Abstract
This study derived estimates of missing values for bilinear time series models BL (p, 0, p, p) with normally distributed innovations 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 bilinear time series models BL (1, 0, 1, 1) 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 for BL (p, 0, p, p). The study recommends OLE estimates for estimating missing values for bilinear time series data with normally distributed innovations.
Highlights
A time series is data recorded sequentially over a specified time period
Estimates of missing values for pure bilinear time series models whose innovations have a Gaussian innovation were derived by minimizing the h-steps-ahead dispersion error
Simulation Results the results of the estimates obtained from the optimal linear estimate, artificial neural networks and exponential smoothing are presented
Summary
A time series is data recorded sequentially over a specified time period. There are cases where some observations that were supposed to be collected are not obtained and this result in missing values. Being unable to account for missing observation may result in a severe misrepresentation of the phenomenon under study. It can cause havoc in the estimation and forecasting of linear and nonlinear time series as in [3]. This problem can be overcome through missing value imputation. This study derived estimates of missing values for the bilinear time series models with normally distributed innovations. The missing values were derived using optimal linear interpolation techniques based on minimizing the hsteps-ahead dispersion error. Imputation can be considered to be an estimation or interpolation technique
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