[Forum SIS] Errata Corrige: DISES/STATLAB Seminar: Guy Mélard (ULB)

[statlab@unisa.it statlab@unisa.it]

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Seminario di Statistica

Dipartimento di Scienze Economiche e Statistiche - DiSES
<http://www.dises.unisa.it/>

*Università degli Studi di Salerno*

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*Guy Mélard (Université Libre de Bruxelles)*

*Time series models with time-dependent coefficients*
<https://www.dises.unisa.it/unisa-rescue-page/dettaglio/id/1359/module/487/row/2441>

October, 30  2018,  2.30 p.m., Sala dei Consigli DISES

*Abstract*

Autoregressive-moving average (ARMA) models with time-dependent
coefficients (tdARMA) and marginally heteroscedastic innovation variance
provide a natural alternative to stationary ARMA models for economic time
series. Several theories have been developed in the last thirty years for
parametric estimation in that context. First, we focus on univariate models
for the case where the coefficients depend both on time and the series
length. Absence of independence, stationarity and ergodicity implies that
assumptions are still more delicate than in the general time series theory.
We summarize our theory based on array processes. Then, we compare our
asymptotic approach to another approach due to Dahlhaus, the local
stationarity theory. We illustrate our theory on a dataset of temperatures
in Alpine cities and on a dataset of economic time series. Secondly, we
provide new theoretical results in a multivariate setup:


   - a fundamental theorem for the asymptotic theory;
   - a lemma for reducing the assumption on moments from 8 to slightly more
   than 4;
   - a theorem to establish convergence for the two covariance matrices
   Vand Winvolved in the sandwich formula.

We apply them on time-dependent vector AR(1) and MA(1) models. In
particular, we show simulation results for different types of distributions
(including multivariate Laplace and multivariate Student) and compare them
to the standard errors deduced from the theory.

*Key words: *nonstationary process, time-varying model.


Information: statlab a unisa.it

*Laboratorio di Ricerca e Formazione avanzata in Statistica* STATLAB
<http://www.statlab.unisa.it/index>

Università degli Studi di Salerno

Via Giovanni Paolo II, 132

84084 Fisciano SA

Tel. +39 089 96 3132
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