Comparison of Some Estimation Methods of Missing Data in Hidden Markov Model
Oluwatoyin Dairo
Department of Statistics, University of Lagos, Akoka, Lagos, Nigeria.
Sheriffdeen Taiwo Oyeyemi *
Department of Research, Planning and Statistics, The Medical Rehabilitation Therapists (Reg.) Board of Nigeria, Nigeria.
Arowolo, O.T
Department of Mathematical Science, Lagos State University of Science and Technology, Ikorodu, Lagos, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This study compares four methods, Mean Imputation (MI), Median Imputation (MDI), Linear Interpolation (LI), and Kalman Filter Algorithm (KAL), for estimating missing values in time series data using Hidden Markov Models (HMM). The evaluation is based on accuracy measures: Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). The findings reveal that KAL outperforms other methods across all sample sizes under linear trend structures. On the other hand, MDI performs best under quadratic and exponential trend structures. HMMs were applied to the estimated series with MDI and KAL and compared with actual series models. The Akaike Information Criterion (AIC) values of the models for series with 12% missingness show minimal divergence from those of the actual series. This study underscores the importance of selecting suitable estimation methods tailored to specific trend structures in time series analysis.
Keywords: State space, stochastic process, missing values, estimation, variable