The article introduces a new method for modeling financial data volatility without assuming specific structures for the mean and variance models. Traditional models make these assumptions, but this new approach uses a Non-Linear AutoRegressive Moving Average with eXogenous inputs (NARMAX) framework. By extending a previous method, researchers can now estimate both mean and variance models without assuming linearity. This method was tested on simulated and real financial data, showing that a constant mean model is often inaccurate. A new Weighted Least Squares approach was also developed for estimating the variance model, improving accuracy in estimating volatility.