HIGH-ORDER MULTIVARIATE MARKOV CHAIN APPLIED IN DOW JONES AND IBOVESPA INDEXES

Cechin, Rafaela Boeira; Corso, Leandro Luís

doi:10.1590/0101-7438.2019.039.01.0205

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Articles • Pesqui. Oper. 39 (1) • Jan-Apr 2019 • https://doi.org/10.1590/0101-7438.2019.039.01.0205 copy

HIGH-ORDER MULTIVARIATE MARKOV CHAIN APPLIED IN DOW JONES AND IBOVESPA INDEXES

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

In this paper we analyzed the probabilities of transitions of state between Ibovespa and Dow Jones indexes using High-order Multivariate Markov Chain. While the stock market may be profitable, the existence of risks can lead to large losses. A mathematical model capable of considering different sources can aid in decision making. This model can work with stochastic data, causing different databases to be transformed into transitional matrices between states. For this, a set of a daily variation data were used between January 2008 and March 2018. Through this application, it was possible to show an interaction between the indexes and that the highest frequency of events was of the variation of -0.49 to 0.5% in Dow Jones to -0.49 to 0.5% in Ibovespa, with 428 cases, and the probability of this situation occurring again, of Dow Jones at time t to Ibovespa at time t+2, is 27.21%. Empirical results suggest that this application can help investors make decisions based on transition probabilities.

Keywords:
Markov Chain; High-order Multivariate Markov Chain; stock market index

Range of variation	Probability
< -2.5%	5.8%
from -2.49% to -1.5%	9.1%
from -1.49% to -0.5%	19.7%
from -0.49% to 0.5%	29.9%
from 0.51% to 1.5%	19.7%
from 1.51% to 2.5%	10.2%
2.51% <	5.6%

Probability of steady-state π_i	Expected recurrence time μ _ii
π₀	17.2 days
π₁	11 days
π₂	5.1 days
π₃	3.4 days
π₄	5.1 days
π₅	9.8 days
π₆	17.9 days

Interval	Probability
< -2.5%	2.3%
from -2.49% to -1.5%	4.4%
from -1.49% to -0.5%	15%
from -0.49% to 0.5%	52.4%
from 0.51% to 1.5%	20.1%
from 1.51% to 2.5%	3.7%
2.51% <	2.1%

Probability of steady-state π_i	Expected recurrence time μ _ii
π₀	47.8 days
π₁	21.8 days
π₂	6.6 days
π₃	1.9 days
π₄	5.1 days
π₅	27.7 days
π₆	44.8 days

Range of variation	π_j for $P_{1}^{(12)}$	π_j for $P_{2}^{(12)}$
< -2.5%	7.36%	8.03%
from -2.49% to -1.5%	9.32%	9.07%
from -1.49% to -0.5%	18.34%	18.62%
from -0.49% to 0.5%	28.75%	27.21%
from 0.51% to 1.5%	19.37%	18.62%
from 1.51% to 2.5%	9.89%	10.61%
2.51% <	6.98%	7.84%

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	< -2.5%
from	-2.49%	to	-1.5%
from	-1.49%	to	-0.5%
from	-0.49%	to	0.5%
from	0.51%	to	1.5%
from	1.51%	to	2.5%
	2.51% <