Time series modeling of tourist accommodation demand in Kenya

Tourism is a very important sector in the world economy and contributes significantly to foreign exchange earnings. Earnings from tourism in Kenya increased annually from Kenya Shillings 24.3 billion in 2001 to 73.7 billion in 2010 (ROK, 2012). The number of tourists coming into the country increased from 1,146,102 in the year 2003 to 1,822,885 in the year 2011. The major tourist zones in Kenya are: Nairobi, Beach, Mombasa, Coast Hinterland, Maasailand, Nyanza basin, Western, Central and North (ROK, 2012). These can further be reduced to three: Nairobi, Coastal and Others. Tourism in Kenya relies on many other sectors and industries, one of which is the hotel and accommodation. In order to enable these related industries match the specific accommodation needs for the tourists arriving in the country, there is needed a model that can forecast the accommodation demands by the tourists. This will make it possible for the hotel industry players to respond in good time to the anticipated changes in demand over time and also to maximize returns on investments. Seasonal variations are important in tourism and hospitality demands. The Box-Jenkins models for time series analysis allow the analyst to forecast future values of a series with only the past period’s data, without having some related variable’s data (Shumway and Stoffer, 2011). The authors therefore focused on the Box-Jenkins models to generate a forecasting model using quarterly data on bed occupancy by tourists visiting Kenya from 1974 to 2011. The SARIMA (1,1,2)(1,1,1)[4] model was found to be suitable for forecasting future quarterly demand on tourist accommodation in Kenya. This model shall therefore be useful to the tourism and related industries in forecasting future demands and maximize their returns on investment. Keywords: Tourist Accommodation Demand, Kenya Tourism Accommodation, Tourism Accommodation Modelin

SEMI-STOCHASTIC MIXTURE MODEL FOR PREDICTING THE RATE OF ROAD CARNAGES IN KENYA

In this paper we consider the problem of modeling and predicting the rate of road carnage in Kenya inthe presence of randomly changing road conditions. In the literature review, accident prediction ratemodels are typically regression models and discrete time series models. We study such models andexamine their strengths and weaknesses and propose a Semi-stochastic Mixture Model to describethe relation between the highway accidents and the road environment dynamics.The aim of theresearch paper is to propose a model that captures both the deterministic and stochastic nature ofroad parameters to explain the cause of high rate of road accidents in Kenya. We apply the proposedmodel to a simulated data set for the local condition. Our analysis from show that apart from annualaverage daily traffic (AADT), road curvature is an important component of road carnage.Keywords: Road system, Semi-stochastic mixture model, road curvature, road carnage,Simulation

Granger Causality and Error Correction Models in Economics: A Case study of Kenyan Market

The U.S. Dollar exchange rate and the interbank lending rate in Kenya are analyzed. An Error Correction Model (ECM) is used to establish if there exists any short term relationship between the lending and the exchange rates. A linear ECM is fitted and there is evidence that a short-term relationship exists between these two rates. A high threshold value exists at the second lag, an indication of simple smoothing in the data. The residual deviance is greater than the degrees of freedom confirming that the model perfectly fit to the data. This is supported by the high R2 value of 0.9308. A Granger Causality model is also built to demonstrate all the long term relationships. Contrary to hypothesis of the study, only the exchange rate granger caused interbank lending rate. This can be explained by the instability in the exchange market. It can be attributed to the economic crisis experienced in recent years; that is, an unexpected and sudden attainment of economic stability. The study concludes that Error Correction Models and Granger Causality models are significantly appropriate in analysing time series. It is suggested that a close track of exchange rates may lead to prediction of interbank lending rate movements. Further research is recommended on the factors influencing exchange rate movements and analysis of tail clustering.Keywords: Granger Causality, Error Correction Model, Economic

Effects of Customer Feedback on the Sustainability of Green Supply Chain System in the Floriculture Industry in Kenya

This is an empirical research with the overall objective of studying the sustainability of green supply chain systems in the floriculture industry in Kenya. The floriculture industry is a crucial sector in the country since it is a key export contributing a significant percentage of the Gross Domestic Product (GDP) and creates employment for tens of thousands of workers. There have, however, been pressing concerns in the country about the non-sustainability of green supply chain systems in the industry. This study focused on customer feedback as one of the study variables and employed survey design where a total of 127 flower farms were sampled; 14 during the pilot study and 113 during the main research. The data collection was done with the aid of questionnaires, observation guides and interviews. The resultant data was analyzed to test the hypotheses. The study, ultimately, came up with recommendations based on the research findings to solve the research problem. Key words: Customer Feedback, Green Supply Chain System, Floriculture, Sustainability

