Robust Estimation of the Vector Autoregressive Model by a Least Trimmed Squares Procedure

Abstract

The vector autoregressive model is very popular for modeling multiple time series.Estimation of its parameters is done by a least squares procedure. However, this estimation method is unreliable when outliers are present in the data, and there is a need for robust alternatives. In this paper we propose to estimate the vector autoregressive model by using a trimmed least squares estimator. We show how the order of the autoregressive model can be determined in a robust way, and how confidence bounds around the robustly estimated impulse response functions can be constructed. The resistance of the estimators to outliers is studied on real and simulated data.

Robust Exponential Smoothing of Multivariate Time Series

“…For resistant analysis of multivariate time series much less work has been done. Estimation of robust VAR models is proposed in Ben et al (1999) and Croux and Joossens (2008), and a projection-pursuit based outlier detection method by Galeano et al (2006).…”

“…Consider the housing data set from the book of Diebold (2001) and used in Croux and Joossens (2008). It concerns a bivariate time series of monthly data.…”

Robust estimation for vector autoregressive models

“…Both series were obtained from the Economic Database of the Federal Reserve Bank of St Louis. The same series were used by Croux and Joossens (2008) at a different period. The series were transformed into stationary ones using first differences of logarithms.…”

“…We can cite the work of García Ben et al (1999) which generalize to VARMA models the RA-estimators for univariate ARMA models proposed by Bustos and Yohai (1986). We can also cite García Ben et al (2001) who propose estimators based on a τ -scale for VAR models, and Croux and Joossens (2008) who define estimators based on a multivariate version of the least trimmed squares (LTS) criterion.…”

The optimal portfolio in respect to Expected Shortfall: a comparative study

“…In this article, conditional mean dynamics is described by the VAR(1) model. For details of the recent study we refer to Croux and Joossens [9]. To model conditional correlation, we use the Dynamic Conditional Correlation (DCC) model with normal conditional distributions.…”