Restriction on Cointegrating Vector

[upani]

Dear All,

Thanks for adding me to the forum. I am doing cointegration analysis of spot and future prices. The model is a bivariate one without intercept or trend. The issues are follows:

1. I want to impose restriction on cointegrating vector Beta(1,-1). How to set up the R transpose matrix to check the restriction.
2. I want to test the short-run causality through the error correction term. The null hypothesis which i want to test is Beta(transpose)alpha = 0.

How to set up the matrix R transpose and Beta transpose to test the restriction.

Waiting for your valuable reply.

With sincere regards,
Upananda

[TomDoan]

You would set the rank to 1. The simplest way to do the (1,-1) restriction is to do "Restrictions on Each Beta Vector". That lets you specify the "shape" of the restriction, so you would put in +1 and -1 in two slots in the dialog.

It sounds like you want the weak exogeneity test, not a test for short-run non-causality. That's the "Test for Weak Exogeneity". You can test that either with the (1,-1) shape imposed or not.

[upani]

Dear Sir,

I am grateful for your reply. I would like to know are the short-run non-causality test are different than weak Exogeneity or not. My argument behind doing the test Beta(transpose)alpha = 0 is to test the importance of spot and futures market ( error correction term alphaspot and alphafuture ). According to Yang, Bessler and Letham(2001):

test on alpha.jpg (92.44 KiB) Viewed 10909 times

I have a doubt how to implement the test. Is it same with weak exogeneity test or not?.

It will be great if you can give me some suggestion.

With sincere regards,
Upananda

[TomDoan]

The zero restrictions on alpha are exactly the same thing as weak exogeneity (which means, more specifically, weak exogeneity for estimating beta). If the loading on one of the series is zero, then that series is weakly exogenous---it has no direct information on beta as the error correcting adjustment doesn't apply to it, only to the second series.