Summary Time series models and forecasting (For the second half of the subject EMF)

Time-series models and forecasting
Time series models : describe the behaviour of variable(s) on the basis of lagged values of these
same variable(s). Only y and lagged y, no x anymore in (OLS) regression.
Time series models are used to:
- Analyse how a (economic / financial) shock affects variables now and in the future
= Impulse response
- Forecas ng variables
- Not/ less useful for establishing causal rela onships

Variables in me series models need to be sta onary:
- Without trend
- Stable variance over me
- Stable autocorrela on structure over me
- No seasonality
If you draw a line through the middle of a sta onary process then it should be flat.
It may have cycles, but overall it does not trend up nor down.

Uncondi onal distribu on = distribu on of variable(s) without having any addi onal informa on
(opposite is condi onal distribu on).

Mathema cally speaking sta onary:
- The uncondi onal joint probability distribu on does not change when shi ed in me
- Parameters such as uncondi onal mean and variance, autocorrela on thus cannot change
over me
- Condi onal mean and variance can change over me




Why do we need sta onary variables?
- OLS assump ons imply sta onarity for the error term
- If variable is not sta onary, OLS gives spurious and false results
- Ma ers for forecas ng

, White noise process : no discernible structure, no autocorrela on.
Autocorrela on func on will be zero apart from a single peak of 1 at s = 0.




If there is no autocorrela on at all (white noise), no need to use me-series model.
If there is evidence for autocorrela on:




Example (there is decay, but not super fast) (H0 is rejected).