Time series model building with Fourier autoregressive model

This paper presents time series model building using Fourier autoregressive models. This model is capable of modelling and forecasting time series data that exhibit periodic and seasonal movements. From the implementation of the model, FAR(1), FAR(2) and FAR(3) models were chosen based on the periodic autocorrelation function (PeACF) and periodic partial autocorrelation function. The coefficients of the tentative modelwere estimated using a discrete Fourier transform estimation method. The FAR(1) model was chosen as the optimal model based on the smallest value of periodic Akaike and Bayesian information criteria, and the residuals of the fitted models were diagnosed to be white noise using the periodic residual autocorrelation function. The out-sample forecasts were obtained for the Nigerian monthly rainfall series from January 2018 to December 2019 using the FAR(1) and SARIMA(1,1,1)x(1,1,1)₁₂ models. The results exhibited a continuous periodic and seasonal movement but the periodic movement in the forecasted rainfall series was better with FAR(1) because its values showed a close reflection of the original series. The values of the forecast evaluation for both models showed that the forecast was consistent and accurate but the FAR(1) model forecast was more accurate since its forecast evaluation values were relatively lower. Hence, the Fourier autoregressive model is adequate and suitable for modelling and forecasting periodicity and seasonality in Nigerian rainfall time series data and any part of the world with rainfall series that are mostly characterised with periodic variation

Comparative Analysis on the Diastolic Blood Pressure of Some Selected Age Groups in Ise-Emure Local Government, Ekiti State

This research work aimed to examine the comparative analysis on the diastolic blood pressure of some selected age group in Ise-Emure Local Government, Ekiti State. The data used for this research work covered the age group between 20 years and above with record of Diastolic blood pressure and patients ages of forty (40) people in Ise-Emure Local Government, Ekiti State. The data used for this research work was secondary which was extracted from the surveyed record of laboratory test department of general hospital, Ise-Emure Local Government, Ekiti State. From the graph, the diagram showed that, as the age increases so also the diastolic blood pressure rises at a slowly manner. The result of the analysis carried out using SPSS from the data revealed that the Pearson’s correlation coefficient computed to be 16r=0.470 "> , which implies  that there is steady relationship between Age and Diastolic blood pressure of the patients at general hospital Ise-Emure, Ekiti.. From the analysis we observed that the p-value (0.002) is less than the alpha level (0.05), of which we reject Ho. Under the test for independence, the 16tcalculated">  was computed to be 163.28">  while that of corresponding 16ttabulated">  was observed to be 1.686, of which 16tcalculated>ttabulated"> , by comparison  16H0">  was rejected. Keywords: Diastolic Blood Pressure, Survey, Hypertension, Pearson Correlation Coefficient, Comparison, Association, Hypothesis, Patients. DOI: 10.7176/JHMN/95-11 Publication date: November 30th 202

PREDICTING PETROLEUM CONSUMPTION USING TRIGONOMETRIC REGRESSION MODEL

This study is used to model and forecast Nigerian motor gasoline consumption using the Trigonometric Regression model which has the capabilities of handling nonlinear time series. The time plot of Nigerian motor gasoline consumption showed the series is nonlinear. The Trigonometric regression model was estimated using the Ordinary Least Square method. From the result, the coefficients of the model influenced Nigerian motor gasoline consumption and a unit increase may lead to an increase or decrease. The values of coefficient of determination (R^2) revealed that the coefficients of the model explained the variations in Nigerian motor gasoline consumption up to 83%. The value of the adjusted coefficient of determination (R ̅^2 ) also revealed that the model is a good fit and has high predictive power. Therefore, the Nigerian motor gasoline consumption forecast from 1980 to 2038 indicated continuous fluctuations from year to year. The shape of the out-sample forecast from 2019 to 2038 exhibited a bell shape. Conclusively, based on the results obtained, the proposed model can be used to obtain future values for Nigerian motor gasoline consumption. This will enhance the Government and shareholders to put in place proper plans and logistics to curtail the challenges that may arise from Nigerian motor gasoline consumption and distribution presently and in the future

