ARIMA_PARAM - Values of the Model's Parameters

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

Syntax

ARIMA_PARAM(X, Order, d, Mean, Sigma, Phi, Theta, Type, MaxIter)

X

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

Order

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

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

d

is the degree of the differencing (i.e., d).

Mean

is the ARMA model mean (i.e., mu). If missing, the mean is assumed to be zero.

Sigma

is the standard deviation value of the model's residuals/innovations.

Phi

are the parameters of the AR(p) component model (starting with the lowest lag).

Theta

are the parameters of the MA(q) component model (starting with the lowest lag).

Type

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

Order	Description
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

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. The integration order argument (d) must be a positive integer.
5. The long-run mean can take any value or may be omitted, in which case a zero value is assumed.
6. The residuals/innovations standard deviation (sigma) must be greater than zero.
7. 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 can be missing or an error code (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).
8. 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).
9. The function was added in version 1.63 SHAMROCK.

Files Examples

Related Links

• Wikipedia - Akaike's Information Criterion (AIC).
• Wikipedia - Autoregressive moving average model.

References

• Hamilton, J.D.; Time Series Analysis, Princeton University Press (1994), ISBN 0-691-04289-6.
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740.