R中GARCH模型的限制测试（H0:alpha1+；beta1=1，H1:alpha1+；beta1≠；1）不起作用
我尝试使用以下假设对GARCH模型（来自“rugarch”包的ugarch）进行限制性检验：R中GARCH模型的限制测试（H0:alpha1+；beta1=1，H1:alpha1+；beta1≠；1）不起作用,r,time-series,restriction,chi-squared,hypothesis-test,R,Time Series,Restriction,Chi Squared,Hypothesis Test,我尝试使用以下假设对GARCH模型（来自“rugarch”包的ugarch）进行限制性检验： H0: alpha1 + beta1 = 1 H1: alpha1 + beta1 ≠ 1 因此，我正试图听从来自中国的建议 1.使用带有选项variance.model=list（model=“sGARCH”）的ugarchspec指定受限模型，并使用ugarchfit进行估算。从时隙拟合子时隙似然中获取对数似然 2.使用带有选项variance.model=list（model=“iGA
H0: alpha1 + beta1 = 1
H1: alpha1 + beta1 ≠ 1
*---------------------------------*
* GARCH Model Fit *
*---------------------------------*
Conditional Variance Dynamics
-----------------------------------
GARCH Model : sGARCH(1,1)
Mean Model : ARFIMA(0,0,0)
Distribution : norm
Optimal Parameters
------------------------------------
Estimate Std. Error t value Pr(>|t|)
mu -0.000355 0.001004 -0.35377 0.723508
archm 0.096364 0.039646 2.43059 0.015074
omega 0.000049 0.000010 4.91096 0.000001
alpha1 0.289964 0.021866 13.26117 0.000000
beta1 0.709036 0.023200 30.56156 0.000000
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
mu -0.000355 0.001580 -0.22482 0.822122
archm 0.096364 0.056352 1.71002 0.087262
omega 0.000049 0.000051 0.96346 0.335316
alpha1 0.289964 0.078078 3.71375 0.000204
beta1 0.709036 0.111629 6.35173 0.000000
LogLikelihood : 5411.828
Information Criteria
------------------------------------
Akaike -3.9180
Bayes -3.9073
Shibata -3.9180
Hannan-Quinn -3.9141
Weighted Ljung-Box Test on Standardized Residuals
------------------------------------
statistic p-value
Lag[1] 233.2 0
Lag[2*(p+q)+(p+q)-1][2] 239.1 0
Lag[4*(p+q)+(p+q)-1][5] 247.4 0
d.o.f=0
H0 : No serial correlation
Weighted Ljung-Box Test on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag[1] 4.695 0.03025
Lag[2*(p+q)+(p+q)-1][5] 5.941 0.09286
Lag[4*(p+q)+(p+q)-1][9] 7.865 0.13694
d.o.f=2
Weighted ARCH LM Tests
------------------------------------
Statistic Shape Scale P-Value
ARCH Lag[3] 0.556 0.500 2.000 0.4559
ARCH Lag[5] 1.911 1.440 1.667 0.4914
ARCH Lag[7] 3.532 2.315 1.543 0.4190
Nyblom stability test
------------------------------------
Joint Statistic: 5.5144
Individual Statistics:
mu 0.5318
archm 0.4451
omega 1.3455
alpha1 4.1443
beta1 2.2202
Asymptotic Critical Values (10% 5% 1%)
Joint Statistic: 1.28 1.47 1.88
Individual Statistic: 0.35 0.47 0.75
Sign Bias Test
------------------------------------
t-value prob sig
Sign Bias 0.2384 0.8116
Negative Sign Bias 1.1799 0.2381
Positive Sign Bias 1.1992 0.2305
Joint Effect 2.9540 0.3988
Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 272.1 9.968e-47
2 30 296.9 3.281e-46
3 40 313.3 1.529e-44
4 50 337.4 1.091e-44
Elapsed time : 0.4910491
*---------------------------------*
* GARCH Model Fit *
*---------------------------------*
