eng
Science and Education Publishing
American Journal of Applied Mathematics and Statistics
2328-7292
2015-10-21
3
5
199
205
10.12691/ajams-3-5-4
AJAMS2015354
article
Imputation of Missing Values for Pure Bilinear Time Series Models with Normally Distributed Innovations
Poti Owili Abaja
abajapoti @gmail.com
1
Dankit Nassiuma
2
Luke Orawo
3
Mathematics and Computer Science Department, Laikipia University, Nyahururu, Kenya
Mathematics Department, Africa International University, Nairobi
Mathematics Department, Egerton University, Private Bag, Egerton-Njoro, Nakuru, Kenya
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.
http://pubs.sciepub.com/ajams/3/5/4/ajams-3-5-4.pdf
optimal linear interpolation
simulation
MAD
innovations
ANN
exponential smoothing