# Apply markov chains model and fuzzy time series for forecasting

The time series forcasting with preditve variable object X changing over time in order to achieve predictive accuracy is always a challenge to scientists, not only in Vietnam but also globally. Because it is not easy to find a suitable probability distribution for this predictive variable object at the point t was born. Historical data need to be collected and analyzed, in order to find a perfect fit. It is, however, a distribution can only fit with statistics in a particular time in time series analysis, and varies at other certain point of time. Therefore, the use of a fixed distribution for the predictable object is not applicable for this analysis. For the above mentioned reason, the building of predictable time series forcasting model requires connection and syncognition between historical and future statistics, in order to set up a dependent model between data obtained at present t and in the past t-1, t-2. If the connection X X X X t t t p t p t t q t q 1 1 2 2 1 1 is set up, we can generate an autoregressive integrated moving average (ARIMA) [15] model. This model is applicatable widely for its practical theory and intergrated into almost current statistical software such as Eviews, SPSS, matlab, R, and etc. It is, however, many real time sequencing shows that they do not change linearly. Therefore, model such as ARIMA does not suit. R. Parrelli pointed it out in [28] that there is a non-linerable connection in economic or financial time series variance indicators. The generalized autoregressive conditional heteroskedasticity (GARCH) [25,28] is the most popular non-linerable time series forecasting analysis to mention. The limitation of this model lies in the assumption that statistics vary in a fixed distribution (normally standard distribution), while actual statistics shows that distribution is statistically significant [39] (while standard distribution has a balanced variation). Another time series forecasting is Artificial Neural Network (ANN which was developed recently. ANN models do not based on deterministic distribution of statistics; instead it functions like human brain trying to find rules and pathes to training data, experimental testing, and result summarizing. ANN model is usually used for statistics classification purpose [23]. More recently, a new theory of statistical machine learning called Support Vector Machine (SVM) serving as answer to forcast and classification which caught attention of scientiests [36,11,31]. SVM is applied widely in many areas such as approximate function, regression analysis and forecast [11,31]. The biggest limitation of SVM is that with huge training files, it requires enomous calculation as awell as complexity of the linear regession exercise.

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