Liquid 45 modeling based on Markov chain and fuzzy linguistic summary using fuzzy stochastic

Abstract

LQ45 is one of many Indeks Harga Saham (IHS) which is included in Bursa Efek Indonesia (BEI). IHS is used by investors to predict the stock prices. The motion of IHS is unpredictable causes the investors in quandary situation. Stochastic model is probabilistic model based on an event which is characterized with parameters value and time-variant. IHS fluctuate causes unpredictable effect that is also the feature of stochastic process. The uncertainty can be measured by fuzzy then the composite of both is fuzzy stochastic. On fuzzy, membership value used as parameter approach is fuzzy linguistic summary (FLS). FLS has not examined chance of fluctuation the stock prices motion, so that Markov chain's combination is used as the approach of parameter r. The r parameter has five state, those are the steady, rising, most rising, falling, and most falling. There are three kinds of stocks return, which are the positive return, negative return, and no return. The clustering process uses fuzzy c-means results the positive return clusters and negative return clusters. This research results interval on five sorted interval clusters -5.17 = x = 1.17 when IHS is most falling, -1.17 < x < 0 when IHS is falling, 0 when IHS is steady, 0 < x < 1.2 when IHS is rising, dan 1.2 = x = 3.73 when IHS is most rising and stochastic model obtained is X (n + 1) = X (n)er along r is the parameter of five states, rsteady = 0, 0001, rrising = 0, 0106, rmostrising = 0, 0135, rfalling = 0, 0072 and rmost falling = 0, 0104. The fuzzy stochastic model with those parameters on five states has MAPE value 0,49% therefore the model has great forecasting capability.