[英]modulus values (roots) in VECM model using R?
謝謝你閱讀我的問題。 我正在嘗試將VECM用於經濟研究,我正在使用Rstudio上的vars和urca包。 考慮到我沒有固定的時間序列,兩者都需要一個區別,兩者都是I(1),我需要使用VECM方法,但我無法得到我需要的所有測試。
例如:首先我加載庫
library(vars)
library(urca)
並創建我的模型
data("Canada")
df <- Canada
VARselect(df)
vecm <- urca::ca.jo(df,K = 3)
model <- vec2var(vecm)
問題是,我無法獲得“模塊”值來證明穩定性,我知道我可以使用roots()函數從“varest”對象獲取此值,例如:
roots(VAR(df,3))
我的問題是:如何從我的vec2var對象獲得模數,roots()不處理這種對象。 我知道Gretl可以做到這一點(用單位圓來證明穩定性),所以從VECM獲得這個值是否可行? 我怎么能在R?
從...開始:
data("Canada")
dim(Canada) #84observations x 4 variables
VARselect(Canada) # since in small samples, AIC>BIC; VAR(3) is chosen.
現在,數據集Canada:1980.1 - 2000.4(20年)的范圍足夠長,可用於建模。 這20年的漫長時期肯定包含許多危機和干預措施。 因此,必須搜索數據中的結構中斷。 這是必要的,因為在結構破壞的序列中,SB的存在改變了非平穩性測試的值(從而影響關於序列是否靜止的決定)。
由於Narayan-Popp 2010在多個結構性斷裂下的非平穩性測試在統計上與以前的相比非常強大(Lee-Strazichic2003,Zivot-Andres1992),並且自從Joyeux 2007(在Rao2007中)證明了這些先前測試的不合邏輯性,並且NP2013已經證明了NP2010的統計功效優勢,必須使用NP2010。 由於NP2010的Gauss代碼對我來說似乎很難看,我將其轉換為R代碼,並且在ggplot2
的幫助下,結果更好。
[由於Osterwald-Lenum1992 CV忽略了SB而Johanse-Mosconi-Nielsen2000 CV關心SBs,因此處理結構性斷裂也是必須進行協整檢查的。
Canada <- as.data.frame(Canada)
head(Canada)
e prod rw U
1 929.6105 405.3665 386.1361 7.53
2 929.8040 404.6398 388.1358 7.70
...................................
# Assign lexiographic row names for dates of observations
row.names(Canada) <- paste(sort(rep(seq(1980, 2000, 1), 4) ), rep(seq(1, 4, 1), 20), sep = ".")
# Insert lexiographic "date" column to the dataframe. This is necessary for creating intervention dummies.
DCanada <- data.frame(date=row.names(Canada),Canada) # dataset with obs dates in a column
head(DCanada)
date e prod rw U
1980.1 1980.1 929.6105 405.3665 386.1361 7.53
1980.2 1980.2 929.8040 404.6398 388.1358 7.70
對該系列進行Narayan-Popp 2010非平穩性測試:
[H0:“(2個結構斷點)系列是非平穩的”; H1:“(2個結構斷點)系列是靜止的”;
“test stat> critical value”=>“hold H0”; “test stat <critical value”=>“持有H1”]
library(causfinder)
narayanpopp(DCanada[,2]) # for e
narayanpopp(DCanada[,3]) # for prod
narayanpopp(DCanada[,4]) # for rw
narayanpopp(DCanada[,5]) # for U
Narayan-Popp 2010非平穩性測試結果(使用obs #s):
variable t stat lag SB1 SB2 Integration Order
e -4.164 2 37:946.86 43:948.03 I(1)
prod -3.325 1 24:406.77 44:405.43 I(1)
rw -5.087 0 36:436.15 44:446.96 I(0) <trend-stationary>
U -5.737 1 43:8.169 53:11.070 I(0) <stationary pattern> (M2 computationally singular; used M1 model)
(critical values (M2): (1%,5%,10%): -5.576 -4.937 -4.596)
(critical values (M1): (1%,5%,10%): -4.958 -4.316 -3.980
由於在VAR結構中,所有變量都被平等對待,因此在確定系統結構斷裂時繼續進行相等處理:
mean(c(37,24,36,43)) # 35; SB1 of system=1988.3
mean(c(43,44,44,53)) # 46; SB2 of system=1990.2
以下是克服"In Ops.factor(left, right) : >= not meaningful for factors"
錯誤。 在某些數據集中,我們需要執行以下操作:
library(readxl)
write.xlsx(Canada, file="data.xlsx", row.names=FALSE) # Take this to the below folder, add "date" column with values 1980.1,....,2000.4
mydata <- read_excel("D://eKitap//RAO 2007 Cointegration for the applied economist 2E//JoyeuxCalisma//Canada//data.xlsx")
