Forecasting stochastic processes

Forecasting

Introduction to forecasting

We observe a series of observations:

\(x_1, x_2,...,x_t)\)

What can we say about \(x_{t+1}\)?

If the data was drawn iid then the past data then we would just want to identify moments.

However if the data is not iid, for example because it is increasing in time, then this is not the best way.

Regression formation

We can model

\(x_t=\alpha + \epsilon_t\)

Monte carlo simulations

N-step ahead

Consensus forecasting