Page 125 - Contributed Paper Session (CPS) - Volume 2

CPS1458 KHOO W.C et al.
for ≤ . Therefore, the autocorrelation function is

() = ∙ ∑ ∙ (| − |)

=1

for ≤ , = 1,2, … , , = 1,2, … , .

4. Result
A set of real data has been fitted by the Poisson MPT(p) model. The data is
available at www.forecastingprinciple.com. The mean and variance of the data
are 0.3333 and 0.3155, respectively. The index of dispersion is 0.94 which is
close to 1 suggests that the Poisson marginal distribution is appropriate. The
autocorrelation value is 0.1263. In Figure 4.1 we notice that the third order
time series model is appropriate. We fitted the data to Poisson MPT(p) process
for = 2,3,4 and compare the results with the CINAR(p) process of Weiß
(2008). Table 4.1 shows the parameter estimates, AIC and BIC values for both
the MPT(p) and CINAR(p) models.

Time series plot of murder crime in Highland town
4
3
2
1
0

-1
0 20 40 60 80 100 120
month
Sample autocorrelation Sample partial autocorrelation
0.4 0.4
Sample Autocorrelation 0.2 Sample Partial Autocorrelations 0.2 0

0

-0.2
2 4 6 8 10 -0.2 2 4 6 8 10
Lag Lag

Figure 4.1: Time series plot of murder crime

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