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# Timeseries interpretation

Fri 17 Mar, 2017 11:11 am
Hello, imagine if one were to use time-series analysis on a sample from the years 2000-2008 with 1 dependent variable and lets say 3 independent variables and end up with a model with estimated parameters and standard errors etc.

(Yt= B0 + B1X1t + B2X2t + B3X3t + et, and could introduce lagged variables too) Let's say the dependent variable is GDP, and the three independent variables are inflation, the price of oil and the unemployment rate. (but as previously stated, the variables could be anything, really)

After this you repeat the process for another time sample (with the same variables) such as 2008 to 2014. The reasoning behind this split-up could be to test if the relationships between the variables have changed after some event that happened in 2008, such as a financial crisis. The two separate models (1 for each time interval, 2000-2008 and 2008-2014) give you different estimates of beta coefficients and their standard errors.

How does one test if there has been a significant change in the relationship between the variables after 2008? In the bivariate case, one can hypothesis-test if the difference in true population means are equal to zero, by using the point estimates and the standard error estimates of both variables, is this still viable in the time series situation I've described? If one were to test if the parameters have changed, should I test variable by variable or try some joint hypothesis by using the F-statistic?

Thanks in advance!
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