ARMA - Defining an ARMA Model.

Returns a unique string to designate the specified ARMA model.

Syntax

ARMA (µ, σ, [φ], [θ])

µ
Optional. Is the ARMA model long-run mean (i.e., mu). If missing, the process mean is assumed to be zero.
σ
Required. Is the standard deviation value of the model's residuals/innovations.
[φ]
Optional. Are the parameters of the AR(p) component model: [φ1 , φ2 … φp] (starting with the lowest lag).
[θ]
Optional. Are the parameters of the MA(q) component model: [θ1, θ2 … θq] (starting with the lowest lag)

Remarks

  1. The underlying model is described here.
  2. The long-run mean can take any value or can be omitted, in which case a zero value is assumed.
  3. The residuals/innovations standard deviation (σ) must be greater than zero.
  4. For the input argument ([φ]):
    • The input argument is optional and can be omitted, in which case no AR component is included.
    • The order of the parameters starts with the lowest lag.
    • One or more parameters may have missing values or error codes (i.e., #NUM!, #VALUE!, etc.).
    • The order of the AR component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).
  5. For the input argument ([θ]):
    • The input argument is optional and can be omitted, in which case no MA component is included.
    • The order of the parameters starts with the lowest lag.
    • One or more values in the input argument can be missing or an error code (i.e., #NUM!,#VALUE!, etc.).
    • The order of the MA component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).

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