Quantile sieve estimates for time series - Jürgen Franke; Jean-Pierre Stockis; Joseph Tadjuidje (Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, 2007)
We consider the problem of estimating the conditional quantile of a time series at time t given observations of the same and perhaps other time series available at time t - 1. We discuss sieve estimates which are a nonparametric versions of the Koenker-Bassett regression quantiles and do not require the specification of the innovation law. We prove consistency of those estimates and illustrate their good performance for light- and heavy-tailed distributions of the innovations with a small simulation study. As an economic application, we use the estimates for calculating the value at risk of some stock price series.
Keywords: C14; C45; 330; conditional quantile; time series; sieve estimate; neural network; qualitative threshold model; uniform consistency; value at risk; Zeitreihenanalyse; Maßzahl; Schätztheorie; Value at Risk; Börsenkurs; Theorie