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STS425 Nur I. et al.
This process will be repeated for some different predetermined K
regimes implemented to MSw(K). Finally, the most representative models
with an optimal number of regimes for the data will be selected using the
smallest AIC ((Frühwirth-Schnatter, 2006) and (Chuffart, 2015)).
When the EM is running, the first step analysis in a Markov process can
always happen in regime = at the following (t+1)-th. It can happen

when the process for the first time leaving from the regime = , i.e.

when =0 and =1 is assigned to be (+1) = 1 and (+1) =0 (Huang,

et. al.,2013). Calculating a run length of regime = , therefore, can be

done by counting the length of serial time t , when =1 before it is set

= 0 for = 1,2, … , . When the EM process has met the
to (+)
convergence, each latent variable , {1,2, … , } will have the series

value, 0 and 1 for the length of . The length of 1’s series for regime =

represents its run length during the associated period. Furthermore, the
distribution of run length, especially ARL, for each regime can be
empirically determined by using its run-length distribution.

3. Results
The increasing price of both shares does not seem linear from day to day
transaction. Both trends tend to decline at the end of the recording period
which the Dicky Fuller test is said not to reject the null hypothesis. This non-
linear price change shows the AALI shareholders scooped up share prices
doubled almost 75 times, while for SSMS shareholders only doubled almost
3.5 times.
Simplification for easier analysis, differencing on lag 1 to both serial data
shares has to be done. Dicky Fuller's test rejects the null hypothesis to the new
both data. The serial plot data coupled with their marginal plot are shown in
Figure 1. Their leptokurtic and fat tail would be impossible to be represented
as a uni-modal normal distribution. Changes in variance during the transaction
make the preliminary testing using the Wolfram Mathworld chi-square in
Mathematica software report that there is still a small difference in mean and
even variance. It is meant that there is a multi-modal pattern and showing that
there are structural changes in the model (Weisstein, 2019).

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