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 |
