As stated, the first difference is a AR(1) process. But we can't use any of the AR(1) formulas on page 193, because we have a mean of 0 and those formulas only work for nonzero means.

Is this statement correct? I'm trying to figure out why equation 9.3.6 can't be used to solve part C.

Also, I had the same problem as pas (when using Chrome, I wasn't able to download the pdfs). But I re-opened this page in IE and was able to download the pdfs.

The PDF downloads for this homework assignment don't work for me. My browser is giving me the error "duplicate headers received from server."

[NEAS: The PDF files work in our browser and have been downloaded 606 times. Can any one else verify if there is a problem with these files?]

I did the reading but can't get started with the homework. The intuitive process NEAS sketched out doesn't make sense either. I think I'm getting confused when notations are written out like in the homework assignment. Can someone please clarify how to go about A?

page 202 has an example of a non-stationary ARIMA(1,1,1) process

So is that what the d means in the ARIMA(p,d,q)? Does that just mean that the d-th difference of the time series is an ARMA(p,q) process?

Also, is a second difference the difference between Y_t and Y_{t-2}?

[NEAS: No, the second difference is the first difference of the first differences.]

AJB, pages 96-97 explain your dilema here.  Also, the AR(1) process is the first difference of the ARIMA(1,1,0) process, so that

ARIMA(1,1,0): unknown, and AR(1): deltaY_t = 5 + (phi)deltaY_t-1 + e_t-1.  Where the 5 is accommidating for a nonzero constant mean by theta = mu(1 - phi), also explained on page 97.

Part B wants to know the AR(1) one period ahead forecast, which is the ARIMA(1,1,0) one period ahead forecast (given) less the ARIMA(1,1,0) actual (given).

RDH

Can someone clarify how the first difference was derived? I think I'm getting confused with the subscripts.

It's given that the first difference is AR(1) --> Yt = 5 + φΔΥt-1 + et-1

Here's how I began to derive the first difference:
ΔΥt = Yt – Yt-1
ΔΥt = φΥt-1 + et – θet-1 – [φΥt-2 + et-1 – θet-2]


Also, for Part B: I believe the formula being used is 9.3.26 --> Y_hat(L) = Yt + (θ-zero)*L
Does "L" = 0 in this case, then? That way Y41 = Y40.

The first differences are an AR(1) model: Δyt = 5 + φ1 Δyt-1 + εt-1

why the last term is et-1 but not et?

So basically, the ARIMA(1,1,0) could have been any type of process - we don't care about what type of process it is because all we really know about is the type of process the first difference is. Is that correct?

[NEAS: An ARIMA(1,1,0) process is the integration (summation) of an AR(1) process. If the first difference is AR(1), the process is ARIMA(1,1,0).]

For forecasting, why don't you use equation 9.3.6 Δyt = 5 + φ1 [Δyt-1 - 5] .

Step 3 will be 0 = 5+ φ1 [10 - 5], φ1 = -1, not .5???

[NEAS: 5 is the constant term (theta-0), not the mean.]