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STS425 Nur I. et al.
market volatility on the price of a stock which can suddenly affect the serial
changes in stock prices at any time. These changes can occur in three
categories, namely changes in mean, variance, or mean and variance
simultaneously. Therefore, some good stocks can maintain their position in
the LQ45 for a long time, but there are also stocks that have only been in the
LQ45 for a few periods.
In this paper, the Markov Switching model (MSwM) coupled with the
Expectation Maximization (EM), which is attached by the method of calculating
run length, is proposed to be applied to two different long-standing stocks
into LQ45, namely Astra Agro Lestari, Tbk (AALI) and Sawit Sumbermas Sarana,
Tbk (SSMS). Both shares come from the plantation sub-sector and have been
registered in sharia stocks, since December 9, 1997, and December 12, 2013,
respectively. Since July 2003, AALI is registered in LQ45 and has been removed
in the period February - July 2018. Meanwhile, SSMS is only registered as a
member of LQ45 in the period February - July 2015 (Britama, 2019).
These two stocks with a significantly different length of stay in LQ45 were
used to show the ability of the MSwM coupled with EM method in capturing
patterns of stock price fluctuations with structural break phenomena.
Integrated with that, this combined method will also demonstrate their ability
to monitor the run length of each structural regime.

2. Methodology
2.1 Markov switching model
The model that contains structural break due to changes in mean and
variance simultaneously can be represented in equation (1)
((Hamilton,1996) and (Kim & Nelson, 1999)).
= + (1)
.

This is a normality based model with is the mean model of regimes

, {1,2, … , } and ~ (0, ) is the related residual. Compatibility
2

with Markov chains, a regime can be set as a state. Thus, the movement
of stock prices from regime i to regime j is represented in the Markov
probability transition matrix as as equation (2).

{ = | −1 = , −2 = , … } = { = | −1 = } = (2)

,

Where ≥ 0 for , = 1,2, … , and ∑ = 1. This is an MSwM

=0

with a certain number of regimes as a Markov process with a finite K-
state.
When each of the K regimes has in equation (1) as Autoregressive

pattern on order r, it is called as the Markov Switching Autoregressive
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