Can NEAS can explain this problem?

[NEAS: Here is the outline of the solution. Many exam problems are similar. Once you get the intuition, the problems are straight-forward.

Hi Tom,

First off, ARIMA(1,1,0) and ARI(1,1) are exactly the same process. Either notation should be acceptable to write in the course of a problem. The ARIMA(1,1,0) process can indeed be written in terms of a nonstationary AR(2) process. To achieve stationary, you would need to take first differences of the ARIMA(1,1,0) process which would result in an AR(1) process. The concept of first differences came up in an earlier module. I've found that writing up the explicit equation for both processes helps here in seeing how to derive the one and two period ahead forecasts.

I am confused as to the relationship between a non-stationary ARIMA(1,1,0) [integrated autoregressive moving average (p,d,q)] and an ARMA.

1st off this question says the process is an ARIMA(1,1,0).  Is the zero necessary.  Isn't this just an ARI(1,1)?

[NEAS: Correct; ARI is an abbreviation for an ARIMA process with q = 0]

An ARIMA(p,d,q) process can be rewritten as am ARMA(p+1,q) process (Cryer Chan page 92).

[NEAS: No, and Cryer Chan do not say this. The first differences of an ARIMA process with d = 1 are an ARMA process of the same order.]

So how can this non-stationary ARIMA(1,1,0) be put into terms of an AR(1)?  Shouldn't it be an AR(2)?

[NEAS: The first differences of ARIMA(1,1,0) are an AR(1) process.]

Also, no where in the Module 15 reading does it mention 1st differences.  I have come across modules like this before where the reading does not match up with the homework assignments very well.  I came across this with the QQ plots in module 14.  I am growing frustrated with doing readings where the corresponding homeworks come out of left field.

[NEAS: Cryer Chan discuss first differences throughout their text, beginning in chapter 5.]

 

 

Tom McNamara III