多元状态空间模型 dlm 奥肯定律

Question

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 模型允许上面的 b1 和 b0 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

我真的不知道如何使用 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)

以上代码运行，但输出不正确。我没有正确指定状态。有没有人有在 R 中使用多维回归构建 dlm 的经验？

Answer 1

我想我已经找到了一个解决方案——我已经设法在论文中重新创建了估计值，该估计值使用 Eviews 估计了这个模型（也使用 Eviews 进行了检查）。

    #--------------------------------------------------------------------------------------------------------------------------
# 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，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 的最佳方式，但模型的结果与使用 Eviews 报告的结果非常接近（在 0.01 以内）。话虽如此，对任何其他规范都非常开放。