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.]

I think that's exactly right.  If you regress on the original series yt and there is a slope (well... a significant slope) then you have to first difference it.  Then, regress on the differenced series to get the coefficient of your AR(1) model.  To do an AR(2) you have to have a two variable regression... unfortunately the add-in in excel won't do this (because you have to do the regression simultaneously).  I found a program online that does multivariate regression.  If you use SAS at all that will do it for you too.  I wish we were given a program that went a long w/ this class and that procedures we needed to do.

If 0 < β < 1, the time series process may be autoregressive and stationary with a positive parameter. We do not necessarily take first differences; we examine the residuals for various ARIMA models, such as AR(1), AR(2), MA(1), ARMA(1,1), starting with the most reasonable model, usually AR(1), and testing other models if the simpler ones don’t fit.

If –1 < β < 0, the time series process may be autoregressive, stationary, and oscillatory with a negative parameter. This process is less common but not unusual. We examine the economic, financial, or actuarial relations to understand the negative parameter. The negative β may also stem from measurement error, rounding, or other random errors.

If β . 1, the time series may be a random walk. It is not stationary, but its first differences may be a stationary white noise process. This type of process is common in financial and actuarial work.

If β > 1, we graph the series on a logarithmic scale. If the series appears linear, we regress ln(y_t) on ln(y_t-1). If β . 1, the logarithm of the time series may be a random walk. This is very common in financial and actuarial work. Stock prices and inflation indices are examples.

If β . –1, or β # –1, the time series is unusual. You should re-check the data before going on.

Jacob: What if β = 0.90? Is that close enough to 1 that the time series is a random walk?

Rachel: That depends on the number of observations. We use tests of significance to see if we can reject the null hypothesis that β = 1.