Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Diberikan forecast error 4 langkah ke depan berdasarkan ARIMA model
\({e_T}\left( 4 \right) = 0,3{\varepsilon _{T + 4}} – 0,4{\varepsilon _{T + 3}} + 0,2{\varepsilon _{T + 2}} – 0,5{\varepsilon _{T + 1}}\)Diketahui pula, standar deviasi dari error, \({\sigma _\varepsilon } = 1,2\) Hitunglah variance dari forecast error tersebut:
- 0,6480
- 0,6911
- 0,7250
- 0,7776
- 0,7930
| Diketahui | Diberikan forecast error 4 langkah ke depan berdasarkan ARIMA model
\({e_T}\left( 4 \right) = 0,3{\varepsilon _{T + 4}} – 0,4{\varepsilon _{T + 3}} + 0,2{\varepsilon _{T + 2}} – 0,5{\varepsilon _{T + 1}}\)
Diketahui pula, standar deviasi dari error, \({\sigma _\varepsilon } = 1,2\) |
| 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 | \(Var\left[ {{e_T}\left( 4 \right)} \right] = \left( {{\psi _0}^2 + {\psi _1}^2 + {\psi _2}^2 + {\psi _3}^2} \right)\sigma _\varepsilon ^2\) \(Var\left[ {{e_T}\left( 4 \right)} \right] = \left[ {{{\left( {0.3} \right)}^2} + {{\left( { – 0.4} \right)}^2} + {{\left( {0.2} \right)}^2} + {{\left( { – 0.5} \right)}^2}} \right]{1.2^2}\) \(Var\left[ {{e_T}\left( 4 \right)} \right] = 0.7776\) |
| Jawaban | D. 0,7776 |