Conditional Variance Dynamics
-----------------------------------
GARCH Model : iGARCH(1,1)
Mean Model : ARFIMA(0,0,0)
Distribution : norm
Optimal Parameters
------------------------------------
Estimate Std. Error t value Pr(>|t|)
mu -0.000355 0.001001 -0.35485 0.722700
archm 0.096303 0.039514 2.43718 0.014802
omega 0.000049 0.000008 6.42826 0.000000
alpha1 0.290304 0.021314 13.62022 0.000000
beta1 0.709696 NA NA NA
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
mu -0.000355 0.001488 -0.2386 0.811415
archm 0.096303 0.054471 1.7680 0.077066
omega 0.000049 0.000032 1.5133 0.130215
alpha1 0.290304 0.091133 3.1855 0.001445
beta1 0.709696 NA NA NA
LogLikelihood : 5412.268
Information Criteria
------------------------------------
Akaike -3.9190
Bayes -3.9105
Shibata -3.9190
Hannan-Quinn -3.9159
Weighted Ljung-Box Test on Standardized Residuals
------------------------------------
statistic p-value
Lag[1] 233.2 0
Lag[2*(p+q)+(p+q)-1][2] 239.1 0
Lag[4*(p+q)+(p+q)-1][5] 247.5 0
d.o.f=0
H0 : No serial correlation
Weighted Ljung-Box Test on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag[1] 4.674 0.03063
Lag[2*(p+q)+(p+q)-1][5] 5.926 0.09364
Lag[4*(p+q)+(p+q)-1][9] 7.860 0.13725
d.o.f=2
Weighted ARCH LM Tests
------------------------------------
Statistic Shape Scale P-Value
ARCH Lag[3] 0.5613 0.500 2.000 0.4538
ARCH Lag[5] 1.9248 1.440 1.667 0.4881
ARCH Lag[7] 3.5532 2.315 1.543 0.4156
Nyblom stability test
------------------------------------
Joint Statistic: 1.8138
Individual Statistics:
mu 0.5301
archm 0.4444
omega 1.3355
alpha1 0.4610
Asymptotic Critical Values (10% 5% 1%)
Joint Statistic: 1.07 1.24 1.6
Individual Statistic: 0.35 0.47 0.75
Sign Bias Test
------------------------------------
t-value prob sig
Sign Bias 0.2252 0.8218
Negative Sign Bias 1.1672 0.2432
Positive Sign Bias 1.1966 0.2316
Joint Effect 2.9091 0.4059
Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 273.4 5.443e-47
2 30 300.4 6.873e-47
3 40 313.7 1.312e-44
4 50 337.0 1.275e-44
Elapsed time : 0.365
*---------------------------------*
* GARCH Model Fit *
*---------------------------------*
Conditional Variance Dynamics
-----------------------------------
GARCH Model : sGARCH(1,1)
Mean Model : ARFIMA(0,0,0)
Distribution : norm
Optimal Parameters
------------------------------------
Estimate Std. Error t value Pr(>|t|)
mu -0.000355 0.001004 -0.35377 0.723508
archm 0.096364 0.039646 2.43059 0.015074
omega 0.000049 0.000010 4.91096 0.000001
alpha1 0.289964 0.021866 13.26117 0.000000
beta1 0.709036 0.023200 30.56156 0.000000
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
mu -0.000355 0.001580 -0.22482 0.822122
archm 0.096364 0.056352 1.71002 0.087262
omega 0.000049 0.000051 0.96346 0.335316
alpha1 0.289964 0.078078 3.71375 0.000204
beta1 0.709036 0.111629 6.35173 0.000000
