RiskARMA11

Description

RiskARMA11 generates a first-order autoregressive moving average (ARMA11) process with mean μ, volatility parameter σ,  autoregressive coefficient , moving average coefficient , value at time 0, and initial error term .

An ARMA11 is characterized by an ACF that decreases geometrically and a PACF that is similar to the PACF of an MA1 process.

Examples

RiskARMA11(100, 40, 0.8, -0.2, 490, 10) generates an ARMA11 process with mean , variance  , autoregressive coefficient 0.8, moving average coefficient -0.2, value 490 at time 0, and initial error term 10.

RiskARMA11(C10, C11, C12, C13, C14, C15) generates an ARMA11 process with parameters taken from cells C10 to C15.

Guidelines

is a necessary condition for stationarity.

Technical Details

Define

= a sample from a Normal(0,1) distribution

Then

The mean and variance are

and