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I have three log-transformed time series variables, which are: I(1) and not cointegrated. I read in a lecture slide that I can rethink my model by adding an LDV. This solves my autocorrelation problem (I add LDV to solve for the autocorrelation), but the effect of external regressor drops significantly. I am trying out these combinations to see how they vary:

Y(t) = X_1(t) + error 
Y(t) = X_1 (t) + X_1 (t-1) + Y (t-1) + error
Y(t) = X_1 (t-4) + X_2 (t) + error
Y(t) = X_1 (t-4) + X_2 (t)+ Y (t-1) + error (I did a sequential test to identify the lag oder of 4 for the variable X_1)

For equation (2) I find that the sign of my coefficient change and for equation (4) the coefficient drops significantly for both variables when compared to equation 3.

I went through this question, which partly answers my question of using LDV in my model, but I wanted to understand why the sign changes for equation 2.

I have moderate knowledge in statistics so please bare with me if the question does not make sense.

modelx1 = dynlm(y~x1)
            Estimate Std. Error  t value Pr(>|t|)
(Intercept)   1.8868     0.0306  61.6351        0
x1           -0.3724     0.0091 -41.0770        0

modelx1.ar1 = dynlm(y~ L(y, 1)+ L (x1, 0:1))


         Estimate Std. Error  t value Pr(>|t|)



(Intercept)    0.17596    0.15926  1.10489  0.27581
L(y, 1)     0.91166    0.09068 10.05375  0.00000
L(x1, 0:1)0 -0.41712    0.14231 -2.93118  0.00556
L(x1, 0:1)1  0.38155    0.16092  2.37113  0.02264

ACF plot for the residual for modelx1

ACF plot for the residual for modelx1.ar1 enter image description here

grain
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  • For equation (2) I find that the sign of my coefficient change and for equation (3) the coefficient drops significantly.---How so? Can you show what you have done so far? May help answerers provide an accurate answer for your question. – Shawn Hemelstrand Dec 18 '23 at 13:34
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    @ShawnHemelstrand I have added the results and acf plots - for the third equation I need to mention that the drop in the coefficient is after i add LDV so I should have one more equation without an LDV. – grain Dec 18 '23 at 13:47
  • Thanks for adding that. I'm not experienced with time-series models but perhaps someone else here may be able to assist with your question. – Shawn Hemelstrand Dec 18 '23 at 13:48
  • @ShawnHemelstrand thank you for the response! :) – grain Dec 18 '23 at 13:59

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