table of Contents
definition
Reference VAR model, also known as vector autoregression model, simply means that characterize the relationship between the number of vectors ① able to return, provided that the stationary data, ② return occurs between vectors, then to a certain relationship between the vectors, causality statistics, and therefore the need for Granger causality test, test the premise is stationary time series ③ so to the first stationary test.
It boils down to this:
- Stability test
- Granger causality test
Were VAR
Stability test
- By unit root test data is stable, continue Granger causality test
Not the stationary data processing will have a smooth, logarithmic or differential
Granger test
When Granger causality test to determine the lag order
VAR model of equation
\ [Y_ {t} = \ beta_ {1} \ cdot y_ {t-1} + \ alpha_ {1} \ cdot x_ {t-1} + \ beta_ {2} \ cdot y_ {t-2} + \ alpha_ {2} \ cdot x_ {
t-2} + \ ldots \] is in addition to the VAR model analysis to the impact itself lags, further influence on future generated values lags other relevant factors reference
Model specific steps VAR
- 1. The first stationary test sequence to see if a smooth sequence, or order one, or a higher order;
- 2. Select lags Var model according to criteria such as AIC SBC;
- 3. VAR model to see whether the roots inside the unit circle in the subsequent analysis may be continued;
- 4. If the same order integration, cointegration is performed to see if a cointegrated variables;
- 5.granger causality test, to see both the two variables have no correlation does not prove a causal relationship;
- 6. The impulse response, see the impact of external feedback variable;
- 7. variance decomposition ...
var regression coefficient is not the main purpose is to variance decomposition and impulse response analysis
Later supplemented formula model
as well as python code
Modeling steps and formulas
Code
The use of Python and numpy package pandas do time series, the first time I was doing