Pembahasan Ujian PAI: A50 – No. 22 – Mei 2018

1. \({\hat y_{T + 1}} = {y_T}\)
2. \({\hat y_{T + 2}} = {y_T}\)
3. Error variance adalah \(\frac{{\sigma _\varepsilon ^2}}{2}\) untuk dua periode forecast

• Model: \({y_t} = {y_{t – 1}} + {\varepsilon _t}\)
• Peramalan:
  \({{\hat y}_{T + 1}} = E\left( {\left. {{y_{T + 1}}} \right|{y_T}, \ldots ,{y_1}} \right)\)
  \({{\hat y}_{T + 1}} = {y_T} + E\left( {{\varepsilon _{T + 1}}} \right) = {y_T}\)
  \({{\hat y}_{T + 2}} = E\left( {\left. {{y_{T + 2}}} \right|{y_T}, \ldots ,{y_1}} \right) = E\left( {{y_{T + 1}} + {\varepsilon _{T + 2}}} \right)\)
  \({{\hat y}_{T + 2}} = E\left( {{y_T} + {\varepsilon _{T + 1}} + {\varepsilon _{T + 2}}} \right) = {y_T}\)
  Untuk peramalan l periode juga mengahsilkan \({\hat y_{T + l}} = {y_T}\)
• Standard error:
  \({e_1} = {y_{T + 1}} – {{\hat y}_{T + 1}}\)
  \({e_1} = {y_T} + {\varepsilon _{T + 1}} – {y_T} = {\varepsilon _{T + 1}}\)
  \({e_2} = {y_{T + 2}} – {{\hat y}_{T + 2}}\)
  \({e_2} = {y_T} + {\varepsilon _{T + 1}} + {\varepsilon _{T + 2}} – {y_T} = {\varepsilon _{T + 1}} + {\varepsilon _{T + 2}}\)
  Seterusnya sampai standard error ke- l

Sumber: Econometric Models and Economic Forecasts (Fourth Edition), 1998, by Pindyck, R.S. and Rubinfeld,D.L., Halaman 490-491