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When to use cointegration in OLS regression?
When there are only two presumably cointegrated variables (and thus a single I (1) I ( 1) variable is used in the first stage OLS regression) the critical values for the levels 10% 10 %, 5% 5 % and 1% 1 % are −3.12 − 3.12, −3.41 − 3.41 and −3.96 − 3.96.
How to test for cointegration of two series?
Following Key Concept 16.5, it seems natural to construct a test for cointegration of two series in the following manner: if two series Xt X t and Y t Y t are cointegrated, the series obtained by taking the difference Y t−θXt Y t − θ X t must be stationary. If the series are not cointegrated, Y t −θXt Y t − θ X t is nonstationary.
Is it safe to run a cointegrated regression?
If there is a cointegrating relationship, that is a linear combination of I (1) variables that is stationary, then it is safe to run an OLS regression. However, the residuals will probably be serially correlated so you might want to adjust the standard errors. One way to do that is by the Newey-West method.
Which is the first stage of OLS regression?
The first-stage OLS regression is T B10Y St = β0 +β1T B3M St +zt. T B 10 Y S t = β 0 + β 1 T B 3 M S t + z t. Thus we have ˆT B10Y St = 2.46+0.81⋅T B3M St, T B 10 Y S ^ t = 2.46 + 0.81 ⋅ T B 3 M S t, where ˆθ = 0.81 θ ^ = 0.81. Next, we take the residual series {ˆzt} { z t ^ } and compute the ADF test statistic.
How to test for cointegration and error correction?
Testing for Cointegration (residuals based test) Cointegration and error correction Procedure in testing for Cointegration Two step Engel and Granger procedure •Step 1: Run a static regression in levels between the variables •Save the residuals series: and •Step 2: Test for stationary of residuals
When to use stationarity and cointegration in regression?
•Has a direct bearing on the appropriateness and statistical validity of regression results •If we wish to regress Y on X when: