I have similar questions as the one asked in these posts: https://stackoverflow.com/questions/47083890/fir-filter-length-is-the-intercept-included-as-a-coefficient-matlab/47085339?noredirect=1#comment81124362_47085339 and Terminologies - lags, order in time series model
But the answer is quite different from the one in books and other online resources such as this tutorial: https://onlinecourses.science.psu.edu/stat510/node/47
If the time series model is of order 2, then according to the answers to the earlier question, there should be 3 coefficients. But, the tutorial link says differently. In the link an AR(1) model has 1 coefficient.
In a research article titled, "X. Xu and J. Guo, "A Fast System Identification Method Based on Minimum Phase Space Volume," 2012 International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery, Sanya, 2012, pp. 523-526." the Authors have doen system identification of AR(2) model. There they have used 2 coefficients to express the model.
Based on my understanding, the number of coefficients that a system has is known as the length, $L$ and the order is $q=L-1$.
I want help to confirm what is the correct representation and terminology. In general for AR and MA models,
Confusion 1) For an AR(1) system of order $q=1$, should there be 2 coefficients or 1 coefficient? Same thing for MA(1)
According to the online course link for AR(1), there is only 1 coefficient.
Confusion 2) What is correct? Considering an AR(2) model having coefficients
[a1,a2,a3] then can I express the model as:
x[t] = a1*x[t] + a2*x[t-1] + a3*x[t-2]+ e[t] and for MA(2) of order 2 as
x[t] = a1*e[t] + a2*e[t-1] + a3*e[t-2]
e[t] is the excitation input driving signal.
What is the correct method? Please help, I am extremely confused.