On the Appropriate Transformation Technique and Model Selection in Forecasting Economic Time Series: An Application to Botswana GDP Data

Selected data transformation techniques in time series modeling are evaluated using real-life data on Botswana Gross Domestic Product (GDP). The transformation techniques considered were modified, although reasonable estimates of the original with no significant difference at α = 0.05 level were obtained: minimizing square of first difference (MFD) and minimizing square of second difference (MSD) provided the best transformation for GDP, whereas the Goldstein and Khan (GKM) method had a deficiency of losing data points. The Box-Jenkins procedure was adapted to fit suitable ARIMA (p, d, q) models to both the original and transformed series, with AIC and SIC as model order criteria. ARIMA (3, 1, 0) and ARIMA (1, 0, 0) were identified, respectively, to the original and log of the transformed series. All estimates of the fitted stationary series were significant and provided a reliable forecast

Specification of Periodic Autocovariance Structures in the Presence of Outliers

This paper focuses on the specification of periodic autocovariance structures in the presence of outliers, we evaluate autocovariance structures using various outliers' generating models. The analytical results indicate that outliers affect the estimates of periodic autocovariance function (PACVF) due to biases and inflated standard errors. Robust autocovariance structures that accommodate the influence of outliers in different periodic processes are proposed. We fit AR (1) model using both the conventional and Jacknife autocovariance structures; the latter shows high precision in the standard errors of the estimates. We demonstrate our proposed methodology with the precipitation data from Maun Airport in Botswana, and the empirical study supports our theoretical findings

Smooth Transition GARCH Models in Forecasting Non-Linear Economic Time Series Data

The need to capture the heterogeneous and volatility nature of both financial and economic time series theory and modeling their behavior in practical work have stimulated interest in the empirical modeling of variances which forms the basis for this study. In the study we augmented GARCH models with smooth transition model by dropping the assumption of autoregression of the model; necessary theoretical frame work was derived and properties of the new model established and illustrated with foreign exchange rate data from Federal Republic of Nigeria (Naira), Great Britain (Pound), Botswana (Pula) and Japanese (Yen) against United States of America (Dollar). The smooth transition GARCH model is better than the classical GARCH model as there were reduction in the variances of the augmented model; this claim is confirmed by the empirical illustration with foreign exchange data. Within the group of smooth transition GARCH model, Logistic Smooth Transition is adjudged the best as it produced the least variance

Linear Cholesky decomposition of covariance matrices in mixed models with correlated random effects

Modelling the covariance matrix in linear mixed models provides an additional advantage in making inference about subject-specific effects, particularly in the analysis of repeated measurement data, where time-ordering of the responses induces significant correlation. Some difficulties encountered in these modelling procedures include high dimensionality and statistical interpretability of parameters, positive definiteness constraint and violation of model assumptions. One key assumption in linear mixed models is that random errors and random effects are independent, and its violation leads to biased and inefficient parameter estimates. To minimize these drawbacks, we developed a procedure that accounts for correlations induced by violation of this key assumption. In recent literature, variants of Cholesky decomposition were employed to circumvent the positive definiteness constraint, with parsimony achieved by joint modelling of mean and covariance parameters using covariates. In this article, we developed a linear Cholesky decomposition of the random effects covariance matrix, providing a framework for inference that accounts for correlations induced by covariate(s) shared by both fixed and random effects design matrices, a circumstance leading to lack of independence between random errors and random effects. The proposed decomposition is particularly useful in parameter estimation using the maximum likelihood and restricted/residual maximum likelihood procedures

An approximation to the optimal subsample allocation for small areas

This paper develops allocation methods for stratified sample surveys in which small area estimation is a priority. We assume stratified sampling with small areas as the strata. Similar to Longford (2006), we seek efficient allocation that minimizes a linear combination of the mean squared errors of composite small area estimators and of an estimator of the overall mean. Unlike Longford, we define mean-squared error in a model-assisted framework, allowing a more natural interpretation of results using an intra-class correlation parameter. This allocation has an analytical form for a special case, and has the unappealing property that some strata may be allocated no sample. We derive a Taylor approximation to the stratum sample sizes for small area estimation using composite estimation giving priority to both small area and national estimation

Time Series Model for Predicting the Mean Death Rate of a Disease

This study develops a time series model to estimate the mean death rate of either an emerging disease or re-emerging disease with a bilinear induced model. The estimated death rate converges rapidly to the true parameter value for a given mean death at time t. The derived model could be used in predicting the m-step future death rate value of a given disease. We illustrated the new concept with real life data