Pembahasan Soal Ujian Profesi Aktuaris
Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
Mata Ujian |
: |
Metoda Statistika |
Periode Ujian |
: |
Mei 2017 |
Nomor Soal |
: |
29 |
SOAL
Diketahui suatu proses autoregressive-moving average \(ARMA\left( {1,1} \right)\) sebagai berikut:
\({y_t} = 0,8{y_{t – 1}} + 3 + {\varepsilon _t} – 0,2{\varepsilon _{t – 1}}\)
Hitunglah \({\rho _1}\) (dibulatkan 2 desimal).
- 0,62
- 0,66
- 0,70
- 0,74
- 0,78
Diketahui |
Diketahui suatu proses autoregressive-moving average \(ARMA\left( {1,1} \right)\) sebagai berikut:
\({y_t} = 0,8{y_{t – 1}} + 3 + {\varepsilon _t} – 0,2{\varepsilon _{t – 1}}\) |
Rumus yang digunakan |
\({\rho _1} = \frac{{\left( {1 – {\phi _1}{\theta _1}} \right)\left( {{\phi _1} – {\theta _1}} \right)}}{{1 + \theta _1^2 – 2{\phi _1}{\theta _1}}}\) |
Proses pengerjaan |
\({\rho _1} = \frac{{\left( {1 – {\phi _1}{\theta _1}} \right)\left( {{\phi _1} – {\theta _1}} \right)}}{{1 + \theta _1^2 – 2{\phi _1}{\theta _1}}}\)
\({\rho _1} = \frac{{\left( {1 – \left( {0.8} \right)\left( {0.2} \right)} \right)\left( {0.8 – 0.2} \right)}}{{1 + {{\left( {0.2} \right)}^2} – 2\left( {0.8} \right)\left( {0.2} \right)}}\)
\({\rho _1} = 0.7\) |
Jawaban |
C. 0,70 |