Volatility forecasting models are becoming more accurate, but noise looks to be an inseparable part of these forecasts. Nonetheless, using adaptive filters to cancel the noise should help improve the performance of the forecasting models. Adaptive filters have the advantage of changing based on the environment. This feature is vital when they are used along with a model for volatility forecasting and error cancellation in the financial markets. Nonlinear Autoregressive (NAR) neural networks have simple structures, but they are efficient tools in error cancelation systems when working with non-stationary and random walk noise processes. For this research, an adaptive threshold filter is designed to respond to changes in its environment when a GARCH(1,1) model makes errors in its volatility forecast. It is shown that this filter can forecast the noise (errors) in the GARCH(1,1) outputs when there is a non-stationary time series of errors. The model reduces the mean squared errors by 42.9%. A sample portfolio of five stocks from the S&P 500 index from 4/2007 to 12/2010 is studied to illustrate the performance of the model.