BGR,
The model that I considered was
Yt = a0 + a1 * Yt-1 + a2 * Yt-2 + ... + an * Yt-n + b0 * Rt + b1 * Rt-1 + ... + bm * Rt-m
where Y is the S&P 500 and R is the outstanding RPs. So the model allows lag points for Y (such as Yt-1, etc., and is therefore autoregressive) as well as the crosscorrelation terms for R (Rt, Rt-1, etc.). I used a statespace method to consider all of the possibilities for n (order of the Ar series for Y) and m (number of signifcant lags in R).
The Durbin-Watson test was significant for Y, so I assumed an autoregressive model. The model was significant in AR(1) (and, I found later, MA(1)), and an ARIMA(1,1,1) fits the series Y pretty well (AIC = -1250). But, as a transfer function, the series R was not significant, so the negative coefficient, while amusing, really doesn't mean much.
Let me know if I should clarify. |
