Univariate Time-Series Analysis of Second-Hand Car Importation in Zambia

Zambia largely depends on the international second-hand car (SHC) market for their motor vehicle supply. The importation of Second hand Cars in Zambia presents a time series problem. The data used in this paper is monthly data on SHC importation from 1st January, 2014 to 31st December, 2016. Data was analyzed using Exponential Smoothing (ES) and Autoregressive Integrated Moving Average (ARIMA) models. The results showed that ARIMA (2, 1, 2) was the best fit for the SHC importation since its errors were smaller than those of the SES, DES and TES. The four error measures used were Root-mean-square error (RMSE), Mean absolute error (MAE), Mean percentage error (MPE) and Mean absolute percentage error (MAPE). The forecasts were also produced using the ARIMA (2, 1, 2) model for the next 18 months from January 2017. Although there is percentage increase of 90.6% from November 2015 to December 2016, the SHC importation generally is on the decrease in Zambia with percentage change of 59.5% from January 2014 to December 2016. The forecasts also show a gradual percentage decrease of 1.12% by June 2018. These results are more useful to policy and decision makers of Government departments such as Zambia Revenue Authority (ZRA) and Road Development Agency (RDA) in a bid to plan and execute their duties effectively.

Forecasting Inflation Rate of Zambia Using Holt’s Exponential Smoothing

In this paper, the Holt’s exponential smoothing and Auto-Regressive Integrated Moving Average (ARIMA) models were used to forecast inflation rate of Zambia using the monthly consumer price index (CPI) data from May 2010 to May 2014. Results show that the ARIMA ((12), 1, 0) is an adequate model which best fits the CPI time series data and is therefore suitable for forecasting CPI and subsequently the inflation rate. However, the choice of the Holt’s exponential smoothing is as good as an ARIMA model considering the smaller deviations in the mean absolute percentage error and mean square error. Moreover, the Holt’s exponential smoothing model is less complicated since you do not require specialised software to implement it as is the case for ARIMA models. The forecasted inflation rate for April and May, 2015 is 7.0 and 6.6 respectively.

Game Ranching: A Sustainable Land Use Option and Economic Incentive for Biodiversity Conservation in Zambia

The ten provinces of Zambia were surveyed to determine number and size of game ranches situated in these areas up to the end of 2012/early 2013. Three classes of game ranches were developed as;1) ≥500 hectares as game ranch proper, 2) ≥50 - <500 hectares as game farm, and 3) <50 hectares as ornamental. A total of 200 game ranches keeping large mammals from the size of common duiker to eland were recorded with a growth rate of 6 per year for the period 1980-2012. The largest number was ornamental 98 (49%);large game ranches were 75 (38%) and the least was game farms 27 (14%). Thirty seven species of large mammals were recorded, of which, 15 were the most abundant with impala topping the list with 21,000 individuals (34%). It was found that of the ten provinces, Luapula, Western and Northern Provinces despite being largely rural with low population densities except for Luapula did not have any game ranch. The province with the largest number was Lusaka 71(36%), Southern 59 (30%), Central 31(16%), Copperbelt 19 (10%), Eastern and Northwestern 9 (4.5% each) and Muchinga was the least with 2 (1%). The rapid increase in the number of ornamental category is mainly attributed to the rise in the development of tourist accommodation facilities and high cost residential properties. This growth provides an opportunity to convert to game ranching schemes abandoned farmlands which are not currently useful to agriculture due to loss of fertility and other forms of land degradation. Similarly, parcels of land with natural ecological limitations should also be considered for such schemes. Rehabilitation of degraded land through ranching could also enhance carbon sequestration, a factor critical in minimizing carbon emissions and other green house gases.

Modeling Consumer Price Index in Zambia: A Comparative Study between Multicointegration and Arima Approach

Consumer Price Index (CPI) is an important indicator used to determine inflation. The main objective of this research was to compare the forecasting ability of two time-series models using Zambia Monthly Consumer Price Index. We used monthly CPI data which were collected from January 2003 to December 2017. The models that were compared are the Autoregressive Integrated Moving average (ARIMA) model and Multicointegration (ECM) model. Results show that the ECM was the best fit model of CPI in Zambia since it showed smallest errors measures. Lastly, a forecast was done using the ECM and results show an average growth rate for food CPI at 6.63% and an average growth rate for nonfood CPI at 7.41%. Forecasting CPI is an important factor for any economy because it is essential in economic planning for the future. Hence, identifying a more accurate forecasting model is a major contribution to the development of Zambia.

Mathematical Model of Classical Kaposi’s Sarcoma

In this paper, the global properties of a classical Kaposi’s sarcoma model are investigated. Lyapunov functions are constructed to establish the global asymptotic stability of the virus free and virus (or infection) present steady states. The model considers the interaction of B and progenitor cells in the presence of HHV-8 virus. And how this interaction ultimately culminates in the development of this cancer. We have proved that if the basic reproduction number, R0 is less than unity, the virus free equilibrium point, ε0, is globally asymptotically stable (GAS). We further show that if R0 is greater than unity, then both the immune absent and infection persistent steady states are GAS.