# arrange your path accordingly in the above line.
mydata <- as.data.frame(mydata)
library(lubridate); library(zoo)
row.names(mydata) <- as.yearqtr(seq(ymd('1980-01-01'), by = '1 quarter', length.out=(84)))
Dmydata <- mydata # Hold it in a variable
用2 SB(35:1988.3和46:1990.2)定義干預虛擬矩陣如下:
library(data.table)
DataTable <- data.table(Dmydata, keep.rownames=FALSE)
Dt <- cbind("bir"=1, # intervention dummies matrix
"D2t" = as.numeric(ifelse( DataTable[,c("date"), with=FALSE] >= "1988.3" & DataTable[,c("date"), with=FALSE] <= "1990.1", 1 , 0)),
"D3t" = as.numeric(ifelse( DataTable[,c("date"), with=FALSE] >= "1990.2" & DataTable[,c("date"), with=FALSE] <= "2000.4", 1 , 0)))
伴隨干預假人的飛行指示變量:
OnTheFlyIndicator <- cbind(
"I2t" = as.numeric(DataTable[, c("date"), with=FALSE] == "1988.3"),
"I3t" = as.numeric(DataTable[, c("date"), with=FALSE] == "1990.2"))
myTimeTrend <- as.matrix(cbind("TimeTrend" = as.numeric(1:nrow(Dt))))
zyDt <- Dt * as.vector(myTimeTrend) # TimeTrendDavranisDegisimleri
colnames(zyDt) <- paste(colnames(myTimeTrend), colnames(Dt), sep="*")
mydata <- mydata[,-1]
VAR訂單的選擇:
library(vars)
# Lag order selection with the effects of intervention dummies
VARselect(mydata, lag.max=5, "both", exogen=cbind(zyDt[drop=FALSE], Dt[drop=FALSE], OnTheFlyIndicator)) # Take VAR(3)
Joyeux2007索引技術的Lagger矩陣:
lagmatrix <- function(x, maxlag){
x <- as.matrix(x)
if(is.null(colnames(x))== TRUE){ colnames(x) <- "VarCol0" }
DondurulenDizey <- embed(c(rep(NA,maxlag),x),maxlag+1)
dimnames(DondurulenDizey)[[2]] <- c(colnames(x)[1, drop = FALSE], paste(colnames(x)[1,drop=FALSE],".",1:maxlag,"l", sep = ""))
return(DondurulenDizey)
}
分配VAR滯后和否。 子樣本:
VARlag <- 3
Subsamples <- 3 # subsamples = no. of str breaks +1
用於2個結構斷裂的虛擬矩陣:
dummymatrix2SB <- matrix(NA,DataTable[,.N], 10)
dummymatrix2SB <- cbind(myTimeTrend,
lagmatrix(zyDt[,c("TimeTrend*D2t"), drop=FALSE], maxlag=VARlag)[,1+VARlag, drop=FALSE],
lagmatrix(zyDt[,c("TimeTrend*D3t"), drop=FALSE], maxlag=VARlag)[,1+VARlag, drop=FALSE],
lagmatrix(Dt[,c("D2t"), drop=FALSE], maxlag=VARlag)[,1+VARlag, drop=FALSE],
lagmatrix(Dt[,c("D3t"), drop=FALSE], maxlag=VARlag)[,1+VARlag, drop=FALSE],
lagmatrix(OnTheFlyIndicator[,c("I2t"), drop=FALSE], maxlag=VARlag-1),
lagmatrix(OnTheFlyIndicator[,c("I3t"), drop=FALSE], maxlag=VARlag-1))
dummymatrix2SB[is.na(dummymatrix2SB)] <- 0 # replace NAs with 0
dummymatrix2SB # Print dummy matrix for 2 str breaks to make sure all are OK
TimeTrend TimeTrend.D2t.3l TimeTrend.D3t.3l D2t.3l D3t.3l I2t I2t.1l I2t.2l I3t I3t.1l I3t.2l
1 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0
...........................................
