I'm analysing possible interdependencies between annual returns on art objects and returns on traditional investments (S&P500, commodities etc). For most variables TS length is around 20 years. For example, I have two variables - art index(var_y) and S&P500 index (var_x)
As far I understand from STATA help, STATA list, literature and other forums I need to do following:
for variables at levels find the optimal lag length
(b) Conduct the ADF test for var_x and var_y in levels with number of lags found in (a)
Conduct the ADF test for var_x and var_yin in differencies with number of lags found in (a)
If variable is non-stationary (contains a unit root) at level and stationary (doesn't contain a unit root) at first differencies then we have I(1).
(c) If both variables are I(1), then conduct Johansen tests with lags obtained at (a) minus 1 (due to reparametrization) Use VECM model with lags as in (c)
(d) if variables are stationary at levels, use VAR model with lags as in (a) and test for the Granger causality
I have two questions:
Question 1. Is this this approach generally correct?
Question 2. For example -varsoc- suggests that I need to use 3 lags. ADF shows that it is non-stationary for
dfuller var_y, lags(3)
and stationary for
dfuller d.var_y, lags(3)
Does it mean that we have a I(1) here? I'm a bit condused because here: http://www.statalist.org/forums/forum/general-stata-discussion/general/1291442-determining-the-order-of-integration it is said that "if the variable is not stationary at first lag and become stationary at first difference, the variable is integrated of order 1". So can it be I(1) for lag length greater than 1?