ARMA_FIT - ARMA Model Fitted Values

Returns an array of cells for the in-sample model fitted values of the conditional mean, volatility, or residuals.

Syntax

ARMA_FIT(X, Order, Mean, sigma, phi, theta, Type)

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).

mean

is the ARMA model mean (i.e., mu).

sigma

is the standard deviation 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 type: (1 = Mean (default), 2 = Volatility, 3 = Raw Residuals, 4 = Standardized Residuals).

Order	Description
1	Fitted mean (default).
2	Fitted standard deviation or volatility.
3	Raw (non-standardized) residuals.
4	Standardized residuals.

Remarks

1. The underlying model is described here.
2. The Log-Likelihood Function (LLF) is described here.
3. The time series is homogeneous or equally spaced.
4. The time series may include missing values (e.g., #N/A) at either end.
5. The integration order argument (d) must be a positive integer.
6. The long-run mean can take any value or may be omitted, in which case a zero value is assumed.
7. The residuals/innovations standard deviation (sigma) must be greater than zero.
8. For the input argument (phi):
   • The input argument is optional and can be omitted, so 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 last value solely determines the order of the AR component model in the array with a numeric value (vs. missing or error).
9. For the input argument (theta):
   • The input argument is optional and can be omitted, so 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 last value solely determines the order of the MA component model in the array with a numeric value (vs. missing or error).
10. The function was added in version 1.63 SHAMROCK.

Files Examples

Related Links

• Wikipedia - Likelihood function.
• Wikipedia - Likelihood principle.
• 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 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.