Strict stationarity, persistence and volatility forecasting in ARCH(∞) processes

Gaussian Processes and Non-parametric Volatility Forecasting

We provide a formulation of stochastic volatility based on Gaussian processes, a flexible framework for Bayesian nonlinear regression. The advantage of using Gaussian processes in this context is to place volatility forecastingwithin a regression framework; this allows a large number of explanatory variables to be used for forecasting, a task difficult with standard volatility-forecasting formu...

A necessary and sufficient condition for the strict stationarity of a family of GARCH processes

We consider a family of GARCH(1,1) processes introduced in He and Teräsvirta (1999a). This family contains various popular GARCH models as special cases. A necessary and sufficient condition for the existence of a strictly stationary solution is given.

Forecasting Volatility

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...

Volatility Forecasting and Interpolation

Forecasting volatility is important to financial asset pricing because a more accurate forecast will allow for a more accurate model to price financial assets. Currently the VIX is used as a measure of volatility in the market as a whole, but a major issue with this is that it is calculated based on manually traded options on the S&P 500. Another method of forecasting volatility is that of solv...