Coursework Statistics
Autor: zhangweishun • November 11, 2015 • Coursework • 841 Words (4 Pages) • 600 Views
Question 4
1.
AR (1) model:
yt =c+φ1yt−1 +ut
C | φ1 | |
Parameter | 0.0290 | 0.9725 |
Standard error | 0.0129 | 0.0089 |
2.
MA (3) model
yt =c+ut +θ1ut−1 +θ2ut−2 +θ3ut−3
We have c = 0.9310, θ1=1.5080, θ2=1.2488, θ3=0.6036
C | θ1 | θ2 | θ3 | |
Parameter | 0.9310 | 1.5080 | 1.2488 | 0.6036 |
Standard error | 0.0546 | 0.0206 | 0.0305 | 0.0238 |
3.
ARMA (1,1) model
yt =c+φ1yt−1 +θ1ut−1 +ut.
C | φ1 | θ2 | |
Parameter | 0.0497 | 0.9506 | 0.4248 |
Standard error | 0.0131 | 0.0082 | 0.0121 |
4. Model selection
Using AIC criteria
The number in the beginning of a row implies AR(x)
The number in the beginning of a row implies MA(x)
0 | 1 | 2 | 3 | 4 | |
0 | 0.20004 | -1.00435 | -1.68537 | -2.10825 | -2.30147 |
1 | -2.65224 | -2.78593 | -2.78893 | -2.78839 | -2.78985 |
2 | -2.75376 | -2.79040 | -2.78932 | -2.78707 | -2.78706 |
3 | -2.77491 | -2.79119 | -2.78892 | -2.79788 | -2.79566 |
4 | -2.77704 | -2.78986 | -2.78759 | -2.79668 | -2.79384 |
ARMA(3,3) is the best.
Using SBIC criteria
The number in the beginning of a row implies AR(x)
The number in the beginning of a row implies MA(x)
0 | 1 | 2 | 3 | 4 | |
0 | 0.20634 | -0.99176 | -1.66648 | -2.08305 | -2.26998 |
1 | -2.63964 | -2.76703 | -2.76374 | -2.75690 | -2.75206 |
2 | -2.73486 | -2.76521 | -2.75782 | -2.74928 | -2.74297 |
3 | -2.74971 | -2.75970 | -2.75113 | -2.75379 | -2.74527 |
4 | -2.74555 | -2.75207 | -2.74350 | -2.74629 | -2.73715 |
ARMA(1,1) is the best.
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