LogLikelihood : 5411.828
Information Criteria
------------------------------------
Akaike -3.9180
Bayes -3.9073
Shibata -3.9180
Hannan-Quinn -3.9141
Weighted Ljung-Box Test on Standardized Residuals
------------------------------------
statistic p-value
Lag[1] 233.2 0
Lag[2*(p+q)+(p+q)-1][2] 239.1 0
Lag[4*(p+q)+(p+q)-1][5] 247.4 0
d.o.f=0
H0 : No serial correlation
Weighted Ljung-Box Test on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag[1] 4.695 0.03025
Lag[2*(p+q)+(p+q)-1][5] 5.941 0.09286
Lag[4*(p+q)+(p+q)-1][9] 7.865 0.13694
d.o.f=2
Weighted ARCH LM Tests
------------------------------------
Statistic Shape Scale P-Value
ARCH Lag[3] 0.556 0.500 2.000 0.4559
ARCH Lag[5] 1.911 1.440 1.667 0.4914
ARCH Lag[7] 3.532 2.315 1.543 0.4190
Nyblom stability test
------------------------------------
Joint Statistic: 5.5144
Individual Statistics:
mu 0.5318
archm 0.4451
omega 1.3455
alpha1 4.1443
beta1 2.2202
Asymptotic Critical Values (10% 5% 1%)
Joint Statistic: 1.28 1.47 1.88
Individual Statistic: 0.35 0.47 0.75
Sign Bias Test
------------------------------------
t-value prob sig
Sign Bias 0.2384 0.8116
Negative Sign Bias 1.1799 0.2381
Positive Sign Bias 1.1992 0.2305
Joint Effect 2.9540 0.3988
Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 272.1 9.968e-47
2 30 296.9 3.281e-46
3 40 313.3 1.529e-44
4 50 337.4 1.091e-44
Elapsed time : 0.4910491
*---------------------------------*
* GARCH Model Fit *
*---------------------------------*
Conditional Variance Dynamics
-----------------------------------
GARCH Model : iGARCH(1,1)
Mean Model : ARFIMA(0,0,0)
Distribution : norm
Optimal Parameters
------------------------------------
Estimate Std. Error t value Pr(>|t|)
mu -0.000355 0.001001 -0.35485 0.722700
archm 0.096303 0.039514 2.43718 0.014802
omega 0.000049 0.000008 6.42826 0.000000
alpha1 0.290304 0.021314 13.62022 0.000000
beta1 0.709696 NA NA NA
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
mu -0.000355 0.001488 -0.2386 0.811415
archm 0.096303 0.054471 1.7680 0.077066
omega 0.000049 0.000032 1.5133 0.130215
alpha1 0.290304 0.091133 3.1855 0.001445
beta1 0.709696 NA NA NA
LogLikelihood : 5412.268
Information Criteria
------------------------------------
Akaike -3.9190
Bayes -3.9105
Shibata -3.9190
Hannan-Quinn -3.9159
Weighted Ljung-Box Test on Standardized Residuals
------------------------------------
statistic p-value
Lag[1] 233.2 0
Lag[2*(p+q)+(p+q)-1][2] 239.1 0
Lag[4*(p+q)+(p+q)-1][5] 247.5 0
d.o.f=0
H0 : No serial correlation
Weighted Ljung-Box Test on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag[1] 4.674 0.03063
Lag[2*(p+q)+(p+q)-1][5] 5.926 0.09364
Lag[4*(p+q)+(p+q)-1][9] 7.860 0.13725
d.o.f=2
Weighted ARCH LM Tests
------------------------------------
Statistic Shape Scale P-Value
ARCH Lag[3] 0.5613 0.500 2.000 0.4538
