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.

Modeling the onset of a pandemic is important for forming inferences and putting measures in place. In this study, we used the Vector autoregressive model to model and forecast the number of confirmed covid-19 cases and deaths in Nigeria, taking into account the relationship that exists between both multivariate variables. Before using the Vector Autoregressive model, a co-integration test was performed. An autocorrelation test and a heteroscedasticity test were also performed, and it was discovered that there is no autocorrelation at lags 3 and 4, as well as no heteroscedasticity. According to the findings of the study, the number of covid-19 cases and deaths is on the rise. To forecast the number of cases and deaths, a Vector Autoregressive model with lag 4 was used. The projection likewise shows a steady increase in the number of deaths over time, but a minor drop in the number of confirmed Covid-19 cases.

The most often used distribution in statistical modeling follows Gaussian distribution. But many real-life time series data do not follow normal distribution and assumptions; therefore, inference from such a model could be misleading. Thus, a reparameterized non-Gaussian Autoregressive (NGAR) model that has the capabilities of handling non-Gaussian time series was proposed, while Anderson Darling statistics was used to identify the distribution embedded in the time series. In order to determine the performance of the proposed model, the Nigerian monthly exchange rate (Dollar-Naira Selling Rate) was analyzed using proposed and classical autoregressive models. The proposed model was used to determine the joint distribution of the observed series by separating the marginal distribution from the serial dependence. The maximum Likelihood (MLE) estimation method was used to obtain an optimal solution in estimating the generalized gamma distribution of the proposed model. The selection criteria used in this study were Akaike Information Criterion (AIC). The result revealed through the value of the Anderson Darling statistics that the data set were not normally distributed. The best model was selected using the minimum values of AIC value. The study concluded that the proposed model clearly shows that the non-Gaussian Autoregressive model is a very good alternative for analyzing time series data that deviate from the assumptions of normality and, in particular, for the estimation of its parameters.