Question

我试图用r中的潜在变量估计状态空间模型，但失败了。我试图用rstan包来做。有人知道如何做得更好吗？

假设我们有两个可观察的变量：gdp和通货膨胀。我们还知道存在三个不可观察的变量：潜在增长，潜在gdp，产出缺口。我们想要估计不可观察的变量和两个系数（a1和a2）。

我们的模型：

状态方程式：

grow [t] = grow [t-1] + e
潜力[t] =潜力[t-1] +成长[t] + e
gap [t] = a1 * gap [t-1] + e

测量方程：

gdp [t] =势[t] +间隙[t]
通货膨胀[t] =通货膨胀[t-1] + a2 *缺口[t] + e

此处生成了数据：

RequestBody body = RequestBody.create(MediaType.APPLICATION_JSON, pbody);
Request request = new Request.Builder()
                .url(url)
                .post(body)
                .build();

这是我的rstan代码：

a1 <- 0.7
a2 <- 0.3

grow <- c()
potential <- c()
gap <- c()
gdp <- c()
inflation <- c()

grow[1] <- 2
potential[1] <- 10
gap[1] <- 0
gdp[1] <- potential[1] + gap[1]/100
inflation[1] <- 2

for (i in 2:100) {
  grow[i] <- grow[i-1] + rnorm(1, 0, 0.1)
  potential[i] <- potential[i-1] + grow[i]/100 + rnorm(1, 0, 0.1)
  gap[i] <- a1*gap[i-1] +  rnorm(1,0,0.1)
  gdp[i] <- potential[i] + gap[i]/100
  inflation[i] <- inflation[i-1] + a2*gap[i]   + rnorm(1,0,0.1)
}

我在这里尝试过模型

data {
  int T; // number of obs
  int P; //number of variables
  matrix[T,P] Y; //dataset of generated series
}

parameters {

  #Coefficients
  vector[1] alfa1; //ar gap
  vector[1] alfa2; //phillips curve

  #State Variables (unobserved economic variables)
  vector[T] gap; // output gap
  vector[T] potential; // potential output
  vector[T] grow; // growth of potential output

  #Innovations
  real<lower = 0> sigma_pot; // The scale of innovations to potential output
  real<lower = 0> sigma_grow; // The scale of innovations to growth in potential output
  real<lower = 0> sigma_gap; // The scale of innovations to output gap
  real<lower = 0> sigma_inf; // The scale of innovations to phillips curve
}


model {
  // priors

  //Innovations
  sigma_pot ~ cauchy(0.2,3);
  sigma_grow  ~ cauchy(0.3,3); 
  sigma_gap ~ cauchy(0.9,5); 
  sigma_inf ~ cauchy(2,5);

  //coefficients
  alfa1 ~ normal(0,1); 
  alfa2 ~ normal(0,1); 


  //Initialize State Equations
  potential[1] ~ normal(0,1);
  grow[1] ~ normal(0,1);
  gap[1] ~ normal(0,1);

  // State Equations
  for(t in 2:T) {
    grow[t] ~ normal(grow[t-1], sigma_grow);
    potential[t] ~ normal(potential[t-1] + grow[t], sigma_pot);
      gap[t] ~ normal( alfa1*gap[t-1], sigma_gap);
  }

  // Measurement Equations
  for(t in 1:T) {
   Y[t,1] = potential[t] + gap[t];
     Y[t,2] ~ normal(Y[t-1,2] + alfa1*gap[t],sigma_inf);
  }
}

这是我遇到的错误

mvf_model <- stan(file = "newstan.stan" , 
                  data = list(T = nrow(data),
                              P = ncol(data),
                              Y = data),
                  chains = 4)

R中具有潜在变量的状态空间模型

0 个答案: