ARMA_PARAM - Values of the Model's Parameters

Returns an array of cells for the quick guess, optimal (calibrated), or standard errors of the values of the model's parameters.

Syntax

ARMA_PARAM ([x], order, µ, σ, [φ], [θ], return, maxiter)

[X]

Required. Is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)).

Order

Optional. Is the time order in the data series (i.e., the first data point's corresponding date (earliest date = 1 (default), latest date = 0)).

Value	Order
1	Ascending (the first data point corresponds to the earliest date) (default).
0	Descending (the first data point corresponds to the latest date).

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).

Return

Optional. Is an integer switch to select the output array: (1 = Quick Guess (default), 2 = Calibrated, 3 = Std. Errors).

Value	Return
1	Quick guess (non-optimal) of parameters' values (default).
2	Calibrated (optimal) values for the model's parameters.
3	Standard error of the parameters' values.

MaxIter

Optional. Is the maximum number of iterations used to calibrate the model. If missing, the default maximum of 100 is assumed.

Remarks

1. The underlying model is described here.
2. The time series is homogeneous or equally spaced.
3. The time series may include missing values (e.g., #N/A) at either end.
4. ARMA_PARAM returns an array for the values (or errors) of the model's parameters in the following order:
1. $\mu$.
2. $\phi_1,\phi_2,...,\phi_p$.
3. $\theta_1,\theta_2,...,\theta_q$.
4. $\sigma$.
5. The function was added in version 1.63 SHAMROCK.

Files Examples

Related Links

• Wikipedia - Autoregressive moving average model.

References

• D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906.
• James Douglas Hamilton; Time Series Analysis, Princeton University Press; 1st edition(Jan 11, 1994), ISBN: 691042896.
• Tsay, Ruey S.; Analysis of Financial Time Series, John Wiley & SONS; 2nd edition(Aug 30, 2005), ISBN: 0-471-690740.
• Box, Jenkins and Reinsel; 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.