Rainfall is of critical importance for many people, particularly those whose livelihoods depend on rain-fed agriculture. Predicting the trend of rainfall is a difficult task, and statistical approaches such as time series analysis provide a means for predicting the patterns of rainfall. The models also offer the potential to improve areas such as increased food production, profitability, and improved food security policing. However, these forecasts and information systems may, in some instances, not be suitable for direct use by stakeholders in their decision-making. The objective of this study was to investigate rainfall variability and develop a Seasonal Auto-Regressive Integrated Moving Average (SARIMA) model for fitting the monthly rainfall using time series data. Secondary monthly data from 1998 to 2017 for Embu County was collected from the Kenya Meteorological Department, Embu and recorded into an excel sheet. R-software was utilized to analyse data for descriptive statistics, rainfall variability, and model fitting. The coefficient of variation for annual and seasonal rainfall was calculated. The Box Jenkin's ARIMA modelling procedure (model identification, model estimation, model validation) was used to determine the best models for the data. The main study findings indicated the existence of annual variability of 34%, March-April-May rainfall variability of 44%, and October-November-December variability of 44%. A first-order differenced SARIMA (1, 1, 1) (0, 1, 2)12 model with an AIC score of 9.99356 was found suitable for predicting rainfall pattern in Embu, County. The study outcome revealed that Embu County experiences high seasonal and rainfall variation of rainfall, thus requires a reliable model for better prediction.

Price forecasting is more sensitive with vegetable crops due to their high nature of perishability and seasonality and is often used to make better-informed decisions and to manage price risk. This is achievable if an appropriate model with high predictive accuracy is used. In this paper, Seasonal Autoregressive Integrated Moving Average (SARIMA) model is developed to forecast price of tomatoes using monthly data for the period 1981 to 2013 obtained from the Ministry of Agriculture, Livestock and Fisheries (MALF) in the agribusiness department. Forecasting tomato prices was done using time series monthly average prices from January 2003 to December 2016. SARIMA (2, 1, 1) (1, 0, 1) 12 was identified as the best model. This was achieved by identifying the model with the least Akaike Information Criterion. The parameters were then estimated through the Maximum Likelihood Estimation method. The time series data of Tomatoes for wholesale markets in Nairobi are considered as the national average. The predictive ability tests RMSE = 32.063, MAPE = 125.251 and MAE = 22.3 showed that the model was appropriate for forecasting the price of tomatoes in Nairobi County, Kenya.

Fertility is one of the major elements in population dynamics that has the highest significant contribution towards population size and structure in the world. In Kenya, fertility levels have been on the decline from approximately 8.1 children in 1979 to 3.9 children in 2014 but still, it is considered high compared to the country's target of 2.6 by 2030. This has potentially negative consequences to the economic growth and development of a country. The main objective of this study is to determine demographic, socio-economic and cultural factors that explain fertility differential among poor women of childbearing age. A binary logistic regression model was fitted to DHS 2014 data using SPSS Version16. The total number of women in childbearing age is based on 7,262 women who have at least one child and whose age ranges from 15 to 49 years. The majority of women were married 4685 (64.5%), followed by never and formally married 1522 (21.0%) and living with partner 1055 (14.5%) respectively). In the analyses, all the variables Region, women educational level, marital status, age at first marriage and age in 5-years group were found to have a significant effect on the total number of children ever born at a significance level of 5%. From the fitted logistic regression model, the estimated odds ratio for the variable region reference category is Nyanza/Western region. The value of the odds ratio exp(β) =1.060775, for the region that the odds of having TCEB greater than or equals to five children for the North Eastern region has 6.0775% more than women in Nyanza/Western Region (OR=1.060775, C.I=0.873716-1.287883) and its effect is statistically significant.