Experiment62Six
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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.
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pas
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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?]
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harusari
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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?
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dclevel
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page 202 has an example of a non-stationary ARIMA(1,1,1) process
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Luke Grady
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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.]
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RayDHIII
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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): deltaYt = 5 + (phi)deltaYt-1 + et-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
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AJB1011
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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.
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benjaminttp
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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?
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Luke Grady
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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).]
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Woody
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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.]
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