Page 126 - Textos de Matemática Vol. 47

116 M. E. SILVA
where 1, ⌘1, . . . , n, ⌘n are independent and independent of the latent process Xt and ⌘t, the random size of the outlier at time t is a random variable with the same support as Xt and mean : ⌘t ⇠ Po( ). The Bayesian approach to estimate model (4.1) requires apriori distribution for the parameters of interest. For the parameters 0 < ↵ < 1 and > 0 the traditionally weakly informative priors for the PoINAR(1) ([45]) are chosen: a non-informative Beta prior with parameters a = 0.01,b = 0.01 and a a non-informative Gamma prior with parameters c = 0.01, d = 0.01, respectively. The prior specifications for pt, the probability of contamination is a Beta distribution with parameters (g = 5, h = 95), with expectation E(pt) = 0.05, reflecting the belief that outliers occur occasionally. The prior for the mean size of the outliers is a non informative Gamma distribution. The result of applying the outlier detection methodology is represented in Figure 3 indicating the occurrence of an outlier at time t = 224 with high probability.
(a)
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t
(b)
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t
Figure 3. IP time series (a) and posterior probability of out- lier occurrence at each time (b).
0.0 0.4 0.8 02468