State Space Modeling of Switching Time Series
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In various fields of scientific research, it is possible to find time series data that cannot be adequately dealt with by using an ordinary linear Gaussian model. As seen in examples such as the concentration of hormone in the blood, electric potential of the nerve, and river-flow rate, such data exhibiting distinct pulse-shaped patterns can be taken as typical exemplification. Analysis using an input-output model can be made, provided that the input data including pulses is known and induces the pulses in the output. For example, Ozaki (1985) identified the changes in river-flow as the output of a non-linear system with the amount of rainfall as the input, and has been successful in predicting the river-flow rate. However, when the input data are not available, an alternative method is required.
KeywordsTime Series Luteinizing Hormone Stochastic Differential Equation State Space Modeling Luteinizing Hormone Level
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