ARMA - Defining an ARMA model

Mohamad

December 08, 2016 20:25

Returns a unique string to designate the specified ARMA model.

Syntax

ARMA(mean, sigma, phi, theta)

mean: is the ARMA model long-run mean (i.e. mu). If missing, mean is assumed to be zero.
sigma: is the standard deviation of the model's raw residuals (aka innovations or shocks).
phi: are the parameters of the auto-regressive (i.e AR) component model (starting with the lowest lag).
theta: are the parameters of the moving-average (i.e. MA) component model (starting with the lowest lag).

The underlying model is described here.
The long-run mean can take any value or can be omitted, in which case a zero value is assumed.
The residuals/innovations standard deviation (sigma) must be greater than zero.
For the input argument (phi):
- 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).
For the input argument (theta):
- 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).

D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906
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Box, Jenkins and Reisel; Time Series Analysis: Forecasting and Control; John Wiley & SONS.; 4th edition(Jun 30, 2008), ISBN: 470272848
Walter Enders; Applied Econometric Time Series; Wiley; 4th edition(Nov 03, 2014), ISBN: 1118808568