residuals, {R }.
n
Finally, open problems, as well as possible extensions and
applications of the analyses given in this thesis are discussed.
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