Mathematical Model of HIV-1 Dynamics with T Cell Activation

A deterministic in-host model of HIV-1 that incorporates naive and activated T cells is being investigated. The model represents the dynamics of five subsets of T cells and one class of HIV-1. The virus free and the infection persistent equilibria are found and their stability analysed. With the aid of suitable Lyapunov functionals, we have shown that the model equilibria are globally asymptotically stable under special conditions. The numerical simulation is performed to illustrate both the short term and long term dynamics of HIV-1 infection. The results of simulation are in agreement with published data with regard to CD4+ T cell concentration and the viral load.

Some Classes of Bounded Sets in Quasi-Metric Spaces

This note deals with some classes of bounded subsets in a quasi-metric space. We study and compare the bounded sets, totally-bounded sets and the Bourbaki-bounded sets on quasi metric spaces. For example, we show that in a quasi-metric space, a set may be bounded but not totally bounded. In addition, we investigate their bornologies as well as their relationships with each other. For example, given a compatible quasi-metric, we intend to give some necessary and sufficient conditions for which a quasi metric bornology coincides with the bornology of totally bounded sets, the bornology of bourbaki bounded sets and bornology of bourbaki bounded subsets.

Forecasting Foreign Direct Investment to Zambia: A Time Series Analysis

Three methods are considered in this paper: Simple exponential smoothing (SES), Holt-Winters exponential smoothing (HWES) and autoregressive integrated moving average (ARIMA). The best fit model was then used to forecast Zambia’s annual net foreign direct investment (FDI) inflows from 1970 to 2014. Foreign direct investment is foreign capital investment to Zambia. Throughout the paper the methods are illustrated using Zambia’s annual Net FDI inflows. A comparison of the three methods shows that the ARIMA (1, 1, 5) is the best fit model because it has the minimum error. Forecasting results give a gradual increase in annual net FDI inflows of about 44.36% by 2024. Forecasting results plays a vital role to policy makers. Decision making, coming up with good policies and suitable strategic plans, depends on accurate forecasts. Zambian FDI policy makers can use the results obtained in this study and create suitable strategic plans to promote FDI.

Using Box-Jenkins Models to Forecast Mobile Cellular Subscription

In this paper, the Box-Jenkins modelling procedure is used to determine an ARIMA model and go further to forecasting. The mobile cellular subscription data for the study were taken from the administrative data submitted to the Zambia Information and Communications Technology Authority (ZICTA) as quarterly returns by all three mobile network operators Airtel Zambia, MTN Zambia and Zamtel. The time series of annual figures for mobile cellular subscription for all mobile network operators is from 2000 to 2014 and has a total of 15 observations. Results show that the ARIMA (1, 2, 1) is an adequate model which best fits the mobile cellular subscription time series and is therefore suitable for forecasting subscription. The model predicts a gradual rise in mobile cellular subscription in the next 5 years, culminating to about 9.0% cumulative increase in 2019.

Modelling Epidemiological Data Using Box-Jenkins Procedure

In this paper, the Box-Jenkins modelling procedure is used to determine an ARIMA model and go further to forecasting. We consider data of Malaria cases from Ministry of Health (Kabwe District)-Zambia for the period, 2009 to 2013 for age 1 to under 5 years. The model-building process involves three steps: tentative identification of a model from the ARIMA class, estimation of parameters in the identified model, and diagnostic checks. Results show that an appropriate model is simply an ARIMA (1, 0, 0) due to the fact that, the ACF has an exponential decay and the PACF has a spike at lag 1 which is an indication of the said model. The forecasted Malaria cases for January and February, 2014 are 220 and 265, respectively.

Forecasting Annual International Tourist Arrivals in Zambia Using Holt-Winters Exponential Smoothing

Tourism is one of the major contributors to foreign exchange earnings to Zambia and world economy. Annual International tourist arrivals in Zambia from 1995 to 2014 are considered in this paper. In this study we evaluated the model performance of Auto-Regressive Integrated Moving Average (ARIMA) and Holt Winters exponential smoothing (HWES). The error indicators: Mean percentage error (MPE), Mean absolute error (MAE), Mean absolute scaled error (MASE), Root-mean-square error (RMSE) and Mean absolute percentage error (MAPE) showed that HWES is an appropriate model with reasonable forecast accuracy. The HWES (α = 1, β = 0.1246865) showed smallest error than those of the ARIMA (0, 1, 2) models. Hence, the HWES (α = 1, β = 0.1246865) can be used to model annual international tourist arrivals in Zambia. Further, forecasting results give a gradual increase in annual international tourist arrivals of about 42% by 2024. Accurate forecasts are key to new investors and Policymakers. The Zambian government should use such forecasts in formulating policies and making strategies that will promote the tourism industry.

On M-Asymmetric Irresolute Multifunctions in Bitopological Spaces

In this paper, our focus is to introduce and investigate a class of mappings called M-asymmetric irresolute multifunctions defined between bitopological structural sets satisfying certain minimal properties. M-asymmetric irresolute multifunctions are point-to-set mappings defined using M-asymmetric semiopen and semiclosed sets. Some relations between M-asymmetric semicontinuous multifunctions and M-asymmetric irresolute multifunctions are established. This notion of M-asymmetric irresolute multifunctions is analog to that of irresolute multifunctions in the general topological space and, upper and lower M-asymmetric irresolute multifunctions in minimal bitopological spaces, but mathematically behaves differently.