TY - JOUR
T1 - Time series models with asymmetric Laplace innovations
AU - Trindade, A. Alexandre
AU - Zhu, Yun
AU - Andrews, Beth
PY - 2010/12
Y1 - 2010/12
N2 - We propose autoregressive moving average (ARMA) and generalized autoregressive 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 modelling of certain types of financial and engineering data. In the case of anARMA 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 minimum 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 distributions.
AB - We propose autoregressive moving average (ARMA) and generalized autoregressive 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 modelling of certain types of financial and engineering data. In the case of anARMA 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 minimum 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 distributions.
KW - ARMA
KW - Conditional maximum likelihood
KW - Financial returns
KW - GARCH
KW - Joint distribution
KW - Prediction
UR - http://www.scopus.com/inward/record.url?scp=78649484288&partnerID=8YFLogxK
U2 - 10.1080/00949650903071088
DO - 10.1080/00949650903071088
M3 - Article
AN - SCOPUS:78649484288
SN - 0094-9655
VL - 80
SP - 1317
EP - 1333
JO - Journal of Statistical Computation and Simulation
JF - Journal of Statistical Computation and Simulation
IS - 12
ER -