PsiAPARCH11(mean,volatility,delta,gamma, err_coef,ar_coef,val0,stdev0)

where a1 ≥ 0, b1 ≥ 0, at least one of a1 or b1 must be positive, ω > 0  and

-1 < γ < 1

PsiAPARCH11 generates an asymmetric, power, generalized first order autoregressive conditional heteroskedasticity time series with mean mean, volatility volatility, parameters delta and gamma, error coefficient err_coef, autoregressive coefficient ar_coef, value at time 0 val0 and initial standard deviation stdev0. 

PsiARCH1 and PsiGARCH11 are special cases of this time series. 

For more information, see the Analytic Solver Reference Guide downloadable from Analytic Solver by clicking Help -- User Guides -- Analytic Solver Reference Guide.