quation:
## data ~ garch(1, 1)
## <environment: 0xa85f084>
## [data = x[1:500]]
##
## Conditional Distribution:
## QMLE
##
## Coefficient(s):
## omega alpha1 beta1
## 0.13398 0.15937 0.40081
##
## Std. Errors:
## robust
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## omega 0.13398 0.11795 1.136 0.2560
## alpha1 0.15937 0.07849 2.030 0.0423 *
## beta1 0.40081 0.44228 0.906 0.3648
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## -405.421 normalized: -0.810842
##
## Description:
## Thu Nov 2 13:01:15 2017 by user:
请注意，参数 \(\beta\)（列为 beta1）发生了巨大变化。不同的截止点又会怎么样？
garchFit(
data = x[1:200], 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: 200
## Recursion Init: mci
## Series Scale: 0.5746839
##
## Parameter Initialization:
## Initial Parameters: $params
## Limits of Transformations: $U, $V
## Which Parameters are Fixed? $includes
## Parameter Matrix:
## U V params includes
## mu -0.61993813 0.6199381 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: 280.63354: 0.100000 0.100000 0.800000
## 1: 280.63302: 0.100315 0.100088 0.800223
## 2: 280.63262: 0.100695 0.0992822 0.800059
## 3: 280.63258: 0.102205 0.0983397 0.800404
## 4: 280.63213: 0.102411 0.0978709 0.799656
## 5: 280.63200: 0.102368 0.0986702 0.799230
## 6: 280.63200: 0.101930 0.0984977 0.800005
## 7: 280.63200: 0.101795 0.0983937 0.799987
## 8: 280.63197: 0.101876 0.0984197 0.799999
## 9: 280.63197: 0.102003 0.0983101 0.799965
## 10: 280.63197: 0.102069 0.0983780 0.799823
## 11: 280.63197: 0.102097 0.0983703 0.799827
## 12: 280.63197: 0.102073 0.0983592 0.799850
## 13: 280.63197: 0.102075 0.0983616 0.799846
##
## Final Estimate of the Negative LLH:
## LLH: 169.8449 norm LLH: 0.8492246
## omega alpha1 beta1
## 0.03371154 0.09836156 0.79984610
##
## R-optimhess Difference Approximated Hessian Matrix:
## omega alpha1 beta1
## omega -26914.901 -6696.498 -8183.925
## alpha1 -6696.498 -2239.695 -2271.547
## beta1 -8183.925 -2271.547 -2733.098
## attr(,"time")
## Time difference of 0.02161336 secs
##
## --- END OF TRACE ---
##
##
## Time to Estimate Parameters:
## Time difference of 0.09229803 secs
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(data = x[1:200], cond.dist = "QMLE", include.mean = FALSE)
##
## Mean and Variance Equation:
## data ~ garch(1, 1)
## <environment: 0xad38a84>
## [data = x[1:200]]
##
## Conditional Distribution:
## QMLE
##
## Coefficient(s):
## omega alpha1 beta1
## 0.033712 0.098362 0.799846
##
## Std. Errors:
## robust
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## omega 0.03371 0.01470 2.293 0.0218 *
## al