## <environment: 0xa636ba4>
## [data = x]
##
## Conditional Distribution:
## QMLE
##
## Coefficient(s):
## omega alpha1 beta1
## 0.20692 0.13862 0.13387
##
## Std. Errors:
## robust
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## omega 0.20692 0.05102 4.056 5e-05 ***
## alpha1 0.13862 0.04928 2.813 0.00491 **
## beta1 0.13387 0.18170 0.737 0.46128
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -782.211 normalized: -0.782211
##
## Description:
## Thu Nov 2 13:01:14 2017 by user:
参数不接近真实参数。人们可能最初将其归因于随机性，但事实似乎并非如此。
例如，当我在前 500 个数据点上拟合模型时，我能得到什么呢？
garchFit(
data = x[1:500], cond.dist = "QMLE", include.mean = FALSE)
##
## Series Initialization:
## ARMA Model: arma
## Formula Mean: ~ arma(0, 0)
## GARCH Model: garch
## Formula Variance: ~ garch(1, 1)
## ARMA Order: 0 0
## Max ARMA Order: 0
## GARCH Order: 1 1
## Max GARCH Order: 1
## Maximum Order: 1
## Conditional Dist: QMLE
## h.start: 2
## llh.start: 1
## Length of Series: 500
## Recursion Init: mci
## Series Scale: 0.5498649
##
## Parameter Initialization:
## Initial Parameters: $params
## Limits of Transformations: $U, $V
## Which Parameters are Fixed? $includes
## Parameter Matrix:
## U V params includes
## mu -0.33278068 0.3327807 0.0 FALSE
## omega 0.00000100 100.0000000 0.1 TRUE
## alpha1 0.00000001 1.0000000 0.1 TRUE
## gamma1 -0.99999999 1.0000000 0.1 FALSE
## beta1 0.00000001 1.0000000 0.8 TRUE
## delta 0.00000000 2.0000000 2.0 FALSE
## skew 0.10000000 10.0000000 1.0 FALSE
## shape 1.00000000 10.0000000 4.0 FALSE
## Index List of Parameters to be Optimized:
## omega alpha1 beta1
## 2 3 5
## Persistence: 0.9
##
##
## --- START OF TRACE ---
## Selected Algorithm: nlminb
##
## R coded nlminb Solver:
##
## 0: 706.37230: 0.100000 0.100000 0.800000
## 1: 706.27437: 0.103977 0.100309 0.801115
## 2: 706.19091: 0.104824 0.0972295 0.798477
## 3: 706.03116: 0.112782 0.0950253 0.797812
## 4: 705.77389: 0.122615 0.0858136 0.788169
## 5: 705.57316: 0.134608 0.0913105 0.778144
## 6: 705.43424: 0.140011 0.0967118 0.763442
## 7: 705.19541: 0.162471 0.102711 0.739827
## 8: 705.16325: 0.166236 0.0931680 0.737563
## 9: 705.09943: 0.168962 0.100977 0.731085
## 10: 704.94924: 0.203874 0.0958205 0.702986
## 11: 704.78210: 0.223975 0.108606 0.664678
## 12: 704.67414: 0.250189 0.122959 0.630886
## 13: 704.60673: 0.276532 0.131788 0.595346
## 14: 704.52185: 0.335952 0.146435 0.520961
## 15: 704.47725: 0.396737 0.157920 0.448557
## 16: 704.46540: 0.442499 0.164111 0.396543
## 17: 704.46319: 0.440935 0.161566 0.400606
## 18: 704.46231: 0.442951 0.159225 0.400940
## 19: 704.46231: 0.443022 0.159284 0.400863
## 20: 704.46230: 0.443072 0.159363 0.400851
## 21: 704.46230: 0.443112 0.159367 0.400807
##
## Final Estimate of the Negative LLH:
## LLH: 405.421 norm LLH: 0.810842
## omega alpha1 beta1
## 0.1339755 0.1593669 0.4008074
##
## R-optimhess Difference Approximated Hessian Matrix:
## omega alpha1 beta1
## omega -8491.005 -1863.4127 -2488.5700
## alpha1 -1863.413 -685.6071 -585.4327
## beta1 -2488.570 -585.4327 -744.1593
## attr(,"time")
## Time difference of 0.02322888 secs
##
## --- END OF TRACE ---
##
##
## Time to Estimate Parameters:
## Time difference of 0.1387401 secs
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(data = x[1:500], cond.dist = "QMLE", include.mean = FALSE)
##
## Mean and Variance E