Econometric take home APPS_Part_33 - Chapter 21 Time Series...

Chapter 21
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Time Series Models
There are no exercises or applications in Chapter 21.
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Chapter 22
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Nonstationary Data
Exercise
1. The autocorrelations are simple to obtain just by multiplying out v
t
2
, v
t
v
t-1
and so on. The
autocovariances are 1+ θ
1
2
+ θ
2
2
, - θ
2
(1 - θ
2
), - θ
2
, 0, 0, 0... which provides the autocorrelations by division by
the first of these. The partial autocorrelations are messy, and can be obtained by the Yule Walker
equations. Alternatively (and much more simply), we can make use of the observation in Section 21.2.3
that the partial autocorrelations for the MA(2) process mirror tha autocorrelations for an AR(2). Thus, the
results in Section 21.2.3 for the AR(2) can be used directly.
Applications
1. ADF Test
+-----------------------------------------------------------------------+
| Ordinary least squares regression Weighting variable = none |
| Dep. var. = R Mean= 8.212678571 , S.D.= .7762719558 |
| Model size: Observations = 56, Parameters = 6, Deg.Fr.= 50 |
| Residuals: Sum of squares= .9651001703 , Std.Dev.= .13893 |
| Fit: R-squared= .970881, Adjusted R-squared = .96797 |
| Model test: F[ 5, 50] = 333.41, Prob value = .00000 |
| Diagnostic: Log-L = 34.2439, Restricted(b=0) Log-L = -64.7739 |
| LogAmemiyaPrCrt.= -3.846, Akaike Info. Crt.= -1.009 |