Limit Moves as Censored Observations of Equilibrium Futures Price in GARCH Processes

We develop an algorithm for estimating generalized autoregressive conditional heteroscedasticity models for time series containing some censored observations. Motivation for the algorithm comes from those futures markets and some equity markets that have limits constraining the maximum allowable movement in price in a day. When a limit is reached, trading stops and the equilibrium price is not observed. We maximize the likelihood function by replacing the unobservable squared error terms with their expected values. We evaluate the algorithm performance by extensive simulation and apply it to treasury-bill futures data from a period of high volatility and frequent limit moves.