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IMSL_RANDOM_ARMA

# IMSL_RANDOM_ARMA

The IMSL_RANDOM_ARMA function generates a time series from a specific IMSL_ARMA model.

The IMSL_RANDOM_ARMA function simulates an IMSL_ARMA(p, q) process, {Wt}, for t = 1, 2, ..., n. The model is:

Let Âµ be the mean of the time series {Wt}. The overall constant Î¸0 (Const) is:

Time series whose innovations have a nonnormal distribution may be simulated by providing the appropriate innovations in Input_Noise and start values in W_Init.

The time series is generated according to the following model:

X(i) = Const + ar(0) * X(i â Ar_Lags(0)) + ... + ar(p â 1) * X(i â Ar_Lags(p â 1)) + A(I) â ma(0) * A(i â Ma_Lags(0)) â ... â ma(q â 1) * A(i â Ma_Lags(q â 1))

where the constant is related to the mean of the series:

W

as follows:

Const = W Â· (1 - ar(0) - ... + (-ar(q - 1)))

and where:

X(t) = W(t), t = 0, 1, ..., n â 1

and:

W(t) = W_Init(t + p), t = âp, âp + 1, ..., â2, â1

and A is either Input_Noise (if Input_Noise is used) or Output_Noise (otherwise).

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