Imputation Of Missing Values For Bilinear Time Series Models

Missing observations is a common occurrence in data collection. To solve this problem, researchers have developed missing value imputation techniques for some linear and nonlinear time series models with normal and stable innovations using estimating function criterion. This criterion does not take into consideration the distribution of the innovation sequence of the time series model. Therefore the aim of this study was to develop explicit optimal linear estimators of missing values for several classes of bilinear models whose innovation sequences are governed by the normal, student-t and generalized autoregressive heteroscedasticity using the minimum dispersion error criterion. For comparison purposes, estimates based on artificial neural networks and exponential smoothing were also obtained. Data was generated using the R statistical software. 100 samples of size 500 each were simulated for different bilinear time series models. In each sample, artificial missing observations were created randomly at points 48, 293 and 496 and estimated. The mean squared error was used to measure the efficiency of the estimates. The study found that the efficiency of the estimates was correlated with the probability distribution of the innovation sequence. Optimal linear estimates were the most efficient estimates when the models had normal and student-t innovations. However, for bilinear models with generalized autoregressive heteroscedasticity innovations, the artificial neural network estimates were the most efficient. The study recommends the use of optimal linear estimates for bilinear models with either normal or student-t errors. When the data is bilinear with generalized autoregressive heteroscedasticity errors, artificial neural network estimates are preferred. These findings can be used by econometricians in developing more accurate models.