Financial markets are complex adaptive systems that are continuously changing behavior.
Financial firms have to manage risk in real time so they need risk management models.
Forecasting price will always be an unreliable business but we will have to do it to manage risk.
Most models assume time invariant time series when doing the models.
This is also known as stationary condition and implies that the probability distribution generating data is time invariant.
Most of these models break down when we make predictions because financial time series are not stationary.
Using Bayesian statistics we can build models that are sequential in nature and are easy to update in real time.
Bayesian Sequential Monte Carlo Methods can detect structural breaks in the financial market in real time.
Models are models meaning we make assumptions when building models which may not hold always.
We can build a number of different models for different market conditions that can be used for forecasting.
Using Bayesian statistics we can then rank these models and select the best model for a given situation.
I have written a blog post in which I explain how to use Bayesian Sequential Monte Carlo Methods in trading.
We can use these methods in predicting price and volatility in real time.