The optimization of a model that expresses time series data is a problem associated with the development of a regression model. This is a two-step optimization problem where the order of past data used in the regression model (number of orders of the solution space) is decided, and weighted coefficients for observed data at each point in time (design variables) are determined. Such a two-step optimization problem cannot calculate the evaluation function after the model is developed despite the fact that design variables cannot be determined during the second step until the orders of solution space are determined in the first step. Thus, it is a problem where simultaneous optimization of both the first and second steps is difficult. However, the self-regressing hidden Markov model requires a large amount of calculation during design variable determination due to the use of the hidden Markov. For such an optimization problem, this study proposes an actual-value genetic algorithm (GA) with a framework capable of simultaneous optimization. The proposed method takes an approach where in individuals that represent the solution space of different orders in the same group are generated. Further, it retains individuals with an order that has a large number of good solutions at a high probability through the transition of the generations. Numerical tests will involve performance validation using estimated artificial data of several states, realized volatility (RV) of the stock, and artificial as well as actual data of inbound visitors to Japan, and they will demonstrate that the optimization of the regression model by the proposed method is more effective than that by the conventional method.