ARCH Lag[5] 1.9248 1.440 1.667 0.4881
ARCH Lag[7] 3.5532 2.315 1.543 0.4156
Nyblom stability test
------------------------------------
Joint Statistic: 1.8138
Individual Statistics:
mu 0.5301
archm 0.4444
omega 1.3355
alpha1 0.4610
Asymptotic Critical Values (10% 5% 1%)
Joint Statistic: 1.07 1.24 1.6
Individual Statistic: 0.35 0.47 0.75
Sign Bias Test
------------------------------------
t-value prob sig
Sign Bias 0.2252 0.8218
Negative Sign Bias 1.1672 0.2432
Positive Sign Bias 1.1966 0.2316
Joint Effect 2.9091 0.4059
Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 273.4 5.443e-47
2 30 300.4 6.873e-47
3 40 313.7 1.312e-44
4 50 337.0 1.275e-44
Elapsed time : 0.365
2*(5411.828-5412.268)=-0.88
为了根据我的H0和H1假设进行限制测试，我可以知道如何解决这个问题吗 估计程序似乎有问题。。。由于一个模型是另一个模型的受限版本，因此使用iGARCH确实会导致更低的可能性 使用数据的子集
fit1 <- ugarchfit(speca, data = data.matrix(P))
# [1] 161.7373
fit2 <- ugarchfit(speca2, data = data.matrix(P))
# [1] 165.333
fit.control = list(scale = 1)
fit1 <- ugarchfit(speca, data = data.matrix(P), fit.control = list(scale = 1))
likelihood(fit1)
# [1] 161.7373
-sum(log(2 * pi * sigma(fit1)^2)) / 2 - sum(residuals(fit1, standardize = TRUE)^2) / 2
# [1] 161.7373
fit2 <- ugarchfit(speca2, data = data.matrix(P), fit.control = list(scale = 1))
likelihood(fit2)
# [1] 19.5233
-sum(log(2 * pi * sigma(fit2)^2)) / 2 - sum(residuals(fit2, standardize = TRUE)^2) / 2
# [1] 19.5233
fit1这是我从软件包作者“Alexios Galanos”那里得到的答案：
问题在于，GARCH模型的平稳性受到限制，这可能会干扰
在平稳边界上的模型的解算器收敛。以下是解决方案：
library(rugarch)
library(xts)
dat<-read.table("data.txt",header = TRUE, stringsAsFactors = FALSE)
dat = xts(dat[,2], as.Date(strptime(dat[,1],"%d/%m/%Y")))
spec1<-ugarchspec(mean.model=list(armaOrder=c(0,0), archm=TRUE, archpow=1), variance.model=list(model="iGARCH"))
spec2<-ugarchspec(mean.model=list(armaOrder=c(0,0), archm=TRUE, archpow=1), variance.model=list(model="sGARCH"))
mod1<-ugarchfit(spec1, dat, solver="solnp")
mod2<-ugarchfit(spec2,dat)
persistence(mod2)
>0.999
# at the limit of the internal constraint
mod2<-ugarchfit(spec2, dat, solver="solnp", fit.control = list(stationarity=0))
likelihood(mod2)
>5428.871
likelihood(mod1)
>5412.268
persistence(mod2)
1.08693
# above the limit
Here is one solution to change the constraint:
.garchconbounds2= function(){
return(list(LB = 1e-12,UB = 0.99999999999))
}
assignInNamespace(x = ".garchconbounds", value=.garchconbounds2, ns="rugarch")
mod2<-ugarchfit(spec2, dat, solver="solnp")
likelihood(mod2)
>5412.268
库（rugarch）
图书馆（xts）
DAT有人知道答案吗，特别是当我使用GARCH-M模型进行限制测试时？有没有一种方法可以发布我使用的完整数据集，以便您复制我的代码和结果？我想附加一个记事本文件，但不能。@Eric，我认为你不能直接附加；想到的两个选择是pastebin.com和dropbox。
fit1 <- ugarchfit(speca, data = data.matrix(P), fit.control = list(scale = 1))
likelihood(fit1)
# [1] 161.7373
-sum(log(2 * pi * sigma(fit1)^2)) / 2 - sum(residuals(fit1, standardize = TRUE)^2) / 2
