Should I be trying to replicate the NEAS results?

[NEAS: This is an independent student project. The NEAS postings are suggestions to get you started. You can construct an ARIMA model, compare two or more models for a given era, compare two or three eras by type of model of by model parameters, examine seasonality, test out-of-sample forecasts, and many other items.]

You are fitting an equation of the form yt = Ayt-1 +B.

[ y_t = A × y_t-1 + B ]

Performing a regression gives least-squares estimates of A and B. This is really just an AR(1) model, but if A >1, it is not stationary (random walk) and you need to first difference. What they are doing in their example is showing that the series have an upward linear trend and so needs to be differenced.

[NEAS:

Jacob: What if A = 1?

Rachel: If A = 1 and B = 0, the current value is the one period forecast. The process is not stationary and does not have a mean. The mean is B / (1 – A), which is not defined if A = 1.]