<p>I'm trying to understand this subject and  I'm stuck in a question found in a book. <a href="https://i.sstatic.net/VMmdX.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/VMmdX.png" alt="enter image description here" /></a></p>
<p>I understand white noise characterization, but I'm having some problems with this... maybe it's too much theory? I kind of get lost when I try to prove that also the new variable <span class="math-container">$Y$</span> is MA, and don't get me started on solving for the parameters. Maybe some hints on how to proceed or explain the steps I need to follow?</p>
<p>Edit 1:</p>
<p>I've posted the question on Cross Validated. Also the book you suggested in the comments,  Hamilton, <em>Time Series Analysis</em>,  is one of the many I'm using in my class and you were right, the solution is right there, just written in a different way. I guess that at page 102 <span class="math-container">$X_t$</span> in the book is my <span class="math-container">$u_t$</span> and <span class="math-container">$v_t$</span> in the book is my <span class="math-container">$w_t$</span>, whereas <span class="math-container">$Y_t$</span> is the same in both cases. Thanks for the answers!</p>

CC BY-SA 4.0
2023-02-27T22:00:13.537Z
Hi: just write out the MA(1) term explicitly. This will allow you to combine the $w_t$ term with the pure noise term in the MA(1) to create a new noise term. But overall process is still MA(1). I'm in a rush so, if this isn't clear, hopefully someone has the time to write it out for you. If not, I'll write it out later tonight when I get back.
mark leeds
CC BY-SA 4.0
2023-02-28T07:05:02.490Z
Do you have or have access to  Hamilton's "Time Series Analysis" text.  The proof of your statement is on page 102 in the section called sums of ARMA processes.
mark leeds
CC BY-SA 4.0
2023-02-28T07:50:04.353Z
This is not about economics but about a statistical time series model, so I think it would be a better fit or [Cross Validated Stack Exchange](https://stats.stackexchange.com/questions).
Richard Hardy
<econometrics><time-series><theory>
Time series question from book (ma)
Blipo
# Time series question from book (ma)

(Asked by: username_0 on 2023-02-27)

I'm trying to understand this subject and I'm stuck in a question found in a book. [![enter image description here](https://i.sstatic.net/VMmdX.png)](https://i.sstatic.net/VMmdX.png)

I understand white noise characterization, but I'm having some problems with this... maybe it's too much theory? I kind of get lost when I try to prove that also the new variable $Y$ is MA, and don't get me started on solving for the parameters. Maybe some hints on how to proceed or explain the steps I need to follow?

Edit 1:

I've posted the question on Cross Validated. Also the book you suggested in the comments, Hamilton, *Time Series Analysis*, is one of the many I'm using in my class and you were right, the solution is right there, just written in a different way. I guess that at page 102 $X\_t$ in the book is my $u\_t$ and $v\_t$ in the book is my $w\_t$, whereas $Y\_t$ is the same in both cases. Thanks for the answers!

**Tags:** econometrics, time-series, theory

> **Comments:**
> **username_1**: Hi: just write out the MA(1) term explicitly. This will allow you to combine the $w_t$ term with the pure noise term in the MA(1) to create a new noise term. But overall process is still MA(1). I'm in a rush so, if this isn't clear, hopefully someone has the time to write it out for you. If not, I'll write it out later tonight when I get back.  
> **username_1**: Do you have or have access to  Hamilton's "Time Series Analysis" text.  The proof of your statement is on page 102 in the section called sums of ARMA processes.  
> **username_2**: This is not about economics but about a statistical time series model, so I think it would be a better fit or [Cross Validated Stack Exchange](https://stats.stackexchange.com/questions).  

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## 0 answers

