We study the properties of an M-estimator arising from the minimisation of an integrated version of the quantile loss function. The estimator depends on a tuning parameter which controls the degree of robustness. We show that the sample median and the sample mean are obtained as limit cases....

This paper addresses the problem of estimating multiple quantiles from a time series. A flexible class of dynamic multiple quantile (DMQ) models is specified, ensuring that estimated quantiles do not cross and that extreme quantiles are estimated by exploiting information coming from all the...

This paper shows that different states of the financial system command a different effect in worsening financial conditions on economic vulnerability. As soon as financial conditions start deteriorating, the economic outlook becomes more pessimistic and uncertain. No increase in macroeconomic...

We develop a semiparametric model to track a large number of quantiles of a time series. The model satisfies the condition of non crossing quantiles and the defining property of fixed quantiles. A key feature of the specification is that the updating scheme for time varying quantiles at each...

This paper studies the behaviour of crypto currencies financial time-series of which Bitcoin is the most prominent example. The dynamic of those series is quite complex displaying extreme observations, asymmetries, and several nonlinear characteristics which are difficult to model. We develop a...

Financial risk managers routinely use non-linear time series models to predict the downside risk of the capital under management. They also need to evaluate the adequacy of their model using so-called backtesting procedures. The latter involve hypothesis testing and evaluation of loss functions....