Can anyone provide a simple representation of what first differencing does to a 1 variable AR model?
Yes, it takes away the tendency of a time series. i mean if you have an upward curve or a downward curve when you graph the data, differenciating the time series “eliminates” this tendency. Particularly if you think about seasonality ( up and down, up and down…) , doing this (differencing) will eliminate this tendency and then it will help you to accomplish with the assumptions the AR model needs to work.
Regards,
Jorge
What’s the math behind this logic?
After a time series has been stationarized by differencing, the next step in fitting an ARIMA model is to determine whether AR or MA terms are needed to correct any autocorrelation that remains in the differenced series.
From what I understand, the math of first differencing a non-covariance stationary model is to change the model into using a variable of the CHANGE in x from time t-1 to t, rather than using an absolute value of x at time t.
Original random walk AR(1) model:
xt = b0 + b1(xt-1) + error term
Since b0 = 0 and b1 = 1, the equation is basically:
xt = xt-1 + error term
FIrst differencing turns this model into an equation in terms of the CHANGE of the value x from time t-1 to time t, rather than in terms of the absulote value of x at time t:
xt - xt-1 = b0 + b1(xt-1 - xt-2) + error term