Imputation of Missing Values for Pure Bilinear Time Series Models with Normally Distributed Innovations

Poti Owili Abaja^1, , Dankit Nassiuma² and Luke Orawo³

¹Mathematics and Computer Science Department, Laikipia University, Nyahururu, Kenya

²Mathematics Department, Africa International University, Nairobi

³Mathematics Department, Egerton University, Private Bag, Egerton-Njoro, Nakuru, Kenya

Cite this paper:
Poti Owili Abaja, Dankit Nassiuma and Luke Orawo. Imputation of Missing Values for Pure Bilinear Time Series Models with Normally Distributed Innovations. American Journal of Applied Mathematics and Statistics. 2015; 3(5):199-205. doi: 10.12691/ajams-3-5-4

Abstract

In this study, estimates of missing values for bilinear time series models with normally distributed innovations were derived by minimizing the h-steps-ahead dispersion error. For comparison purposes, missing value estimates based on artificial neural network (ANN) and exponential smoothing (EXP) techniques were also obtained. Simulated data was used in the study. 100 samples of size 500 each were generated for different pure bilinear time series models using the R-statistical software. In each sample, artificial missing observations were created at data positions 48, 293 and 496 and estimated using these methods. The performance criteria used to ascertain the efficiency of these estimates were the mean absolute deviation (MAD) and mean squared error (MSE). The study found that optimal linear estimates were the most efficient estimates for estimating missing values. Further, the optimal linear estimates were equivalent to one step-ahead forecast of the missing value. The study recommends OLE estimates for estimating missing values for pure bilinear time series data with normally distributed innovations.

Keywords:
optimal linear interpolation simulation MAD innovations ANN exponential smoothing

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