Robust-M new two-parameter estimator for linear regression models: Simulations and applications

In the presence of multicollinearity and outliers, the ordinary least squares estimator remains inconsistent and unreliable. Several estimators have been proposed that can co-handle the problems of multicollinearity and outliers simultaneously. However, there is still a need to explore some other robust methods when the two anomalies appear in the linear regression model and recommend it to end users of statistics. Therefore, this study proposed Robust-M New Two Parameter (RNTP) and examined its performance over some already existing ones in the presence of multicollinearity and outliers in the x-direction. The theoretical expression under some conditions was established to showcase the new estimator's superiority. A simulation study was carried out alongside some factors to show that the RNTP is better than all other estimators considered in the study. The simulation study results revealed that RNTP outperformed other estimators in the study using the minimum MSE as the criterion. Likewise, real-life data was applied to affirm this claim

Time Series Analysis of Nigeria External (Foreign) Reserves

Economy of a country can absorb shock and as well boost confidence through external reserves. Hence, external reserves play an important role to the extent that it helps in stabilizing the country’s economy. This study focuses on modeling the Nigeria external reserves using time series technique. 30-year data were extracted from the Central Bank of Nigeria (CBN) bulletin from 1990 – 2019. Some economic tools used to diagonize the data are Augmented Dickey Fuller (ADF) test, unit root tests Kwaitkowshi – philips – Schmiot – Shin test in order to ascertain the stationary of the data. Meanwhile, Auto Regression Integrated Moving Average (ARIMA) model was used as model for prediction whereby Akaike Information Criterion (AIC) and Hannan-Quinn Information Criterion (HQIC) were used as model diagnostic checking. At original level, the data showed an upward trend and found out to be non-stationary. When further examined using the diagnostic economic tools, at first difference the data were found to maintain a state of equilibrium. Also, model diagnostic checking revealed that ARIMA (2,1,7) was found to be the appropriate optimal model and thereby used for forecast for the next five years. Hence, the forecasted values revealed that the Nigeria external reserves will continue to increase steadily. Consequently, government should put in place legal policies that will enhance, increase accumulation and proper management of external reserves