# [1] 161.7373
fit2 <- ugarchfit(speca2, data = data.matrix(P), fit.control = list(scale = 1))
likelihood(fit2)
# [1] 19.5233
-sum(log(2 * pi * sigma(fit2)^2)) / 2 - sum(residuals(fit2, standardize = TRUE)^2) / 2
# [1] 19.5233
fit1 <- ugarchfit(speca, data = data.matrix(P), fit.control = list(scale = 0), solver.control = list(trace = TRUE))
#
# Iter: 1 fn: -161.7373 Pars: -0.0454619 0.0085993 0.0002706 0.0593231 # 0.6898473
# Iter: 2 fn: -161.7373 Pars: -0.0454619 0.0085993 0.0002706 0.0593231 0.6898473
# solnp--> Completed in 2 iterations
coef(fit1)
# mu mxreg1 omega alpha1 beta1
# -0.0454619274 0.0085992743 0.0002706018 0.0593231138 0.6898472858
fit1 <- ugarchfit(speca, data = data.matrix(P), fit.control = list(scale = 1), solver.control = list(trace = TRUE))
# Iter: 1 fn: 114.8143 Pars: -0.72230 0.13663 0.06830 0.05930 0.68988
# Iter: 2 fn: 114.8143 Pars: -0.72228 0.13662 0.06830 0.05931 0.68986
# solnp--> Completed in 2 iterations
coef(fit1)
# mu mxreg1 omega alpha1 beta1
# -0.045463099 0.008599494 0.000270610 0.059310622 0.689858216
fit2 <- ugarchfit(speca2, data = data.matrix(P), fit.control = list(scale = 0), solver.control = list(trace = TRUE))
# Iter: 1 fn: -165.3330 Pars: 0.0292439 -0.0051098 0.0002221 0.7495846
# Iter: 2 fn: -165.3330 Pars: 0.0292434 -0.0051097 0.0002221 0.7495853
# solnp--> Completed in 2 iterations
coef(fit2)
# mu mxreg1 omega alpha1 beta1
# 0.0292434276 -0.0051096984 0.0002221457 0.7495853224 0.2504146776
fit2 <- ugarchfit(speca2, data = data.matrix(P), fit.control = list(scale = 1), solver.control = list(trace = TRUE))
# Iter: 1 fn: 111.2185 Pars: 0.46462 -0.08118 0.05607 0.74959
# Iter: 2 fn: 111.2185 Pars: 0.46458 -0.08118 0.05607 0.74959
# solnp--> Completed in 2 iterations
coef(fit2)
# mu mxreg1 omega alpha1 beta1
# 0.46458110 -0.08117626 0.05607215 0.74959242 0.25040758
library(rugarch)
library(xts)
dat<-read.table("data.txt",header = TRUE, stringsAsFactors = FALSE)
dat = xts(dat[,2], as.Date(strptime(dat[,1],"%d/%m/%Y")))
spec1<-ugarchspec(mean.model=list(armaOrder=c(0,0), archm=TRUE, archpow=1), variance.model=list(model="iGARCH"))
spec2<-ugarchspec(mean.model=list(armaOrder=c(0,0), archm=TRUE, archpow=1), variance.model=list(model="sGARCH"))
mod1<-ugarchfit(spec1, dat, solver="solnp")
mod2<-ugarchfit(spec2,dat)
persistence(mod2)
>0.999
# at the limit of the internal constraint
mod2<-ugarchfit(spec2, dat, solver="solnp", fit.control = list(stationarity=0))
likelihood(mod2)
>5428.871
likelihood(mod1)
>5412.268
persistence(mod2)
1.08693
# above the limit
Here is one solution to change the constraint:
.garchconbounds2= function(){
return(list(LB = 1e-12,UB = 0.99999999999))
}
assignInNamespace(x = ".garchconbounds", value=.garchconbounds2, ns="rugarch")
mod2<-ugarchfit(spec2, dat, solver="solnp")
likelihood(mod2)
>5412.268