Data Analysis & Forecasting Faculty of Development Economics

Phung Thanh Binh (2010) 1

TIME SERIES ANALYSIS STANDARD/STATIC GRANGER CAUSALITY

1. THE MODEL The Standard/Static Granger Causality test for the of two stationary variables ∆Y t and ∆X t, involves as a first step the estimation of the following VAR model:

yt

m

1jjtj

n

1iitit uXYY +∆γ+∆β+α=∆ ∑∑

=−

=− (1)

xt

m

1jjtj

n

1iitit uYXX +∆δ+∆θ+α=∆ ∑∑

=−

=− (2)

Important note: In practice, the lag n and m in equation (1) and (2) might be not the same. However, if you perform the test in Eviews, the routine VAR model assumes that both n and m in both equation are the same. This kind of selection can lead to model mispecification. Therefore, we should manually determine the optimal lag length for them (see the guide in step 4 below).

2. TEST PROCEDURE

Suppose we have Yt and Xt are nonstationary.

THE STANDER GRANGER CAUSALITY is performed as follows:

Step 1: Testing for the unit root of Yt and Xt

(using either DF, ADF, or PP tests)

Suppose the test results indicate that both Yt and Xt are I(1).

Step 2: Testing for cointegration between Yt and Xt

(usually use Engle-Granger (EG) or Johansen approach)

If the test results indicate that Yt and Xt are not cointegrated, we have only one choice of Standard Version of Granger Causality. Conversely, if Y t and Xt are cointegrated, we can apply either Standard or ECM Version of Granger Causality, depending on our research objectives.

Step 3: Taking the first differences of Yt and Xt (i.e., �Yt and �Xt)

Step 4: Determining the optimal lag length of �Yt and �Xt

a) Automatically determine the optimal lag length of ∆Y t and ∆X t in their AR models (using AIC or SIC, see Section 8 of my lecture).

yt

n

1iitit uYY +∆β+α=∆ ∑

=− (3)

Then estimate (3) by OLS, and obtain the RSS of this regression (which is the restricted one) and label it as RSSRY.

Data Analysis & Forecasting Faculty of Development Economics

Phung Thanh Binh (2010) 2

xt

'n

1iitit uXX +∆θ+α=∆ ∑

=− (4)

Then estimate (4) by OLS, and obtain the RSS of this regression (which is the restricted one) and label it as RSSRX.

b) Manually determine the optimal lag length of ∆X t (m in equation (1)) and ∆Y t (m in equation (2)), (using AIC or SIC, depending on which one you use in step 4a, see Section 8 of my lecture).

yt

m

1jjtj

n

1iitit uXYY +∆γ+∆β+α=∆ ∑∑

=−

=− (5)

Then estimate (5) by OLS, and obtain the RSS of this regression (which is the unrestricted one) and label it as RSSUY.

xt

'm

1jjtj

'n

1iitit uYXX +∆δ+∆θ+α=∆ ∑∑

=−

=− (6)

Then estimate (6) by OLS, and obtain the RSS of this regression (which is the unrestricted one) and label it as RSSUX.

Step 5: Set the null and alternative hypotheses

a) For equation (3) and (5), we set:

tt

m

1jj0 Y causenot does Xor 0 :H ∑

=

=γ

tt

m

1jj1 Y causes Xor 0 :H ∑

=

≠γ

a) For equation (4) and (6), we set:

tt

m

1jj0 X causenot does Yor 0 :H ∑

=

=δ

tt

m

1jj1 X causes Yor 0 :H ∑

=

≠δ

Step 6: Calculate the F statistic for the normal Wald test

a) For equation (3) and (5), we set:

)kN/(RSS

m/)RSSRSS(F

UY

UYRY

−−

=

b) For equation (4) and (6), we set:

)kN/(RSS

'm/)RSSRSS(F

UX

UXRX

−−

=

Data Analysis & Forecasting Faculty of Development Economics

Phung Thanh Binh (2010) 3

If the computed F value exceeds the critical F value, reject the null hypothesis and conclude that Xt causes Yt, or Yt causes Xt.

Question: How to explain the test results?