r - 多元状态空间模型 dlm okuns 定律
问题描述
我正在尝试使用 R 中的 dlm 包估计带有 dlm 的奥肯定律方程。我可以使用 nls 估计非时变模型,如下所示:
const_coef <- nls(formula = dur~ b1*dur_lag1 + b2*(d2lgdp-b0) + b3*d2lrulc_lag2 ,
start = list(b0 =0.1, b1=0.1, b2=0.1, b3=0.1),
data = mod_data)
我希望能够估计的 dlm 模型允许b1
并b0
在上面遵循随机游走。我可以在 Eviews 中通过声明测量方程并附加状态来做到这一点(以下是原始论文作者提供的一些代码,我可以复制:
'==========================
' SPECIFY THE KALMAN FILTER
'==========================
'Priors on state variables
vector(2) mprior
mprior(1) = 4 'Prior on starting value for trend GDP growth (annual average GDP growth over 1950s)
mprior(2) = 0 'Prior on starting value for lagged dependent variable
sym(2) vprior
vprior(1,1) = 5 'Prior on variance of trend GDP growth (variance of annual GDP growth over 1950s)
vprior(2,2) = 1 'Prior on variance of lagged dependent variable
'Specify coefficient vector
coef(8) ckf
'Declare state space
sspace ss1
ss1.append dur = lag*dur(-1) + ckf(2)*(d2lgdp-trend)+ckf(3)*D2LRULC(-2)+[var=exp(ckf(4))] 'Measurement equation
ss1.append @state trend = 1*trend(-1) + [var = exp(ckf(5))] 'State equation for trend GDP growth (random walk)
ss1.append @state lag = 1*lag(-1) + [var = exp(ckf(6))] 'State equation for lagged dependent variable (random walk)
'Apply priors to state space
ss1.append @mprior mprior
ss1.append @vprior vprior
'Set parameter starting values
param ckf(2) -0.0495 ckf(3) 0.01942 ckf(4) -2.8913 ckf(5) -4.1757 ckf(6) -6.2466 'starting values for parameters
'=====================
' ESTIMATE THE MODEL
'=====================
'Estimate state space
smpl %estsd %ested 'Estimation sample
ss1.ml(m=500,showopts) 'Estimate Kalman filter by maximum likelihood
freeze(mytab) ss1.stats
我真的不确定如何使用 dlm 包做到这一点。我尝试了以下方法:
buildSS <- function(v){
dV <- exp(v[1]) # Variance of the measurment equation (ckf4)
dW <- c(exp(v[2]), # variance of the lagged dep (ckf6)
0, # variance of the coef on d2lgdp ckf(2) set to 0
0, # variance of the coef on d2lrulc ckf(3) set to 0
exp(v[3]) # variance of the random walk intercept (ckf5)
)
beta.vec <- c(1,v[4],v[5],1) # Params ckf(2) ckf3(3)
okuns <- dlmModReg(mod_data.tvp[,-1], addInt = TRUE, dV =dV, dW = dW, m0 = beta.vec)
}
#'Set parameter starting values
ckf4Guess <- -2.8913
ckf2guess <- -0.0495
ckf3guess <- 0.01942
ckf5guess <- -4.1757
ckf6guess <- -6.2466
params <- c(ckf4Guess,
ckf5guess,
ckf6guess,
ckf2guess,
ckf3guess)
tvp_mod.mle <- dlmMLE(mod_data.tvp[,"dur"] , parm = params, build = buildSS)
tvp_mod <- buildSS(tvp_mod.mle$par)
tvp_filter <- dlmFilter(mod_data$dur,tvp_mod)
上面的代码运行,但输出不正确。我没有正确指定状态。有没有人有在 R 中使用多变量回归构建 dlms 的经验?
解决方案
我想我已经找到了一个解决方案——我已经设法重新创建了论文中的估计,该估计使用 Eviews 估计了这个模型(也使用 Eviews 检查了这个)。
#--------------------------------------------------------------------------------------------------------------------------
# tvp model full model - dur = alpha*dur(-1)+ beta(dgdp-potential) + gamma*wages
#--------------------------------------------------------------------------------------------------------------------------
# Construct DLM
OkunsDLMfm <- dlm(
FF = matrix(c(1,1,1,1),ncol = 4, byrow = TRUE),
V = matrix(1),
GG = matrix(c(1,0,0,0,
0,1,0,0,
0,0,1,0,
0,0,0,1), ncol = 4, byrow = TRUE),
W = matrix(c(1,0,0,0,
0,1,0,0,
0,0,1,0,
0,0,0,1), ncol = 4, byrow = TRUE),
JFF = matrix(c(1,2,3,0),ncol = 4, byrow = TRUE),
X = cbind(mod_data$dur_lag1,mod_data$d2lgdp, mod_data$d2lrulc_lag2), # lagged dep var, dgdp, wages.
m0 = c(0,0,0,0),
C0 = matrix(c(1e+07,0,0,0,
0,1e+07,0,0,
0,0,1e+07,0,
0,0,0,1e+07), ncol = 4, byrow = TRUE)
)
buildOkunsFM <- function(p){
V(OkunsDLMfm) <- exp(p[2])
GG(OkunsDLMfm)[1,1] <- 1
GG(OkunsDLMfm)[2,2] <- 1
GG(OkunsDLMfm)[3,3] <- 1
GG(OkunsDLMfm)[4,4] <- 1
W(OkunsDLMfm)[1,1] <- exp(p[3])
W(OkunsDLMfm)[2,2] <- 0
W(OkunsDLMfm)[3,3] <- 0
W(OkunsDLMfm)[4,4] <- exp(p[4])
m0(OkunsDLMfm) <- c(0,0,0,p[1]*4)
C0(OkunsDLMfm)[1,1] <- 1
C0(OkunsDLMfm)[4,4] <- 5
return(OkunsDLMfm)
}
okuns.estfm <- dlmMLE(y = mod_data$dur, parm = c(-0.049,-1.4,-6,-5), build = buildOkunsFM)
OkunsDLM1fm <- buildOkunsFM(okuns.estfm$par)
时变水平,即潜在输出的估计值,是通过将状态向量的第 4 个元素除以第二个 * 除以负 1 得出的。
不确定这是否是指定 DLM 的最佳方法,但模型的结果非常接近使用 Eviews 报告的结果(在 0.01 以内)。话虽如此,对任何其他规范都非常开放。
推荐阅读
- android - Android textview setVisibilty GONE 无法唤醒
- jquery - 在这种情况下,什么命令代码功能等于“this”?
- javascript - 如何使用 Ajax 同时上传多个带有描述的图像?
- node.js - Express 服务器对某些路径返回 404,但对其他路径不返回
- python - 如何解释 conda 包规范,例如“feature:/win-64::__cuda==11.1=0”?
- ros - 在 ROS turtlesim 中如何在正弦曲线路径上移动海龟
- firebase - Expo firebase facebook日志错误:auth/invalid-credential
- google-cloud-platform - 使用使用 Streaming Insert 插入的控制台从 BigQuery 中删除数据
- docker - Go app Dockerfile 总是在重启时下载模块
- mysql - MySQL 查询 - 不在两个日期之间