ANALYSIS OF NIGERIA GROSS DOMESTIC PRODUCT USING PRINCIPAL COMPONENT ANALYSIS

Nigeria is classified as a mixed economy emerging market, and has already reached middle income status according to the World Bank, with its abundant supply of natural resource, well developed financial, legal, communications, transport sectors and stock exchange which is the second largest in Africa. The main purpose of this research is to build a model that can capture the best variables that predict the Gross Domestic Product (GDP) of Nigeria. Correlation matrix was used to know the degree of relationship that exists between the pairs of predictors of GDP. The principal component analysis was employed to reduce the multidimensional data. Scree plot was used to determine the spread of the trend of the components and bi plot was used to determine the degree of closeness of Agriculture, oil Export, External Reserves, Exchange Rate, Transportation, Education, and Communication. There is a strong relationship between pairs of Agriculture, oil Export, External Reserves, Exchange Rate, Transportation, Education, and Communication. The proportion of variance accounted for by the first component is 92%. This implied that only component 1 is sufficient to explain GDP. The Scree plot showed that the best component is component 1. The bi plot showed that Agriculture, oil Export, External.Reserves, Exchange.Rate, Transportation, Education, and Communication are closely related and stand as good predictors of GDP

MODELLING NIGERIA POPULATION GROWTH RATE

Thomas Robert Malthus Theory of population highlighted the potential dangers of over population. He stated that while the populations of the world wouldincrease in geometric proportions, the food resources available for them would increase in arithmetic proportions. This study was carried out to find the trend, fit a model and forecast for the population growth rate of Nigeria.The data were based on the population growth rate of Nigeria from 1982 to 2012 obtained from World Bank Data (data.worldbank.org). Both time and autocorrelation plots were used to assess the Stationarity of the data. Dickey-Fuller test was used to test for the unit root. Ljung box test was used to check for the fit of the fitted model. Time plot showed that the random fluctuations of the data are not constant over time. There was an initial decrease in the trend of the growth rate from 1983 to 1985 and an increase in 1986 which was constant till 1989 and then slight fluctuations from 1990 to 2004 and a general increase in trend from 2005 to 2012. There was a slow decay in the correlogram of the ACF and this implied that the process is non stationary. The series was stationary after second differencing, Dickey-Fuller = -4.7162, Lag order = 0, p-value = 0.01 at a= 0.05. The p-value (0.01) and concluded that there is no unit root i.e the series is stationary having d=2. Correlogram and partial correlogram for the second-order differenced data showed that the ACF at lag 1 and lag 5 exceed the significant bounds and the partial correlogram tailed off at lag 2.The identified order for the ARIMA(p,d,q) model was ARIMA(2,2,1). The estimate of AR1 co-efficient =1.5803 is observed to be statistically significant but the estimated value does not conforms strictly to the bounds of the stationary parameter hence was excluded from the model. =-0.9273 is observed to be statistically significant and conformed strictly to the bounds of the stationary parameter , hence was maintained in the model. The estimate of MA1 co-efficient = - 0.1337 was observed to be statistically significant conformed strictly to the bounds of the parameter invertibility. For ARIMA (2, 2, 0) the estimate of AR1 co-efficient =1.5430 was observed to be statistically significant and not conformed strictly to the bounds of the parameter stationary, hence excluded from the model. The estimate of AR 2 co-efficient=-0.9000 is observed to be statistically significant and conformed strictly to the bounds of the parameter stationary, hence retained in the model. The ARIMA (2, 2, 0) is considered the best model. It has the smallest AIC. The Ljung test showed that residuals are random and  implies that the model is fit enough for the data. The forecast Arima function gives us a forecast of the Population Growth Rate in the next thirty eight (38) years, as well as 80% and 95% prediction intervals for those predictions i.e up to 2050