Definition of a Sinusoidal (SIN) Process

SIN(alpha2 = 9e-04, beta = 0.06, U = NULL)

Arguments

alpha2: A double value for the squared amplitude parameter $\alpha^2$ (see Note for details).
beta: A double value for the angular frequency parameter $\beta$ (see Note for details).
U: A double value for the phase parameter $U$ (see Note for details).

Value

An S3 object containing the specified ts.model with the following structure:

process.desc: Used in summary: "ALPHA2","BETA"
theta: Parameter vector including $\alpha^2$, $\beta$
plength: Number of parameters
print: String containing simplified model
desc: "SIN"
obj.desc: Depth of Parameters e.g. list(1,1)
starting: Find starting values? TRUE or FALSE (e.g. specified value)

Note

We consider the following sinusoidal process : $$X_t = \alpha \sin(\beta t + U)$$, where $U \sim \mathcal{U}(0, 2\pi)$ and $\beta \in (0, \frac{\pi}{2})$

Author

Lionel Voirol

Examples

SIN()
SIN(alpha2 = .5, beta = .05)