Time Series of Rainfall Model with Markov Switching Autoregressive

Abstract

The intensity of rainfall can sometimes change due to seasonal changes, extreme weather changes or weather effects in other areas around a particular location. The changes of rainfall can be categorized as a change in structure or condition that often occur in time series data, it be influenced by an unobserved random variable, that is called as a state. Then structural change of rainfall can be modeled by using Markov Switching Autoregressive (MSAR) as the result from merging the Markov chain and the classic Autoregressive model in the data mining analysis. Therefore, this study will determine the best model for rainfall at the specific hilly location but close to the shore of the Indian Ocean, that is Limau Manis sub-district of Padang city, this is to obtain the probability of displacement and survival of a state, and the amount of suspected duration of each state. The rainfall data are defined in two states of rainfall condition, high rainfall and low rainfall. The best model MSAR is obtained as MS(2)-AR(2) with the probability of transition from state high rainfall to high rainfall has 0.84379, state high rainfall to state low rainfall has 0.15621, state low rainfall to state low rainfall has 0.37516 and state low rainfall to state high rainfall has 0.62485. While the expected duration of high rainfall is 6.40161 months and the expected duration of low rainfall is 1.60039 months. This result confirms that the high rainfall duration is longer than the low rainfall duration which is very specific intensity of rainfall at the selected location.