Application of Queuing Theory to Vehicular Traffic on Nakuru Total Road Stretch

 Nations strive to avoid losing revenue and human lives through long traffic snarl ups and frequent accidents on the roads. For this reason Considerations must be made to increase the number of lanes or even better to change from a single carriage to more robust dual carriages. However number of lanes and dual carriage alone serve no purpose for the accidents frequencies and traffic snarl ups that appear to defy even the most modern and sophisticated highway designs. Service time for traffic using such roads would need to be improved. Clearly therefore a numerical model is necessary for the road designers and developers to help understand road improvement demands. In this paper we establish the queue model for the Nakuru – Salgaa road Stretch and test the model with real data from the Case Study. Data is collected between the Soil- junction and the Total junction. We derive the arrival rate, service rate, utilization rate and the probability of Bulking using the M/M/1 queuing model. It is estimated that the arrival rate at the Soil- junction is 37 vehicles per minute and at total junction the service rate is 44 Vehicles per minute this does not march the dwindle service rates in section that are now black spots. The average number of vehicles on single road stretch is on average 15 per minute with some sections recording a high of 40 vehicles per minute and the utilization of the sections of stretch is on average 0.8. The benefit of performing the queue analysis for the road stretch is finally discussed and recommendations provided. 

Bayesian Hierarchical Spatial Modeling and Mapping of Adult Illiteracy in Kenya

Regional disparity in literacy levels must be addressed if Kenya is to achieve its international goals such as Education for All (EFA) and Millennium Development Goals (MDG). Literacy level in Kenya has been on the rise. However, the 2007 Kenya National Literacy Survey crude rates showed that on average 38.5 per cent (7.8 million) of Kenya’s adult population was illiterate with significant regional and gender variation. Bayesian binary logistic models (with and without CAR spatial and unstructured random effects)  are applied to the Kenya National Adult Literacy Survey (2007) data that was obtained from sampled 18000 households, 4782 in urban and 10914 in rural areas, to investigate spatial variation of illiteracy levels in Kenya. There were 15734 successful interviews that were comprised of 6493 were male and 9241 female The best fitted model was found to be the CAR model with age, sex, disability and awareness of adult literacy programs as the significant explanatory variables. Smoothed map of illiteracy from the best fitted model was then produced together with its corresponding confidence interval maps for regional variation in Kenya, in order to capture visual uncertainty in estimation. These maps can be used by policy makers to identify the pattern and tailor make programs appropriate for each region. Keywords: Illiteracy, Bayesian Hierarchical Models, Spatial modelin

Deriving Penalized Splines For Estimation Of Time Varying Effects In Survival Data

Abstract: The major interests of survival analysis are either to compare the failure time distribution function or to assess the effects of covariate on survival via appropriate hazards regression models. Cox’s proportional hazards model (Cox, 1972) is the most widely used framework, the model assumes that the effect on the hazard function of a particular factor of interest remains unchanged throughout the observation period (Proportionality assumption). For a continuous prognostic factor the model further assumes linear effect on the log hazard function (Linearity assumption). Assumptions that many authors have found to be questionable when violated since they may result to biased results and conclusions and as such non-linear risk functions have been suggested as the suitable models.In this paper, we propose a flexible method that models dynamic effects in survival data within the Cox regression framework. The method is based on penalized splines. The model offers the chance to easily verify the presenceof PH and timevariation. We provide a detailed analysis and derivation of the penalized splines in the context of survival data

GENERALISED MODEL BASED CONFIDENCE INTERVALS IN TWO STAGE CLUSTER SAMPLING

Chambers and Dorfman (2002) constructed bootstrap confidence intervals in model based estimation for finite population totals assuming that auxiliary values are available throughout a target population and that the auxiliary values are independent. They also assumed that the cluster sizes are known throughout the target population. We now extend to two stage sampling in which the cluster sizes are known only for the sampled clusters, and we therefore predict the unobserved part of the population total. Jan and Elinor (2008) have done similar work, but unlike them, we use a general model, in which the auxiliary values are not necessarily independent. We demonstrate that the asymptotic properties of our proposed estimator and its coverage rates are better than those constructed under the model assisted local polynomial regression model

NONPARAMETRIC MIXED RATIO ESTIMATOR FOR A FINITE POPULATION TOTAL IN STRATIFIED SAMPLING

We propose a nonparametric regression approach to the estimation of a finite population total in model based frameworks in the case of stratified sampling. Similar work has been done, by Nadaraya and Watson (1964), Hansen et al (1983), and Breidt and Opsomer (2000). Our point of departure from these works is at selection of the sampling weights within every stratum, where we treat the individual strata as compact Abelian groups and demonstrate that the resulting proposed estimator is easier to compute. We also make use of mixed ratios but this time not in the contexts of simple random sampling or two stage cluster sampling, but in stratified sampling schemes, where a void still exists