Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Metoda Statistika |
| Periode Ujian | : | Agustus 2023 |
| Nomor Soal | : | 15 |
SOAL
Diberikan model ARMA (1) dengan rata-rata 0 serta informasi berikut:
\(\rho_2 = 0{,}215 \; ; \; \rho_3 = -0{,}100 \; ; \; y_T = -0{,}431\)
Hitunglah nilai perkiraan (forecast) dari \(\hat{y}_{T+1}\)!
a. – 0,40
b. – 0,20
c. 0,00
d. 0,20
e. 0,40
| Diketahui | \(\rho_2 = 0{,}215 \; ; \; \rho_3 = -0{,}100 \; ; \; y_T = -0{,}431\) |
| Rumus yang digunakan | Formula, AR(1), - \(\rho_k = \phi_1^k\)
- \(\hat{y}_T(1) = \phi_1 y_T + \delta\)
- \(\mu = \dfrac{\delta}{1 – \phi_1}\)
- \(\phi_1 < 0\)
|
| Proses pengerjaan | - \(\rho_2 = \phi_1^2 = 0{,}215\)
\(\phi_1 = -\sqrt{0{,}215} = -0{,}4637\)- \(\mu = \dfrac{\delta}{1 – \phi_1} \rightarrow \mu = 0\)
\(\delta = 0\)- \(\hat{y}_{T+1} = \phi_1 y_T + \delta\)
\(\hat{y}_{T+1} = -0{,}4637 \cdot (-0{,}431) + 0\)
\(\hat{y}_{T+1} = 0{,}19985 \approx \mathbf{0{,}20}\) |
| Jawaban | d. 0,20 |
