;ged", "sged", "std", "sstd", "snig", "QMLE"), include.mean = TRUE,
## include.delta = NULL, include.skew = NULL, include.shape = NULL,
## leverage = NULL, trace = TRUE, algorithm = c("nlminb", "lbfgsb",
## "nlminb+nm", "lbfgsb+nm"), hessian = c("ropt", "rcd"),
## control = list(), title = NULL, description = NULL, ...)
## NULL
该函数提供了一些选项，要最大化的分布（cond.dist）和用于优化的算法（algorithm）。除非另有说明，否则我将始终选择 cond.dist = QMLE 来指示函数使用 QMLE 估算器。
这是一次调用。
garchFit(
data = x, 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: 1000
## Recursion Init: mci
## Series Scale: 0.5320977
##
## Parameter Initialization:
## Initial Parameters: $params
## Limits of Transformations: $U, $V
## Which Parameters are Fixed? $includes
## Parameter Matrix:
## U V params includes
## mu -0.15640604 0.156406 0.0 FALSE
## omega 0.00000100 100.000000 0.1 TRUE
## alpha1 0.00000001 1.000000 0.1 TRUE
## gamma1 -0.99999999 1.000000 0.1 FALSE
## beta1 0.00000001 1.000000 0.8 TRUE
## delta 0.00000000 2.000000 2.0 FALSE
## skew 0.10000000 10.000000 1.0 FALSE
## shape 1.00000000 10.000000 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: 1419.0152: 0.100000 0.100000 0.800000
## 1: 1418.6616: 0.108486 0.0998447 0.804683
## 2: 1417.7139: 0.109746 0.0909961 0.800931
## 3: 1416.7807: 0.124977 0.0795152 0.804400
## 4: 1416.7215: 0.141355 0.0446605 0.799891
## 5: 1415.5139: 0.158059 0.0527601 0.794304
## 6: 1415.2330: 0.166344 0.0561552 0.777108
## 7: 1415.0415: 0.195230 0.0637737 0.743465
## 8: 1415.0031: 0.200862 0.0576220 0.740088
## 9: 1414.9585: 0.205990 0.0671331 0.724721
## 10: 1414.9298: 0.219985 0.0713468 0.712919
## 11: 1414.8226: 0.230628 0.0728325 0.697511
## 12: 1414.4689: 0.325750 0.0940514 0.583114
## 13: 1413.4560: 0.581449 0.143094 0.281070
## 14: 1413.2804: 0.659173 0.157127 0.189282
## 15: 1413.2136: 0.697840 0.155964 0.150319
## 16: 1413.1467: 0.720870 0.142550 0.137645
## 17: 1413.1416: 0.726527 0.138146 0.135966
## 18: 1413.1407: 0.728384 0.137960 0.134768
## 19: 1413.1392: 0.731725 0.138321 0.132991
## 20: 1413.1392: 0.731146 0.138558 0.133590
## 21: 1413.1392: 0.730849 0.138621 0.133850
## 22: 1413.1392: 0.730826 0.138622 0.133869
##
## Final Estimate of the Negative LLH:
## LLH: 782.211 norm LLH: 0.782211
## omega alpha1 beta1
## 0.2069173 0.1386221 0.1338686
##
## R-optimhess Difference Approximated Hessian Matrix:
## omega alpha1 beta1
## omega -8858.897 -1839.6144 -2491.9827
## alpha1 -1839.614 -782.8005 -531.7393
## beta1 -2491.983 -531.7393 -729.7246
## attr(,"time")
## Time difference of 0.04132652 secs
##
## --- END OF TRACE ---
##
##
## Time to Estimate Parameters:
## Time difference of 0.3866439 secs
##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(data = x, cond.dist = "QMLE", include.mean = FALSE)
##
## Mean and Variance Equation:
## data ~ garch(1, 1)