34 0 0 0 0 0 0 0 0 0 0
35 0 0 0 0 1 0 0 0 0 0
36 0 0 0 0 0 1 0 0 0 0
37 0 0 0 0 0 0 1 0 0 0
38 35 0 1 0 0 0 0 0 0 0
39 36 0 1 0 0 0 0 0 0 0
40 37 0 1 0 0 0 0 0 0 0
41 38 0 1 0 0 0 0 0 0 0
42 39 0 1 0 0 0 0 1 0 0
43 40 0 1 0 0 0 0 0 1 0
44 41 0 1 0 0 0 0 0 0 1
45 0 42 0 1 0 0 0 0 0 0
46 0 43 0 1 0 0 0 0 0 0
............................................
83 0 80 0 1 0 0 0 0 0 0
84 0 81 0 1 0 0 0 0 0 0
VAR的穩定性:
維克多,理論上你錯了。 即使在受限(協整)VAR模型的情況下,也從VAR側檢查穩定性。 有關詳細信息,請參閱Joyeux2007。 此外,雙方的估計是相同的:
“無限制的VAR =無限制的VECM”和
“限制VAR =限制VECM”。
因此,檢查無限制VAR的穩定性等於檢查不受限制的VECM的穩定性,反之亦然。 它們在數學上是平等的,它們只是不同的表示形式。
此外,檢查受限VAR的穩定性等於檢查受限VECM的穩定性,反之亦然。 它們在數學上是平等的,它們只是不同的表示形式。 但是,由於我們在可行VAR的子空間中進行沖浪,因此您不需要檢查受限制的VECM情況。 也就是說,如果對應於休息的VeCM的原始unr VAR是穩定的,那么一切都OK。
如果您的系列是協整的,那么即使在這種情況下也可以檢查VAR側的穩定性! 如果你想知道“你是否應該檢查限制VECM的穩定性”,答案是否定的。 你不應該檢查。 因為,在協整的情況下,您處於可行解的子空間中。 也就是說,如果你堅持要檢查受限(協整)VECM的穩定性,你仍然可以通過urca :: ca.jo extentions和vars :: vec2var extentions來做到這一點:
print(roots(VAR(mydata, p=3, "both", exogen=cbind(zyDt[drop=FALSE], Dt[drop=FALSE], OnTheFlyIndicator)), modulus=TRUE))
# [1] 0.96132524 0.77923543 0.68689517 0.68689517 0.67578368 0.67578368
[7] 0.59065419 0.59065419 0.55983617 0.55983617 0.33700725 0.09363846
print(max(roots(VAR(mydata, p=3, "both", exogen=cbind(zyDt[drop=FALSE], Dt[drop=FALSE], OnTheFlyIndicator)), modulus=TRUE)))
#0.9613252
(可選)通過OLS-CUSUM檢查穩定性:
plot(stability(VAR(mydata, p=3, "both", exogen=cbind(zyDt[drop=FALSE], Dt[drop=FALSE], OnTheFlyIndicator)), type="OLS-CUSUM"))
VAR殘差的非自相關測試:
for (j in as.integer(1:5)){
print(paste("VAR's lag no:", j))
print(serial.test(VAR(mydata, p=j, "both", exogen=cbind(zyDt[drop=FALSE], Dt[drop=FALSE], OnTheFlyIndicator)), lags.bg=4, type= c("ES")))
# lags.bg: AR order of VAR residuals
}
VAR殘差檢驗的正態性:
print(normality.test(VAR(mydata, p=3, "both", exogen=cbind(zyDt[drop=FALSE], Dt[drop=FALSE], OnTheFlyIndicator)), multivariate=TRUE))
library(normtest)
