Ljung-BoxのQ統計量, Breusch-Pagan test, Breusch-Godfrey Test
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Box-Jenkins procedures
Procedure BJIDENT
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OPTIONS FOR THIS ROUTINE
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IAC = FALSE NDIFF = 0 NLAG = 20
NLAGP = 10 NSDIFF = 0 NSPAN = 12
PACMETH = BURG PLOT = TRUE PLOTAC = TRUE
PLTRAW = FALSE SILENT = FALSE
Autocorrelations
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Series: R
Mean = 0.82122470
Std. Error = 2.8366440
Lags
Autocorrelations -0.101 0.172 -0.188E-01-0.395E-02-0.638E-01
Standard Errors 1- 5 0.670E-01 0.676E-01 0.696E-01 0.696E-01 0.696E-01
Q-statistics 2.31 9.06 9.14 9.15 10.1
Autocorrelations -0.213E-01-0.915E-01 0.945E-01 0.942E-01 0.186E-01
Standard Errors 6-10 0.699E-01 0.699E-01 0.704E-01 0.710E-01 0.716E-01
Q-statistics 10.2 12.1 14.2 16.3 16.4
Autocorrelations 0.394E-02 0.207 0.702E-01-0.276E-01 0.139
Standard Errors 11-15 0.716E-01 0.716E-01 0.742E-01 0.745E-01 0.746E-01
Q-statistics 16.4 26.5 27.7 27.9 32.6
Autocorrelations -0.238E-01 0.139E-01-0.226E-01-0.642E-01-0.130E-02
Standard Errors 16-20 0.757E-01 0.758E-01 0.758E-01 0.758E-01 0.760E-01
Q-statistics 32.7 32.8 32.9 33.9 33.9
Partial Autocorrelations
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Series: R
Standard Error of Autocorrelations = 0.66964953E-01
Lags
Partial Autocorrs 1- 5 -0.102 0.167 0.177E-01-0.379E-01-0.732E-01
Partial Autocorrs 6-10 -0.320E-01-0.847E-01 0.999E-01 0.160 0.835E-02
Autocorrelation Function of: R
-1.00 -0.60 -0.20 0.20 0.60 1.00
|-+---------+---------+----0----+---------+---------+-|
1 | R | + | -0.10114
2 | + | +R | 0.17243
3 | + R + | -0.018770
4 | + R + | -0.0039485
5 | +R | + | -0.063820
6 | + R| + | -0.021345
7 | +R | + | -0.091488
8 | + | R+ | 0.094453
9 | + | R+ | 0.094230
10 | + R + | 0.018629
11 | + R + | 0.0039379
12 | + | +R | 0.20676
13 | + | R + | 0.070215
14 | + R| + | -0.027591
15 | + | R+ | 0.13942
16 | + R| + | -0.023833
17 | + R + | 0.013865
18 | + R| + | -0.022614
19 | + R | + | -0.064229
20 | + R + | -0.0013002
|-+---------+---------+----0----+---------+---------+-|
-1.00 -0.60 -0.20 0.20 0.60 1.00
Partial Autocorrelation Function of: R
-1.00 -0.60 -0.20 0.20 0.60 1.00
|-+---------+---------+----0----+---------+---------+-|
1 | R | + | -0.10205
2 | + | +R | 0.16722
3 | + R + | 0.017692
4 | + R| + | -0.037906
5 | +R | + | -0.073190
6 | + R| + | -0.032039
7 | +R | + | -0.084651
8 | + | R+ | 0.099873
9 | + | +R | 0.16032
10 | + R + | 0.0083497
|-+---------+---------+----0----+---------+---------+-|
-1.00 -0.60 -0.20 0.20 0.60 1.00
Equation 1
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Method of estimation = Ordinary Least Squares
Dependent variable: PAI
Current sample: 1953:1 to 1971:7
Number of observations: 223
Mean of dep. var. = 2.34560
Std. dev. of dep. var. = 3.24604
Sum of squared residuals = 1786.22
Variance of residuals = 8.08243
Std. error of regression = 2.84296
R-squared = .236385
Adjusted R-squared = .232930
LM het. test = 2.96299 [.085]
Durbin-Watson = 2.18459 [.906,.927]
Breusch/Godfrey LM: AR/MA1 = 2.31285
Breusch/Godfrey LM: AR/MA2 = 9.58182
Breusch/Godfrey LM: AR/MA3 = 10.0529
Breusch/Godfrey LM: AR/MA4 = 10.0968
Breusch/Godfrey LM: AR/MA5 = 10.6326
Breusch/Godfrey LM: AR/MA6 = 10.7752
Breusch/Godfrey LM: AR/MA7 = 12.5138
Breusch/Godfrey LM: AR/MA8 = 13.6195
Breusch/Godfrey LM: AR/MA9 = 19.0371
Breusch/Godfrey LM: AR/MA10 = 20.9904
Breusch/Godfrey LM: AR/MA11 = 20.4067
Breusch/Godfrey LM: AR/MA12 = 30.8899
Breusch-Pagan het. test = 2.67891
Jarque-Bera test = 4.43683 [.109]
Ramsey's RESET2 = .127172 [.722]
F (zero slopes) = 68.4129 [.000]
Schwarz B.I.C. = 553.827
Log likelihood = -548.420
Estimated Standard
Variable Coefficient Error t-statistic P-value
C -.867767 .431225 -2.01233 [.045]
TB1 1.01470 .112201 9.04353 [.000]
Standard Errors are heteroskedastic-consistent (HCTYPE=0).
T(221) Test Statistic: 0.1309850, Two-tailed area: .89591
NORMAL Test Statistic: 0.1309850, Two-tailed area: .89579
Breusch-Godfrey Test (1). (Use period 1952/1-1971/7)
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Current sample: 1952:1 to 1952:12
We set e_0=e_{-1}=...e_{-11}=0 (1952/1-1952/12)
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Current sample: 1953:1 to 1971:7
CHISQ(12) Test Statistic: 27.00019, Upper tail area: .00773
Breusch-Godfrey Test (2). (Use period 1953/1-1971/7)
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Current sample: 1954:1 to 1971:7
Use nR^2
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CHISQ(12) Test Statistic: 28.60422, Upper tail area: .00451
Use p x F
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CHISQ(12) Test Statistic: 30.88991, Upper tail area: .00205
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