1,511 research outputs found
Statistical inference for time-inhomogeneous volatility models
This paper offers a new approach for estimating and forecasting the
volatility of financial time series. No assumption is made about the parametric
form of the processes. On the contrary, we only suppose that the volatility can
be approximated by a constant over some interval. In such a framework, the main
problem consists of filtering this interval of time homogeneity; then the
estimate of the volatility can be simply obtained by local averaging.
We construct a locally adaptive volatility estimate (LAVE) which can perform
this task and investigate it both from the theoretical point of view and
through Monte Carlo simulations. Finally, the LAVE procedure is applied to a
data set of nine exchange rates and a comparison with a standard GARCH model is
also provided. Both models appear to be capable of explaining many of the
features of the data; nevertheless, the new approach seems to be superior to
the GARCH method as far as the out-of-sample results are concerned
Locally adaptive factor processes for multivariate time series
In modeling multivariate time series, it is important to allow time-varying
smoothness in the mean and covariance process. In particular, there may be
certain time intervals exhibiting rapid changes and others in which changes are
slow. If such time-varying smoothness is not accounted for, one can obtain
misleading inferences and predictions, with over-smoothing across erratic time
intervals and under-smoothing across times exhibiting slow variation. This can
lead to mis-calibration of predictive intervals, which can be substantially too
narrow or wide depending on the time. We propose a locally adaptive factor
process for characterizing multivariate mean-covariance changes in continuous
time, allowing locally varying smoothness in both the mean and covariance
matrix. This process is constructed utilizing latent dictionary functions
evolving in time through nested Gaussian processes and linearly related to the
observed data with a sparse mapping. Using a differential equation
representation, we bypass usual computational bottlenecks in obtaining MCMC and
online algorithms for approximate Bayesian inference. The performance is
assessed in simulations and illustrated in a financial application
- …