for (i in as.integer(1:4)){ # there are 4 variables
print(skewness.norm.test(resid(VAR(mydata, p=3, "both", exogen=cbind(zyDt[drop=FALSE], Dt[drop=FALSE], OnTheFlyIndicator)))[,i]))
print(kurtosis.norm.test(resid(VAR(mydata, p=3, "both", exogen=cbind(zyDt[drop=FALSE], Dt[drop=FALSE], OnTheFlyIndicator)))[,i]))
print(jb.norm.test(resid(VAR(mydata, p=3, "both", exogen=cbind(zyDt[drop=FALSE], Dt[drop=FALSE], OnTheFlyIndicator)))[,i]))
}
VAR殘差檢驗的同質性:
print(arch.test(VAR(mydata, p=3, "both", exogen=cbind(zyDt[drop=FALSE], Dt[drop=FALSE], OnTheFlyIndicator))), lags.multi=6, multivariate.only=TRUE)
由於系列的整合訂單不同,因此無法將它們整合在一起。 也就是說,假設有一段時間我都是I(1)並使用Johansen-Mosconi-Nielsen 2000 CV進行多重結構分解的協整檢驗:(將urca :: cajo擴展到causfinder :: ykJohEsbInc(即,將功能添加到進程1) SB和2 SBs))
summary(ykJohEsbInc(mydata, type="trace", ecdet="zamanda2yk", K=3, spec="longrun", dumvar=dummymatrix2SB[,c(-1,-2,-3)]))
# summary(ykJohEsbInc(mydata, type="trace", ecdet="zamanda2yk", K=3, spec="transitory", dumvar=dummymatrix2SB[,c(-1,-2,-3)])) gives the exactly same result.
由於系統中有2個SB(1988.3,1990.2),因此有q = 2 + 1 = 3個子樣本。
第一SB比率:v1 =(35-1)/ 84 = 0.4047619
第二SB比率:v2 =(46-1)/ 84 = 0.5357143
因此,JMN2000 CV用於2個SB的協整測試:
(以下是TR本地化。可以在Giles網站上找到原始的EN-本地代碼)
library(gplots)
# Johansen vd. (2000) nin buldugu, yapisal kirilmalarin varliginda esbutunlesim incelemesinin degistirilmis iz sinamalarinin yanasik p degerleri ve karar degerlerini hesaplama kodu
# Ryan Godwin & David Giles (Dept. of Economics, Univesity of Victoria, Canada), 29.06.2011
# Kullanici asagidaki 4 degeri atamalidir
#======================================
degiskensayisi <- 4 # p
q<- 3 # q: verideki farkli donemlerin sayisi; q=1: 1 donem, hicbir yapisal kirilma yok demek oldugundan v1 ve v2 nin degerleri ihmal edilir
v1<- 0.4047619 # (35-1)/84 # 1.yk anı=34+1=35. Johansen et. al 2000 v1 def'n , v1: SB1 - 1
v2<- 0.5357143 # (46-1)/84 # 2nd SB moment 45+1=46.
