Exercise

# ARMA (p, q) model

An *auto-regressive moving average* model (`ARMA(p, q)`

) combines the autoregression (`AR(p)`

) and moving average (`MA(q)`

) models into one. The current value of the simulated vector depends both on previous values of the same vector as well as previous values of the noise vector.

Complete the function definition of `arma()`

.

Instructions

**100 XP**

- Define an integer variable,
`start`

, equal to the maximum of`p`

and`q`

, plus one.*Recall that*`max()`

is in the`std`

namespace. - Inside the outer for loop, define a
`double`

variable,`value`

, as`mu`

plus the`i`

th noise value. - Inside the first inner for loop, increase
`value`

by the`j`

th element of`theta`

times the "`i`

minus`j`

minus`1`

"th element of`eps`

. - Inside the second inner for loop, increase
`value`

by the`j`

th element of`phi`

times the "i minus j minus 1"th element of`x`

.