Forecasting ultra-high frequency returns using order flow and volume information : an Armax-Garchx model

The purpose of this thesis is to find a model to forecast the return and the financial volatility of one of the most traded Italian stock. Considering the markets efficiency theory, it should not be possible to forecast the future price of any financial instruments, because market prices include all the available information. This thesis investigates if there are some relationships among market prices, returns and financial volatility. To do this, it has been used a dataset which includes ultra high frequency data about Eni stock. Because of their complexity, it has been necessary to realize some sample algorithms. The first one refers to the traditional calendar time, while the other two use orders volume as sample driver. After having implemented these algorithms, the obtained information has been used to find a suitable model to implement an interesting trading strategy. Firstly, some GARCH variants models (ARX-GARCHX) have been realized at different frequencies, using the spline interpolation to compare unconstrained and constrained models. Afterwards, a final model of the ARMAX-GARCHX class has been implemented, considering all the three algorithms. To see if these models are able to obtain good performances, a trading strategy has been implemented. In conclusion, it has been possible to model the first and the second moment and verify them through a practical application.