Modelling and Forecasting Climate Time Series with State-Space Model

This study modelled and estimated climatic data using the state-space model. The study was specifically to identify the pattern of the trend movement i.e., increase or decrease in the occurrence of the climatic change; to use of Univariate Kalman Filter for the computation of the likelihood function for climatic projections; to modelling the climatic dataset using the state-space model and to assess the forecasting power of the state-space models. The data used for the work includes temperature and rainfall for periods January 1991 to December 2017. The data are tested for normality. Shapiro-Wilk, Anderson-Darling and Kolmogorov-Smirnov test of normality for the climatic data all showed that the variables are not normally distributed. The work spans the use of breaking trend regression model to fit climatic data to estimate the slopes which show much increase in climatic data has been recorded from the initial time data collection until the present. Investigations and diagnostic are carried out by checking for corrections in the residuals and also checking for periodicity in the residuals. The results of this investigation show significant autocorrelation in the residuals indicating the presence of underlying noise terms which is not accounted for. By treating the residual as an autoregressive moving average (ARMA) process whereby we can obtain its spectral density, the result from the parametric spectral estimate shows underlying periodic patterns for monthly data, thus, leads to a discussion on the need to treat climatic data as a structural time series model. We select appropriate models by considering the goodness of fit of the model by comparing the Akaike information criterion (AIC) values. Parameters are estimated and accomplished with some measures of precision

Vector Autoregressive Modeling of COVID-19 Incidence Rate in Nigeria

With the outbreak of COVID-19, a lot of studies have been carried out in various science disciplines to either reduce the spread or control the increasing trend of the disease. Modeling the outbreak of a pandemic is pertinent for inference making and implementation of policies. In this study, we adopted the Vector autoregressive model which takes into account the dependence that exists between both multivariate variables in modeling and forecasting the number of confirmed COVID-19 cases and deaths in Nigeria. A co-integration test was carried out prior to the application of the Vector Autoregressive model. An autocorrelation test and a test for heteroscedasticity were further carried out where it was observed that there exists no autocorrelation at lag 3 and 4 and there exists no heteroscedasticity respectively. It was observed from the study that there is a growing trend in the number of COVID-19 cases and deaths. A Vector Autoregressive model of lag 4 was adopted to make a forecast of the number of cases and death. The forecast also reveals a rising trend in the number of infections and deaths. The government therefore needs to put further measures in place to curtail the spread of the virus and aim towards flattening the curve

Ridge Estimation’s E�ectiveness for Multiple Linear Regression with Multicollinearity: An Investigation Using Monte-Carlo Simulations

The goal of this research is to compare multiple linear regression coe�cient estimation technique with multicollinearity. In order to quantify the e�ectiveness of estimations by the mean of average mean square error, the ordinary least squares technique (OLS), modified ridge regression method (MRR), and generalized Liu-Kejian method (LKM) are compared with the Average Mean Square Error (AMSE). For this study, the simulation scenarios are 3 and 5 independent variables with zero mean normally distributed random error of variance 1, 5, and 10, three correlation coe�cient levels; i.e., low (0.2), medium (0.5), and high (0.8) are determined for independent variables, and all combinations are performed with sample sizes 15, 55, and 95 by Monte Carlo simulation technique for 1,000 times in total. As the sample size rises, the AMSE decreased. The MRR and LKM both outperformed the OLS. At random error of variance 10, the MRR is the most suitable for all circumstance

Analysis of Reported Cases of Diabetes Disease in Nigeria: A Survival Analysis Approach

The goal of this study is to look at the survival time distribution for diabetes patients at the National Hospital Abuja, taking into account a variety of variables. The Kaplan Meierestimator indicated that there is no statistically significant difference in the distribution of survival time by sex, despite the fact that married patients were seen to live longer than single patients. Patients in urban and rural areas had the same estimated survival distribution after testing. It is observed that the Cox proportional model was significant when tested since the pvalue = 0.000 was less than the 0.05 threshold. The distribution of survival time for patients with diabetes is shown to be substantially different for patients of the four age categories included in the study, indicating that the relative risk of patients is based on age. Every patient is predicted to acquire the danger at about the same time, with no sex-related multiplication impact. It was found out that the disease's prevalence is unaffected by several of the variables studied, indicating that more regular medical checks are required