Abbey National: A stable distribution

Buckle considers the price of Abbey National shares on 50 conscutive working days. He models the price return using a stable distribution with unknown parameters. We run two chains for 101000 iterations. Our results are in fair agreement with Buckle who estimated the following mean values alpha = 1.61, beta = -0.55, gamma = 0.00053 and delta = 0.0079.
   model{
      for(i in 2 : N){
         z[i] ~ dstable(alpha, beta, gamma, delta)   
         z[i] <- price[i] / price[i - 1] - 1
      }
      
      alpha ~ dunif(1.1, 2)
      beta ~ dunif(-1, 1)
      gamma ~ dunif(-0.05, 0.05)
      delta ~ dunif(0.001, 0.5)
      
      mean.z <- mean(z[2:50])
      sd.z <- sd(z[2:50])
      z.pred ~ dstable(alpha, beta, gamma, delta)
   }
Data
list(N = 50, price = c(
296, 296, 300, 302, 300, 304, 303, 299, 293, 294, 294, 293, 295,
287, 288, 297, 305, 307, 307, 304, 303, 304, 304, 309, 309, 309,
307, 306, 304, 300, 296, 301, 298, 295, 295, 293, 292, 297, 294,
293, 306, 303, 301, 303, 308, 305, 302, 301, 297, 299)
)
Inits for chain 1
list(alpha = 1.7, beta = 0.5,
gamma = 0.00029, delta = 0.0065)
   
Inits for chain 2
list(alpha = 1.2, beta = -0.5,
gamma = 0.00029, delta = 0.0065)

Results

[abbey1]

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