Sets up the necessary backend for the MA(Q) process.
MA(theta = NULL, sigma2 = 1)A double value for the parameter \(\theta\) (see Note for details).
A double value for the variance parameter \(\sigma ^2\) (see Note for details).
An S3 object with called ts.model with the following structure:
Used in summary: "MA-1","MA-2", ..., "MA-Q", "SIGMA2"
\(\theta_1\), \(\theta_2\), ..., \(\theta_q\), \(\sigma^2\)
Number of parameters
"MA"
String containing simplified model
Depth of parameters e.g. list(q,1)
Guess starting values? TRUE or FALSE (e.g. specified value)
We consider the following model: $$X_t = \sum_{j = 1}^q \theta_j \varepsilon_{t-1} + \varepsilon_t$$, where \(\varepsilon_t\) is iid from a zero mean normal distribution with variance \(\sigma^2\).
MA(1) # One theta
MA(2) # Two thetas!
MA(theta=.32, sigma=1.3) # 1 theta with a specific value.
MA(theta=c(.3,.5), sigma=.3) # 2 thetas with specific values.