Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Informasi di bawah ini adalah tentang model ARIMA:
mean = 0
\({\psi _1}\) = 1,58
\({\psi _2}\) = -1,22
\({\psi _3}\) = 0,348
\({\psi _4}\) = -0,032
\({\sigma ^2}\) = 7
Hitunglah deviasi standar atas kesalahan perkiraan tiga langkah ke depan (forecast error three steps ahead).
- 3,29
- 4,25
- 4,86
- 5,91
- 6,62
| Diketahui | mean = 0 \({\psi _1}\) = 1,58 \({\psi _2}\) = -1,22 \({\psi _3}\) = 0,348 \({\psi _4}\) = -0,032 \({\sigma ^2}\) = 7 |
| Rumus yang digunakan | \(Var\left[ {{e_T}\left( l \right)} \right] = \left( {{\psi _0}^2 + {\psi _1}^2 + \ldots + {\psi _{l – 1}}^2} \right)\sigma _\varepsilon ^2\) |
| Proses pengerjaan | Karena model ARIMA tersebut memiliki mean = 0 maka untuk \({\psi _0} = 1\) sehingga \(Var\left[ {{e_T}\left( 3 \right)} \right] = \left( {{\psi _0}^2 + {\psi _1}^2 + {\psi _2}^2} \right)\sigma _\varepsilon ^2\) \(= \left( {{1^2} + {{1,58}^2} + {{\left( { – 1,22} \right)}^2}} \right) \cdot 7\) \(= 34,8936\) Deviasi Standar \(= \sqrt {Var\left[ {{e_T}\left( 3 \right)} \right]} \) \(= \sqrt {34,8936} \) \(= 5,90708\) |
| Jawaban | d. 5,91 |