#======================================
# iz istatistiginin biri veya her ikisi icin p degerlerinin olmasi istendiginde, sonraki 2 satirin biri veya her ikisini degistir
izZ <- 15.09 # Vz(r) istatistiginin degeri
izK <- 114.7 # Vk(r) istatistiginin degeri
#=========================================
enbuyuk_p_r<- degiskensayisi # "p-r > 10" olmasın; bkz: Johansen vd. (2000)
# "a" ve "b" nin değerleri yapısal kırılmaların sayısına (q-1) bağlıdır
# q=1 iken, hiçbir yapısal kırılma olmadığı bu durumda a=b=0 ata
# q=2 iken, 1 yapısal kırılma olduğu bu durumda a=0 (Johansen vd. 2000 4.Tabloda) ve b=min[V1 , (1-V1)] ata
# q=3 iken, 2 yapısal kırılma olduğu bu durumda a=min[V1, (V2-V1), (1-V2)] ve b=min[geriye kalan iki V ifadesi] ata
a = c(0, 0, min(v1, v2-v1, 1-v2))[q]
b = c(0, min(v1, 1-v1), median(c(v1,v2-v1,1-v2)))[q]
# YanDagOrtLog: yanaşık dağılımın ortalamasının logaritması
# YanDagDegLog: yanaşık dağılımın değişmesinin logaritması
# V(Zamanyönsemsi) veya V(Kesme) sınamalarını yansıtmak üzere adlara z veya k ekle.
# Bkz. Johansen vd. (2000) 4. Tablo.
# Önce Vz(r) sınamasının sonra Vk(r) sınamasının karar değerlerini oluştur
pr<- c(1:enbuyuk_p_r)
YanDagOrtLogZ <- 3.06+0.456*pr+1.47*a+0.993*b-0.0269*pr^2-0.0363*a*pr-0.0195*b*pr-4.21*a^2-2.35*b^2+0.000840*pr^3+6.01*a^3-1.33*a^2*b+2.04*b^3-2.05/pr-0.304*a/pr+1.06*b/pr
+9.35*a^2/pr+3.82*a*b/pr+2.12*b^2/pr-22.8*a^3/pr-7.15*a*b^2/pr-4.95*b^3/pr+0.681/pr^2-0.828*b/pr^2-5.43*a^2/pr^2+13.1*a^3/pr^2+1.5*b^3/pr^2
YanDagDegLogZ <- 3.97+0.314*pr+1.79*a+0.256*b-0.00898*pr^2-0.0688*a*pr-4.08*a^2+4.75*a^3-0.587*b^3-2.47/pr+1.62*a/pr+3.13*b/pr-4.52*a^2/pr-1.21*a*b/pr-5.87*b^2/pr+4.89*b^3/pr
+0.874/pr^2-0.865*b/pr^2
OrtalamaZ<- exp(YanDagOrtLogZ)-(3-q)*pr
DegismeZ<- exp(YanDagDegLogZ)-2*(3-q)*pr
# Sinama istatistiginin yanasik dagilimina yaklasmakta kullanilacak Gama dagiliminin sekil ve olcek degiskelerini elde etmek icin yanasik ortalama ve degismeyi kullanarak
# V0 varsayimi altinda istenen quantilelari elde et:
# quantilelar: olasilik dagiliminin araligini veya bir ornekteki gozlemleri, esit olasiliklara sahip birbirlerine bitisik araliklarla bolen kesim noktalari.
tetaZ <- DegismeZ/OrtalamaZ
kZ <- OrtalamaZ^2/DegismeZ
YanDagOrtLogK<- 2.80+0.501*pr+1.43*a+0.399*b-0.0309*pr^2-0.0600*a*pr-5.72*a^2-1.12*a*b-1.70*b^2+0.000974*pr^3+0.168*a^2*pr+6.34*a^3+1.89*a*b^2+1.85*b^3-2.19/pr-0.438*a/pr
+1.79*b/pr+6.03*a^2/pr+3.08*a*b/pr-1.97*b^2/pr-8.08*a^3/pr-5.79*a*b^2/pr+0.717/pr^2-1.29*b/pr^2-1.52*a^2/pr^2+2.87*b^2/pr^2-2.03*b^3/pr^2
YanDagDegLogK<- 3.78+0.346*pr+0.859*a-0.0106*pr^2-0.0339*a*pr-2.35*a^2+3.95*a^3-0.282*b^3-2.73/pr+0.874*a/pr+2.36*b/pr-2.88*a^2/pr-4.44*b^2/pr+4.31*b^3/pr+1.02/pr^2-0.807*b/pr^2
OrtalamaK <- exp(YanDagOrtLogK)-(3-q)*pr
DegismeK <- exp(YanDagDegLogK)-2*(3-q)*pr
# Sinama istatistiginin yanasik dagilimina yaklasmakta kullanilacak Gama dagiliminin sekil ve olcek degiskelerini elde etmek icin yanasik ortalama ve degismeyi kullanarak
# V0 varsayimi altinda istenen quantilelari elde et:
# quantilelar: olasilik dagiliminin araligini veya bir ornekteki gozlemleri, esit olasiliklara sahip birbirlerine bitisik araliklarla bolen kesim noktalari.
