Basic Time Series Stats Question: Using MA(1) Results to Reproduce Predicted Values Given by Stata

[Adam Guerrero]

Hi All,

My goal is to use results from Stata's ARIMA command for an MA(1) model to reproduce predicted values, also given by Stata.

I have used the attached data to estimate an ARIMA MA(1) model using the following code (data are weekly paper towel sales):
Code:

use "t9-1 towel.dta", clear
rename y sales
generate time = _n
tsset time
arima sales, arima(0 1 1)
predict psales, y
predict pD_sales, xb
predict resids, residuals
generate D_sales = D.sales

The results from the ARIMA MA(1) model are (attached below, too):



My question is how to use the results to reproduce the predicted values for sales (psales) and/or the predicted values for the first differences of sales (pD_sales)?

The first four observations of the data are also attached:



As you can see, the predicted value for the first difference of sales for the 4th time period is .2535219.

How can I use Stata output to reproduce these results?

I thought that the value of the predicted first difference of the 4th observation should be equal to a constant plus the current error plus the MA(1) parameter times the previous error. For example,

.00577 + .8455773 + .3518248*.7137719 = 1.1025

I can see that this is close to the actual value of the first difference of sales equal to 1.099099.

I am teaching myself time series analysis, so please pardon my rudimentary question.

Again, I have attached the data, output of my ARIMA(0 1 1) model, and a list of the first 4 observations.

Cheers,
Adam

[Nick Cox]

You have asked this question more than once. Please be patient now. Sorry, but there is no rule that obliges anyone to answer.

[Adam Guerrero]

Thanks, Nick. I experienced some issues with my previous posts, even after working with the Sandbox, so I wanted to repost the question with the proper dialogue, code, attachments, etc. If I don't get a response, I will definitely not post this one again. Do you think this question is too stats oriented, or maybe too basic for this forum? Thanks so much.

Adam

[Nick Cox]

I see no problem with your post.

[Adam Guerrero]

Well, that definitely makes me feel better coming from you! I'll keep my fingers crossed for a response, but will likely enroll in Stata's NC time series course, too.

Adam