ECM-GARCH model estimation

[xin_zh]

Dear Tom,

I’ve looked through the existing questions in this section, and I read the GARCH part in the RATS 8.2 user’s guide and the reference manual, but I still cannot solve my problem. I raise it here and I appreciate very much if you could help me.

I need to test for the first-order and second-order causality between wheat futures and cash price. The ADF and PP unit root tests show that both the price series are I(1) process, so I conduct a trace test and a maximum eigenvalue test on them and find the existence of one cointegrating vector. Therefore, my model for the first and second order causality test is an ECM-GARCH model.

Since I cannot type math here, I put the model description in the following attachment. Also attached is the data file I am using. Could you please help me with the estimation of the parameters using RATS? Thank you very much!

Yingzi

[TomDoan]

The usual way to do that is to use a two-step estimator, where beta (the cointegrating vector) is estimated first, then the GARCH model is estimating with beta assumed as given. You get consistent estimates of beta using standard Johansen ML estimators even in the presence of GARCH effects. With beta given, the rest can be done with GARCH.

[xin_zh]

Tom, thank you very much for your reply!

[xin_zh]

Dear Tom,

Thank you so much for your last reply! I followed your suggestion and got the estimates. Now I have two more questions:

1. After using CATS to estimate the error correction part, I exported the model as a VAR and then used "impulse(model=catsmodel,steps=20,results=impulses)" trying to get the impulse responses. However, the impulse responses are all zero. Could you please let me know how I can get the impulse responses and have the impulse response function plot? Thanks!

2. By using the two-step estimation, the parameter estimates are consistent. But will the significance test of the parameters also be valid? For example, will the weak exogeneity test be valid? I have concern about this because the IID error assumption is violated.

Thank you very much for your help!
yingzi