Least absolute deviation estimation for fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity

We consider a unified least absolute deviation estimator forstationary and nonstationary fractionally integrated autoregressivemoving average models with conditional heteroscedasticity. Itsasymptotic normality is established when the second momentsof errors and innovations are finite. Several other alternativeestimators are also discussed and are shown to be less efficientand less robust than the proposed approach. A diagnostic tool,consisting of two portmanteau tests, is designed to check whetheror not the estimated models are adequate. The simulation experimentsgive further support to our model and the results for the absolutereturns of the Dow Jones Industrial Average Index daily closingprice demonstrate their usefulness in modelling time seriesexhibiting the features of long memory, conditional heteroscedasticityand heavy tails.     

A vector autoregressive moving average time series approach for describing asymmetries of antennal control of two millipede species

This article presents a statistical method, vector autoregressive moving average time series analysis, which makes no initial assumptions about the controlling interactions between variables in the data beyond those of linear systems, and has been designed to be statistically valid without requiring several repetitions of data sets. It is therefore very useful for studying physiological and behavioral phenomena.This new methodology is applied to a kinematic analysis of antennal scanning movements in two species of millipede. The analysis demonstrates features of the generation of the antennal and head movements, the direction of information flow within the central nervous system and consequent asymmetric control relationships between bilaterally homologous body parts.