Browsing by Author "Wagala, Adolphus"

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Application of Response Surface Methodology in Optimization of the Yields of Common Bean (Phaseolus vulgaris L.) Using Animal Manures
(Science and Education Publishing, 2020-07) Masai, Kimtai Leonard; Muraya, Moses M; Wagala, Adolphus
The objective of design and analysis of experiments is to optimize a response variable which is influenced by several independent variables. In agriculture, many statistical studies have focused on investigating the effect of application of organic manure on the yield and yield components of crops. However, many of these studies do not try to optimize the application of the manures for maximum productivity, but select the best treatment among the treatment range used. This is mainly due to design and analysis of experiments applied. Therefore, there is a need to apply a statistical method that would establish the effect of the application of organic manures on crop production and in addition optimize the levels of application of these manures for maximum productivity. This study aimed at application of response surface methodology for optimization of the yields of common bean (Phaseolus vulgaris L.) using animal manure. The study was conducted at Chuka University Horticultural Demonstration Farm. The experiment was laid down in a Randomized Complete Block Design. The treatments consisted of three organic manure sources (cattle manure, poultry manure and goat manure) each at three levels (0, 3 and 6 tonnes per ha). Data was collected from six weeks after sowing to physiological maturity. Data was collected on the weight of the grain yield harvested in each experimental plot measured by use of a weighing scale. The data collected was analysis using the R-statistical software. The study findings indicated that animal manures had a significant effect (p < 0.05) on the yield of common beans. The results also showed that the optimum levels of application of the manures in the area of study were 2.1608 t ha-1 , 12.7213 t ha-1 and 4.1417 t ha-1 cattle manure, poultry manure and goat manure, respectively. These were the optimum levels that would lead to maximum yield of common beans without an extra cost of input.
Efficiency Evaluation When Modelling Nairobi Security Exchange Data Using Bilinear and Bilinear-Garch (Bl-Garch) Models
(2012-06) Wagala, Adolphus; Islam, Ali S.; Nassiuma, Dankit K.
In this paper, the weekly returns of the Nairobi Securities Market (NSE) are modelled using bilinear models and the bilinear-GARCH models so as to determine the most efficient and adequate model for forecasting of the Nairobi Equity market. The data used was obtained from the Nairobi Stock Exchange (NSE) for the period between 3rd June 1996 to 31st 30th October 2011for the company share prices while for the NSE 20-share index was for period between 2nd March 1998 to 30th October 2011.The share prices for three companies; Bamburi Cement, National Bank of Kenya and Kenya Airways which were selected at random from each of the three main sectors as categorized in the Nairobi Stock Exchange were used. The results indicate that the combination of bilinear-GARCH model is more adequate and efficient in modelling the weekly returns of the Nairobi Securities Exchange.
Forecasting Commodity Price Index of Food and Beverages in Kenya Using Seasonal Autoregressive Integrated Moving Average (SARIMA) Models
(EJ-MATH, European Journal of Mathematics and Statistics, 2021) Wanjuki, Teddy Mutugi; Wagala, Adolphus; Muriithi, Dennis K.
Price stability is the primary monetary policy objective in any economy since it protects the interests of both consumers and producers. As a result, forecasting is a common practice and a vital aspect of monetary policymaking. Future predictions guide monetary and fiscal policy tools that that be used to stabilize commodity prices. As a result, developing an accurate and precise forecasting model is critical. The current study fitted and forecasted the food and beverages price index (FBPI) in Kenya using seasonal autoregressive integrated moving average (SARIMA) models. Unlike other ARIMA models like the autoregressive (AR), Moving Average (MA), and non-seasonal ARMA models, the SARIMA model accounts for the seasonal component in a given time series data better forecasts. The study relied on secondary data obtained from the KNBS website on monthly food and beverage price index in Kenya from January 1991 to February 2020. R-statistical software was used to analyze the data. The parameter estimation was done using the Maximum Likelihood Estimation method. Competing SARIMA models were compared using the Mean Absolute Error (MAE), Mean Absolute Scaled Error (MASE),.and Mean Absolute Percentage Error (MAPE). A first-order differenced SARIMA (1,1,1) (0,1,1)12 minimized these model evaluation criteria (AIC = 1818.15, BIC =1833.40). The forecasting ability evaluation statistics MAE = 2.00%, MAPE = 1.62% and MASE = 0.87%. The 24-step ahead forecasts showed that the FPBI is unstable with an overall increasing trend. Therefore, the monetary policy committee ought to control inflation through monetary or fiscal policy, strengthening food security and trade liberalization.
A likelihood ratio test for correlated paired multivariate samples
(Chilean Statistical Society, 2020-04) Wagala, Adolphus
Many laboratory experiments in the fields of biological sciences usually involve two main groups say the healthy and infected subjects. In one of these kind of experiments, each specimen from each group can be divided in two portions; one portion is stimulated while the other remains unstimulated. Consequently resulting into two main groups with paired measurements that are correlated. For all the groups, p genes are measured for expression. The stimulation in this case can be done by introducing a known infection causing micro-organism like the group A streptococcus which is usually associated with the acute rheumatic fever. An important question in such experiment would be to statistically test for the di↵erences in the di↵erences in means for the healthy and the infected groups. That is, the di↵erence in the means of the healthy group (stimulated and unstimulated) is tested against the di↵erence in the means of the infected (stimulated and unstimulated) group. In this paper, a likelihood ratio test statistic is developed for such kind of problems. The developed statistics and the Hotelling T2 statistic are both applied to the data are simulated from real biological situations and their performances are compared. The simulated data exhibit the correlation structure similar to that of real biological data obtained from experiments involving the milliplex analyst biomarker data sets. The results indicate that the proposed test statistic give the same conclusions for the hypotheses tested as those of the Hotelling T2 test. However, the proposed test is intuitively more appealing since it takes care of the correlations between the pairs in the data. The simulation study confirms that the test statistics follow a chi-square distribution. This research contributes a theoretical analysis of paired correlated samples motivated by a practical problem for which the existing statistical methods in use have seldomly taken into account the correlation structure of the data.
