This research was set to examine the effect Multicollinearity has, on the standard error for regression coefficients when it is present in a Classical Linear Regression model (CLRM 84.472, 191.715,502.179 and 675.633
Inferences on the parameter estimates of Ordinary Least Square (OLS) estimator in regression model when regressors exhibit multicollinearity is a problem in that large standard errors of the regression coefficients which cause low t-statistic value often result into the acceptance of the null hypothesis. This paper, therefore, makes efforts to investigate the effect of multicollinearity on the power rates of the OLS estimator. A regression model with constant term (β 0 ) and two independent variables (with (β 1 and (β 2 as their respective regression coefficients) that exhibit multicollinearity was considered. A Monte Carlo study of 1000 trials was conducted at eight levels of multicollinearity (0, 0.25, 0.5, 0.7, 0.75, 0.8, 0.9 and 0.99) and sample sizes (10, 20, 40, 80, 100, 150, 250 and 500). At each specification, the true regression coefficients were set at unity while 1.5, 2.0 and 2.5 were taken as their hypothesized values. Results show that at each hypothesized value of β 0 the power rate is the same at all the levels of multicollinearity at a specified sample size and that the error rate decreases asymptotically. Furthermore as the hypothesized value increases, results do not only show that the power rate increases but tends faster to one asymptotically. The pattern of effect of power rate of β 1 and β 2 is the same as that of β 0 except that at each hypothesized value the power rate decreases as level of multicollinearity increases at a specified sample size. Consequently, increasing the sample size increase the power rate of the OLS estimator in all the levels of multicollinearity.
Most frequently used models for modeling and forecasting periodic climatic time series do not have the capability of handling periodic variability that characterizes it. In this paper, the Fourier Autoregressive model with abilities to analyze periodic variability is implemented. From the results, FAR(1), FAR(2) and FAR(2) models were chosen based on Periodic Autocorrelation function (PeACF) and Periodic Partial Autocorrelation function (PePACF). The coefficients of the tentative model were estimated using a Discrete Fourier transform estimation method. FAR(1) models were chosen as the optimal model based on the smallest values of Periodic Akaike (PAIC) and Bayesian Information criteria (PBIC). The residual of the fitted models was diagnosed to be white noise. The in-sample forecast showed a close reflection of the original rainfall series while the out-sample forecast exhibited a continuous periodic forecast from January 2019 to December 2020 with relatively small values of Periodic Root Mean Square Error (PRMSE), Periodic Mean Absolute Error (PMAE) and Periodic Mean Absolute Percentage Error (PMAPE). The comparison of FAR(1) model forecast with AR(3), ARMA(2,1), ARIMA(2,1,1) and SARIMA( 1,1,1)(1,1,1)12 model forecast indicated that FAR(1) outperformed the other models as it exhibited a continuous periodic forecast. The continuous monthly periodic rainfall forecast indicated that there will be rapid climate change in Nigeria in the coming yearly and Nigerian Government needs to put in place plans to curtail its effects.
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