Page 125 - Textos de Matemática Vol. 47

MODELLING TIME SERIES OF COUNTS: AN INAR APPROACH
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(a)
(c)
Residuals
ACF
−2 0 2 4 6
−0.2
−0.1 0.0 0.1
0.2
0.3
0.4 0.5
−0.2
−0.1
0.0 0.1
0.2 0.3
Correlation

5 10 15 20
lag
5
10
lag
Residual Arrival Departure
15

Data
Acceptance bounds
Residuals Arrival Departure

0 50 100 150 200
t
Figure 2. Parametric bootstrap exercise (a), component residu- als (b) and corresponding autocorrelations (c) for IP data set.
[42] propose a Bayesian approach to model such outliers assuming that the observed process Yt is obtained from the unobservable clean process Xt con- taminating each Xt with probability t with an outlier of random size ⌘t. Thus
Yt = Xt + ⌘t t,
with Xt =↵⇧Xt 1 +et and t ⇠Be(pt), (4.1)
(b)