VECM estimation

[kirsti]

Hi!

I am conducting a research for my dissertation to see whether a cointegrating relation exists between macroeconomic variables and stock market index. I used six variables: unemployment, euribor, inflation, industrial production, money supply and stock market index. I took the natural logarithms of the last four variables and the two first variables stayed the same as they are interest rates.

In the next step I checked if all my variables are integrated into order one. I used ADF, PP and KPSS. For the stock market index, money supply and industrial production all three tests indicated that in levels the series have a unit root/not stationary. For inflation, ADF and PP test indicated that there is a unit root, whereas the KPSS test indicated that even after taking the first difference the series is not stationary. For unemployment PP test and KPSS test showed that there is a unit root, but after first difference the data becomes stationary. However, ADF showed that even after first difference the series has a unit root. For euribor, ADF and KPSS test indicated that after first difference the unit root disappears whereas the PP test indicated that there is no unit root in the levels data.
As at least two tests are for each time series indicated that there is a unit root, I decided to accept that the all my variables are I(1).

In the next step I estimated a VAR (with levels data) and looked for the best lag length. As I only have 84 monthly observations for each variable, the AIC showed that the best is 7 lags, but SIC and HQ indicated 2 lags. LR test showed 3 lags.

I then estimated the cointegration rank. First I tested with 1 lag (I have understood that when I estimate the lag length using levels VAR I should deduct one lag if I want to estimate VECM or find the cointegration rank, correct me please if I'm wrong). With lag one I got the following results: trace stat. 4 cointegrating equations, max. eig. stat. 1 cointegration equation.

Here is where I get really lost. After I estimate a VECM, lets say with 1 lag and 1 cointegration equation, can I check the autocorrelation, heteroskedasticity and normality straight away or do I have estimate one of the equations, for example where the dependant variable is the stock market index, and then do the above mentioned tests?
I tested both and I believe I found that the residuals are serially correlated. I then looked at the lag 1 and 4 cointegrating equations and again found that residuals are serially correlated. In addition, the cointegrating equations had many zeros in them and it was hard to make sense of them.

I then checked how many cointegrating equations there would be if the lag length is 6 (AIC found 7 lags for the VAR). Both test showed that there are 4 cointegrating equations. I estimated the VECM and then ordered it by variable. Copied the first equation where the dependent variable was the stock market and estimated the equation. I found none the cointegrating relations to be singificant plus the residuals were still serially correlated.

As a last option, I used the lag length that the LR test indicated (3 lags in VAR). I found that there are either one or four cointegration equations. I estimated a VECM with two lags and one cointegrating equation. The residuals were not correlated, no heteroskedasticity and normally distributed. However, my cointegrating equation coefficient is 0.008906 and I have read that it should be negative, but coefficient is significant. In addition, values in the cointegrating vector seem to be very high and I am not sure if this is good. I added this VECM to the attachments.

I hope somebody can help me. I don't know if the last model is good. Can the speed of adjustment value be positive as well? Have I understood correctly that when VAR indicates 4 lags I should use 3 in the cointegration test and estimation of VECM? When I am doing the model diagnostic should I do it straight from the VECM output page or estimate each equation separately and then do the model diagnostic? Maybe there are some other mistakes that I did. I would appreciate much if somebody, who understands EViews and the VECM more than I do, could help me. I am so confused and don't know where to go from here. :(