tetaK <- DegismeK/OrtalamaK
kK <- OrtalamaK^2/DegismeK
# (izZ veya izK den biri 0 dan farklı ise) karar değerlerini ve p değerlerini tablolaştır:
windows(6,3.8)
KararDegerleri <- cbind(sapply(c(.90,.95,.99) , function(x) sprintf("%.2f",round(c(qgamma(x, shape=kZ,scale=tetaZ)),2))),
sapply(c(.9,.95,.99) , function(x) sprintf("%.2f",round(c(qgamma(x, shape=kK,scale=tetaK)),2))))
colnames(KararDegerleri) <- rep(c(0.90,0.95,0.99),2)
# rownames(KararDegerleri) <- pr
rownames(KararDegerleri) <- c(sapply((degiskensayisi -1):1, function(i) paste(degiskensayisi - i, " ","(r<=", i, ")",sep="")), paste(degiskensayisi, " ( r=0)", sep=""))
textplot(KararDegerleri, cex=1)
text(.064,.91,"p-r",font=2)
text(.345,1,expression(paste(plain(V)[z],"(r) test")),col=2)
text(.821,1,expression(paste(plain(V)[k],"(r) test")),col=4)
title("Yanasik Karar Degerleri \n (p:duzendeki degisken sayisi; r:esbutunlesim ranki)")
if(izZ!=0){
windows(4,3.8)
pDegerleri <- matrix(sprintf("%.3f",round(1 - pgamma(izZ, shape=kZ, scale = tetaZ),3)))
# rownames(pDegerleri) <- pr
rownames(pDegerleri) <- c(sapply((degiskensayisi -1):1, function(i) paste(degiskensayisi - i, " ","(r<=", i, ")",sep="")), paste(degiskensayisi, " ( r=0)", sep=""))
textplot(pDegerleri,cex=1,show.colnames=F)
text(.69,.96,substitute(paste("Pr(",plain(V)[z],">",nn,")"),list(nn=izZ)),col=2)
text(.45,.96,"p-r",font=2)
title("Yanasik p Degerleri \n (p:duzendeki degisken sayisi; \n r:esbutunlesim ranki)")
}
if(izK!=0){
windows(3,3.8)
pDegerleri <- matrix(sprintf("%.3f",round(1 - pgamma(izK, shape=kK, scale = tetaK),3)))
#rownames(pDegerleri) <- pr
rownames(pDegerleri) <- c(sapply((degiskensayisi -1):1, function(i) paste(degiskensayisi - i, " ","(r<=", i, ")",sep="")), paste(degiskensayisi, " ( r=0)", sep=""))
textplot(pDegerleri,cex=1,show.colnames=F)
text(.78,.96,substitute(paste("Pr(",plain(V)[k],">",nn,")"),list(nn=izK)),col=4)
text(.43,.96,"p-r",font=2)
title("Yanasik p Degerleri \n (p:duzendeki degisken sayisi; \n r:esbutunlesim ranki)")
}
因此,根據JMN2000 CV,也沒有協整。 所以,你對vec2var的使用毫無意義。 因為,在協整案例中需要vec2var。 再次,假設所有系列都是協整的,以使你快樂(創建需要使用vec2var)並繼續最困難的情況(具有多個結構中斷的系列的協整); 也就是說,我們正在繼續進行“一個雄心勃勃地撒尿的人”的邏輯。
將vars :: vec2var擴展為causfinder :: vec2var_ykJohEsbInc以處理具有相關干預假人的“多個結構中斷”情況下的轉換。 上面的JMN2000應用顯示協整等級r不在[1,4-1] = [1,3]范圍內。 盡管假設JMN2000 CV在上面因為參數而導致r = 1。
