Multivariate rotated ARCH models

Arch Models ”

Arch Models by Tim Bollerslev

Adaptive Estimation in Arch Models

We construct efficient estimators of the identifiable parameters in a regression model when the errors follow a stationary parametric ARCH(P) process. We do not assume a functional form for the conditional density of the errors, but do require that it be symmetric about zero. The estimators of the mean parameters are adaptive in the sense of Bickel [2]. The ARCH parameters are not jointly ident...

Arch Models and Conditional Volatility

w t here {e } is independent white noise. The width of the forecast interval is proportional to the square r root of the one-step forecast error variance, var [x − f ] = var [e ] =σ , a constant. On the othe n +1 n , 1 n +1 e t i hand, actual financial time series often show sudden bursts of high volatility. For example, if a recen nnovation was strongly negative (indicating a crash, etc.), a p...

Co-Volatility and Correlation Clustering : A Multivariate Correlated ARCH Framework

We present a new, full multivariate framework for modelling the evolution of conditional correlation between financial asset returns. Our approach assumes that a vector of asset returns is shocked by a vector innovation process the covariance matrix of which is timedependent. We then employ an appropriate Cholesky decomposition of the asset covariance matrix which, when transformed using a Sphe...