ARMA_SIM - Simulated values of an ARMA Model

X is the univariate time series for the latest observation (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)).

mean is the ARMA model long-run 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).

T is the simulation time/horizon (expressed in terms of steps beyond end of the time series).

seed is an unsigned integer for setting up the random number generator(s).

1. The underlying model is described here.
2. The Log-Likelihood Function (LLF) is described here.
3. ARMA_SIM returns an array of one simulation path starting from the end of the input data.
4. The input data argument (i.e. latest observations) is optional. If omitted, an array of zeroes is assumed.
5. The time series is homogeneous or equally spaced.
6. The time series may include missing values (e.g. #N/A) at either end.
7. The long-run mean can take any value or be omitted, in which case a zero value is assumed.
8. The residuals/innovations standard deviation (sigma) must be greater than zero.
9. 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 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).
10. 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).
11. 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