Least absolute deviation estimation for all-pass time series models

摘要: An autoregressive moving average model in which all of the roots of polynomial are reciprocals roots average polynomial and vice versa is called an all-pass time series model. All-pass models generate uncorrelated (white noise) series, but these are not independent non-Gaussian case. approximation to likelihood of the case Laplacian (two-sided exponential) noise yields a modified absolute deviations criterion, can be used even if the underlying not Laplacian. Asymptotic normality for least absolute deviation estimators parameters established under general conditions. Behavior finite samples studied via simulation. The methodology applied exchange rate returns show that linear models mimic “nonlinear” behavior, is applied stock market volume data illustrate a two-step procedure for fitting noncausal autoregressions.