因此,要將受限制的VECM轉換為受限制的VAR(在多個= 2個結構中斷下),請應用:
vec2var_ykJohEsbInc(ykJohEsbInc(mydata, type="trace", ecdet="zamanda2yk", K=3, spec="longrun", dumvar=dummymatrix2SB[,c(-1,-2,-3)]),r=1)
這些結果如下:
Deterministic coefficients (detcoeffs):
e prod rw U
kesme 22.6612871 -0.215892151 32.0610121 -9.26649249 #(const)
zyonsemesi 0.2505164 -0.009900004 0.3503561 -0.10494714 #(trend)
zy*D2t_3 0.2238060 -0.008844454 0.3130007 -0.09375756
zy*D3t_3 -0.1234803 0.004879743 -0.1726916 0.05172878
$deterministic
kesme zyonsemesi zy*D2t_3 zy*D3t_3 D2t.3l D3t.3l
e 22.6612871 0.250516390 0.223806048 -0.123480327 -8.8012612 5.3052074
prod -0.2158922 -0.009900004 -0.008844454 0.004879743 -0.1157137 -0.3396206
rw 32.0610121 0.350356063 0.313000702 -0.172691620 -12.5838458 7.2201840
U -9.2664925 -0.104947142 -0.093757559 0.051728781 3.5836119 -2.2921099
I2t I2t.1l I2t.2l I3t I3t.1l I3t.2l
e -0.2584379 0.08470453 0.2102661 -0.51366831 -1.0110891 -2.08728944
prod 0.3013044 0.25103445 -0.8640467 0.08804425 -0.2362783 -0.05606892
rw -0.5838161 0.28400182 1.2073483 -0.67760848 -2.2650094 -0.70586316
U 0.1305258 0.03559119 0.1476985 0.14614290 0.6847273 1.27469940
$A
$A$A1
e.1g prod.1g rw.1g U.1g
e 1.4817704 0.1771082 -0.2274936 0.2332402
prod -0.1605790 1.1846699 0.0406294 -0.9398689
rw -0.8366449 -0.1910611 0.9774874 0.4667430
U -0.4245817 -0.1498295 0.1226085 0.7557885
$A$A2
e.2g prod.2g rw.2g U.2g
e -0.8441175 -0.04277845 0.01128282 -0.01896916
prod -0.3909984 -0.25960184 -0.20426749 0.79420691
rw 1.4181448 -0.03659278 -0.12240211 -0.06579174
U 0.4299422 0.09070905 0.04935195 -0.12691817
$A$A3
e.3g prod.3g rw.3g U.3g
e 0.40149641+0i -0.07067529+0i -0.008175418-0i 0.2286283+0i
prod 0.55003024+0i 0.07241639+0i 0.172505474-0i 0.1281593+0i
rw -0.52674826+0i 0.31667695+0i -0.168897398-0i 0.2184591+0i
U -0.02176108-0i 0.03245409-0i -0.077959841+0i 0.1855889-0i
那么,現在,檢查根:
print(roots(vec2var_ykJohEsbInc(ykJohEsbInc(mydata, type="trace", ecdet="zamanda2yk", K=3, spec="longrun", dumvar=dummymatrix2SB[,c(-1,-2,-3)]),r=1), modulus=TRUE))
這導致“ Please provide an object of class 'varest', generated by 'VAR()'.
”因為vars::roots
沒有擴展,因為:我們不需要這個擴展! 正如我之前所說,即使在VECM受限的情況下,也會從VAR側檢查穩定性。 您必須逐行閱讀Joyeux2007才能看到這一點。
我將繼續提供上述功能的輸出(打印屏幕)以進一步澄清。
我還會將擴展寫入vars::root
,這只是出於教學原因。
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