Stata Technical Bulletin
43
. use http ://fmwww.be.edu∕ec-p∕data∕Mills2d∕fta.dta
. tsset
time variable: month, 1965ml to 1995ml2
. gphudak ftaret,power(0.5 0.6 0.7)
GPH estimate of fractional differencing parameter
|
— Power |
Ords |
Est d |
StdErr |
t(H0: d=0) |
p>∣t∣ |
Asy. StdErr |
z(HO: d=0) |
— P>∣z∣ |
|
— .εo |
20 |
-.00204 |
.160313 |
-0.0127 |
0.990 |
. 187454 |
-0.0109 |
— 0.991 |
|
.60 |
35 |
.228244 |
.145891 |
1.5645 |
0.128 |
. 130206 |
1.7529 |
0.080 |
|
.70 |
64 |
.141861 |
.089922 |
1.5776 |
0.120 |
.091267 |
1.5544 |
0.120 |
. modlpr ftaret, power(0.5 0.55:0.8)
Modified LPR estimate of fractional differencing parameter
|
— Power |
Ords |
Est d |
Std Err |
t(H0: d=0) |
p>∣t∣ |
z(HO: d=l) |
— P>∣z∣ |
|
— .50 |
19 |
.0231191 |
.139872 |
0.1653 |
0.870 |
-6.6401 |
— 0.000 |
|
.55 |
25 |
.2519889 |
.1629533 |
1.5464 |
0.135 |
-5.8322 |
0.000 |
|
.60 |
34 |
.2450011 |
.1359888 |
1.8016 |
0.080 |
-6.8650 |
0.000 |
|
.65 |
46 |
.1024504 |
.1071614 |
0.9560 |
0.344 |
-9.4928 |
0.000 |
|
.70 |
63 |
.1601207 |
.0854082 |
1.8748 |
0.065 |
-10.3954 |
0.000 |
|
.75 |
84 |
.1749659 |
.08113 |
2.1566 |
0.034 |
-11.7915 |
0.000 |
|
.80 |
113 |
.0969439 |
.0676039 |
1.4340 |
0.154 |
-14.9696 |
0.000 |
. roblpr ftaret
Robinson estimates of fractional differencing parameter
Power Ords Est d StdErr t(HO: d=0) P>∣t∣
.90 205 .1253645 .0446745 2.8062 0.005
. roblpr ftap ftadiv
Robinson estimates of fractional differencing parameters
|
Power = |
.90 |
Ords |
= |
205 |
|
— Variable |
I Est d |
Std Err t |
— | |
|
— ftap |
I .8698092 |
.0163302 53.2640 |
— 0.000 | |
|
ftadiv |
I .8717427 |
.0163302 53.3824 |
0.000 |
Test for equality of d coefficients: F(l,406) = .00701 Prob > F = 0.9333
. constraint define 1 ftap=ftadiv
. roblpr ftap ftadiv ftaret, c(l)
Robinson estimates of fractional differencing parameters
|
Power = |
.90 |
Ords |
= |
205 |
|
— Variable |
I Est d |
Std Err t |
— | |
|
— ftap |
I .8707759 |
.0205143 42.4473 |
— 0.000 | |
|
ftadiv |
I .8707759 |
.0205143 42.4473 |
0.000 | |
|
ftaret |
I .1253645 |
.0290116 4.3212 |
0.000 |
Test for equality of d coefficients: F(l,610) = 440.11 Prob > F = 0.0000
The GPH test, applied to the stock returns series, generates estimates of the long memory parameter that cannot reject the
null at the ten percent level using the t test. Phillips’ modified LPR, applied to this series, finds that d = 1 can be rejected for
all powers tested, while d = 0 (stationarity) may be rejected at the ten percent level for powers 0.6, 0.7, and 0.75. Robinson’s
estimate for the returns series alone is quite precise. Robinson’s multivariate test, applied to the price and dividends series,
finds that each series has d > 0. The test that they share the same d cannot be rejected. Accordingly, the test is applied to all
three series subject to the constraint that price and dividends series have a common d, yielding a more precise estimate of the
difference in d parameters between those series and the stock returns series.