<p>I'm having difficulty expressing the following process in its most reduced form. Every time I try to simulate it with the arima.sim function, I end up with a non-stationary AR part that cannot be simulated.</p>
<p>The process is part of a school project where it says :</p>
<blockquote>
<p>Simulate under <span class="math-container">$R$</span>, for <span class="math-container">$n = 500$</span>, the process</p>
<p><span class="math-container">$(1 - B^{52})(1 - 2B + B^2)(1 - 2B)X_t = \varepsilon_t - \varepsilon_{t-1}, \quad t = 1, \ldots, n,$</span></p>
<p>ensuring to express it in its most reduced form, under the assumption
that the residuals are i.i.d. Gaussian <span class="math-container">$N(0,1)$</span>.</p>
</blockquote>

CC BY-SA 4.0
2024-01-24T13:42:01.137Z
Hi! Can you please explain the notation? Is $B$ a lag operator, or is it something else? What does $-> \epsilon_{t-1}$ mean?
Giskard
CC BY-SA 4.0
2024-01-24T13:53:36.860Z
Hi, $B$ is the lag/backshift operator. $-> \varepsilon_{t-1}$ was a blocknote typo, sorry.
NoNameBoyy
CC BY-SA 4.0
2024-01-24T14:25:48.807Z
Your process contains multiple unit roots, so you may need to simulate it manually (without use of  `arima.sim`).
Richard Hardy
<econometrics><mathematical-economics><statistics><time-series>
Help with Simulating a Time Series Process in R
NoNameBoyy
# Help with Simulating a Time Series Process in R

(Asked by: username_0 on 2024-01-24)

I'm having difficulty expressing the following process in its most reduced form. Every time I try to simulate it with the arima.sim function, I end up with a non-stationary AR part that cannot be simulated.

The process is part of a school project where it says :

> Simulate under $R$, for $n = 500$, the process
>
> $(1 - B^{52})(1 - 2B + B^2)(1 - 2B)X\_t = \varepsilon\_t - \varepsilon\_{t-1}, \quad t = 1, \ldots, n,$
>
> ensuring to express it in its most reduced form, under the assumption
> that the residuals are i.i.d. Gaussian $N(0,1)$.

**Tags:** econometrics, mathematical-economics, statistics, time-series

> **Comments:**
> **username_1**: Hi! Can you please explain the notation? Is $B$ a lag operator, or is it something else? What does $-> \epsilon_{t-1}$ mean?  
> **username_0**: Hi, $B$ is the lag/backshift operator. $-> \varepsilon_{t-1}$ was a blocknote typo, sorry.  
> **username_2**: Your process contains multiple unit roots, so you may need to simulate it manually (without use of  `arima.sim`).  

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## 0 answers

