I have four variables (Y, X1, X2, X3). The original Y and original X1 both have positive trends and have a Pearson Correlation 0.845 (significantly positive correlation). Based on theories, the hypothesized model is Y= X1 + X2 + X3. Then I first log the four variables, and run an ARIMA (1,1,1) on the four variables, using the first difference.In the output of ARIMA (1,1,1), log Y= -.052 log X1+ ....... The relationship between Y and X1 became "negative (-.052)".
(1) Is this normal or ok? What is wrong? How to fix this? (The initial correlation between Y and X1 was positive 0.845. Now it becomes -.052.)
(2)Can I interpret that the relationship between X1 and Y is: One percent increase in X is associated with .052 percent "decrease" in Y. Is this the correct way to interpret ARIMA output?