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)).

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

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).

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