What do yt and yt-1 stand for?
For starters, yt and yt-1 represent the values in the current period and 1 period ago respectively. As was the case with the AR model, we’re using the past values as a benchmark for future estimates.
What do ϵ t and ϵ t-1 stand for?
Similarly, ϵ t and ϵ t-1 are the error terms for the same two periods. The error term from the last period is used to help us correct our predictions. By knowing how far off we were in our last estimate, we can make a more accurate estimation this time.
What does c stand for?
As always, “c” is just a baseline constant factor. In simply means we can plug in any constant factor here. If the equation doesn’t have such a baseline, we just assume c=0.
What do ϕ1 and θ1 stand for?
The two remaining parameters are ϕ1 and θ1. The former, ϕ1, expresses on average what part of the value last period (yt-1) is relevant in explaining the current one. Similarly, the latter, θ1, represents the same for the past error term (ϵ t-1). Just like in previous models, these coefficients must range between -1 and 1 to prevent the coefficients from blowing up.
Of course, in more complex models, ϕi, and θiexpress the importance of the values and error terms for the “i-th” lag. For example, ϕ4, expresses what part of the value 4 periods ago is still relevant, while θ3describes what portion of the residual from 3 periods ago is important today.
Title
What Is an ARMA Model?
URL
https://365datascience.com/tutorials/time-series-analysis-tutorials/arma-model/
Summary
explains ARMA equation and its part
Key Points
yt = c + ϕ1 yt-1 + θ1 ϵ t-1 + ϵ t
What do yt and yt-1 stand for? For starters, yt and yt-1 represent the values in the current period and 1 period ago respectively. As was the case with the AR model, we’re using the past values as a benchmark for future estimates.
What do ϵ t and ϵ t-1 stand for? Similarly, ϵ t and ϵ t-1 are the error terms for the same two periods. The error term from the last period is used to help us correct our predictions. By knowing how far off we were in our last estimate, we can make a more accurate estimation this time.
What does c stand for? As always, “c” is just a baseline constant factor. In simply means we can plug in any constant factor here. If the equation doesn’t have such a baseline, we just assume c=0.
What do ϕ1 and θ1 stand for? The two remaining parameters are ϕ1 and θ1. The former, ϕ1, expresses on average what part of the value last period (yt-1) is relevant in explaining the current one. Similarly, the latter, θ1, represents the same for the past error term (ϵ t-1). Just like in previous models, these coefficients must range between -1 and 1 to prevent the coefficients from blowing up.
Of course, in more complex models, ϕi, and θiexpress the importance of the values and error terms for the “i-th” lag. For example, ϕ4, expresses what part of the value 4 periods ago is still relevant, while θ3describes what portion of the residual from 3 periods ago is important today.
Citation
“What Is an Arma Model?” 365 Data Science, 20 Oct. 2021, https://365datascience.com/tutorials/time-series-analysis-tutorials/arma-model/.
Repo link