Pembahasan Soal Ujian Profesi Aktuaris
Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
Mata Ujian |
: |
Metoda Statistika |
Periode Ujian |
: |
Mei 2018 |
Nomor Soal |
: |
30 |
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 |