ABSTRACT
Suppose a realization x1, x2, …, xn is observed. The problem of fitting an ARMA(p,q) model to the data is the problem of estimating
p q
, , , ,
, , ,
, .
φ φ φ θ θ θ
μ σ
… …
(7.1)
The estimation of p and q is called order identification, and this topic will be covered in detail in Chapter 8. In the current chapter, we assume that p and q are known, and techniques will be discussed for estimating the additional parameters in (7.1). An analysis of a time series using an ARMA model will typically first involve order identification followed by the estimation procedures to be discussed in this chapter. However, the dichotomy between the order identification and parameter estimation steps is not clear-cut since the order identification techniques usually involve some parameter estimation as a means of selecting the appropriate model orders. For now, we discuss parameter estimation assuming known p and q.
