# Applied Econometrics Assignment - II (Kaneez Fatima) - Copy

```Submitted to: Dr. Tanweer ul Islam
Submitted by: Kaneez Fatima
MS ECONOMICS 2K20
NUST SCHOOL OF SOCIAL SCIENCES &amp; HUMANITIES
Applied Econometrics Assignment # 2
Q. Proof
ππππ(ππ , ππ−π ) = πππ
ππππ(ππ , ππ−π ) = ππ
Solution:
Before giving the proof, we have to check the data for stationarity
If it is stationary, then the mean value will remain constant over time i.e. π = 0. If ππ is constant,
then its mean value is also constant; the absolute value of ππ is less than 1.
Using autoregressive model AR (1):
Let ππ =ππ ππ−π + πΊπ i.e., put ππ = π → π = π
πππ(ππ , ππ−π ) = π¬[(ππ ππ−π + πΊπ )ππ−π ]
πππ(ππ , ππ−π ) = ππ π¬(πππ−π )
πππ(ππ , ππ−π ) = ππ πππ
ππππ(ππ , ππ−π ) =
πππ(ππ , ππ−π )
πππ(ππ , ππ−π )
Due to stationarity, the variance of ππ = the variance of ππ−π
ππππ(ππ , ππ−π ) = ππ
πππ(ππ , ππ−π ) = π¬[(ππ ππ−π + πΊπ )ππ−π ]
πππ(ππ , ππ−π ) = π¬[(ππ (ππ ππ−π + πΊπ−π ) + πΊπ )ππ−π ]
πππ(ππ , ππ−π ) = π¬(πππ πππ−π + ππ πΊπ−π ππ−π + πΊπ ππ−π )
πππ(ππ , ππ−π ) = πππ πππ
Due to stationarity, the variance of ππ = the variance of ππ−π
ππππ(ππ , ππ−π ) =
πππ(ππ , ππ−π )
πππ(ππ , ππ−π )
ππππ(ππ , ππ−π ) = πππ
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