Calculates the out-of-sample simulated values.
Syntax
ARIMA_SIM(X, Order, d, mean, sigma, phi, theta, T, seed)
- 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).
- 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).
Remarks
- The underlying model is described here.
- The Log-Likelihood Function (LLF) is described here.
- ARMA_SIM returns an array of one simulation path starting from the end of the input data.
- The input data argument (i.e. latest observations) is optional. If omitted, an array of zeroes is assumed.
- The time series is homogeneous or equally spaced.
- The time series may include missing values (e.g. #N/A) at either end.
- 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).
- 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).
- The function was added in version 1.63 SHAMROCK.
Files Examples
Related Links
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
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