On loss functions and ranking forecasting performances of multivariate volatility models

Abstract

The ranking of multivariate volatility models is inherently problematic because when the unobservable volatility is substituted by a proxy, the ordering implied by a loss function may be biased with respect to the intended one. We point out that the size of the distortion is strictly tied to the level of the accuracy of the volatility proxy. We propose a generalized necessary and sufficient functional form for a class of non-metric distance measures of the Bregman type which ensure consistency of the ordering when the target is observed with noise. An application to three foreign exchange rates is provided

Forecasting volatility with empirical similarity and Google Trends

“…Regarding the choice of this loss function, we rely on the work of Laurent et al (2013) and Patton (2011). They show that it is crucial for forecasting volatility to select a loss function from the family of consistent loss functions, where consistency means that the true ranking of the models is preserved, regardless if the true conditional volatility or a noisy volatility proxy is used.…”

Model Uncertainty and Forecast Combination in High‐Dimensional Multivariate Volatility Prediction

“…A discussion on the properties of above reported loss functions can be found in Laurent et al (2012Laurent et al ( , 2013. The second class of estimators is based on the minimization of loss functions which are not directly related to measures of predictive accuracy but to statistical criteria aimed at enforcing some theoretical optimality properties in the forecast errors.…”

Multivariate high‐frequency‐based volatility (HEAVY) models

“…Since  tCs is unobservable, our analysis will be based on some proxy denoted by  tCs , which we take to be the realized covariance matrix, V tCs . The loss function (18) evaluates the s-step predicted density from model a using the proxy  tCs as data, 6 and it provides a consistent ranking of volatility models in the sense of Patton (2011) and Patton and Sheppard (2009) as it is robust to noise in the proxy  tCs ; see also Laurent et al (2009).…”