[abbey0]    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 1100 iterations with the thin box in the update tool set to 10. 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])
   }


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

list(alpha = 1.7, beta = 0.5,
gamma = 0.00029, delta = 0.0065)


list(alpha = 1.2, beta = -0.5,
gamma = 0.00029, delta = 0.0065)

Results

      mean   sd   MC_error   val2.5pc   median   val97.5pc   start   sample
   alpha   1.558   0.1995   0.008487   1.17   1.56   1.923   1001   20000
   beta   -0.5499   0.3628   0.01235   -0.9743   -0.65   0.3909   1001   20000
   delta   0.008204   0.00158   6.989E-5   0.005828   0.007991   0.0121   1001   20000
   gamma   7.936E-4   0.002908   1.506E-4   -0.003841   1.917E-4   0.007961   1001   20000
   
   

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