PLS Generalized Linear Regression and Kernel Multilogit Algorithm (KMA) for Microarray Data Classification Problem
(Revista Colombiana de Estadística - Applied Statistics, 2020) Wagala, Adolphus; González-Farías, Graciela; Ramos, Rogelio
This study involves the implentation of the extensions of the partial least squares generalized linear regression (PLSGLR) by combining it with logistic regression and linear discriminant analysis, to get a partial least squares generalized linear regression-logistic regression model (PLSGLR-log), and a partial least squares generalized linear regression-linear discriminant analysis model (PLSGLRDA). A comparative study of the obtained classifiers with the classical methodologies like the k-nearest neighbours (KNN), linear discriminant analysis (LDA), partial least squares discriminant analysis (PLSDA), ridge partial least squares (RPLS), and support vector machines(SVM) is then carried out. Furthermore, a new methodology known as kernel multilogit algorithm (KMA) is also implemented and its performance compared with those of the other classifiers. The KMA emerged as the best classifier based on the lowest classification error rates compared to the others when applied to the types of data are considered; the unpreprocessed and preprocessed.
PLS Generalized Linear Regression and Kernel Multilogit Algorithm (KMA) for Microarray Data Classification Problem
(2020) Wagala, Adolphus; González-Farías, Graciela; Ramos, Rogelio; Dalmau, Oscar
This study involves the implentation of the extensions of the partial least squares generalized linear regression (PLSGLR) by combining it with logistic regression and linear discriminant analysis, to get a partial least squares generalized linear regression-logistic regression model (PLSGLR-log), and a partial least squares generalized linear regression-linear discriminant analysis model (PLSGLRDA). A comparative study of the obtained classifiers with the classical methodologies like the k-nearest neighbours (KNN), linear iscriminant analysis (LDA), partial least squares discriminant analysis (PLSDA), ridge partial least squares (RPLS), and support vector machines(SVM) is then carried out. Furthermore, a new methodology known as kernel multilogit algorithm (KMA) is also implemented and its performance compared with those of the other classifiers. The KMA emerged as the best classifier based on the lowest classification error rates compared to the others when applied to the types of data are considered; the unpreprocessed and preprocessed.
Price and Volumes Reaction to Annual Earnings Announcement: A Case of the Nairobi Securities Exchange
(2013-02) Kiremu, Mercy Kangai Gatabi; Galo, Nebat; Wagala, Adolphus; Mutegi, James Kinyua
Modern corporate organizations listed in the security markets periodically communicate their financial performance to stakeholders through earnings announcements. Efficient markets immediately absorb and reflect the new information into the share prices. This paper examines the effect of annual earnings announcement at the Nairobi Securities Exchange (NSE) by analyzing changes in share prices and trading volumes for the period from 2006 to 2010. Abnormal returns during the event window of 91 days were determined using the event study methodology employing the market model on data from 5 listed companies. Further, the volume reactions were examined by use of the trading activity ratio (TAR). Inferential and descriptive statistics were used to test for significant effect on TAR and price changes. The results obtained indicate that the abnormal returns and TAR were not significant at 5% probability level. Thus the NSE is of semi-strong efficiency, whereby it is not possible to earn abnormal returns in the NSE using the publicly available information.
SARIMA MODELS: REVIEW AND ITS APPLICATION TO KENYAN’S COMMODITY PRICE INDEX OF FOOD AND BEVERAGE.
(Chuka University, 2021) Wanjuki, Teddy, M.; Wagala, Adolphus; Muriithi, Dennis, K.
Attaining price stability is one of the objectives of monetary policy in any economy to protect both consumers' and producers' interest. Unpredictable food and beverages prices make it difficult for consumers to plan for their expenditure in case of unexpected inflation. On the flip side, low prices may hurt producers as they may not be able to protect their profit margins. It is therefore imperative to develop a precise and accurate model to forecast Kenya's commodity prices. Therefore, the current sought to model the commodities price of food and beverage in Kenya using a Seasonal Autoregressive Integrated Moving Average (SARIMA). SARIMA model takes into account the seasonal periodic fluctuations in a series that usually recur with about the same time interval. Secondary data on monthly food price index was obtained from the KNBS website. The data covered the period from January 1991 to June 2017 with a total of 318 monthly observations. Data analysis was carried out using the R-statistical software. Using the Maximum Likelihood Estimation method, the SARIMA (0,1,2) (0,1,1)12 model had better forecasts accuracy than other competing orders based on the Bayesian Information Criterion (BIC=1638.42) criterion with MAE of 2.25 in its forecasting ability. The two-year predictions of food and beverages price index showed an oscillatory behaviour with an increasing trend. The forecasts can help consumers adjust expenditure in preparation for periods of inflation. Policymakers should make priorities to ensure stability of future commodity prices.
Singular Spectrum Analysis: An Application to Kenya’s Industrial Inputs Price Index
(EJ-MATH, European Journal of Mathematics and Statistics, 2021) Kimutai, K. Emmanuel; Wagala, Adolphus; Muriithi, Dennis K.
Abstract —Time series modeling and forecasting techniques serve as gauging tools to understand the time-related properties of a given time series and its future course. Most financial and economic time series data do not meet the restrictive assumptions of normality, linearity, and stationarity of the observed data, limiting the application of classical models without data transformation. As non-parametric methods, Singular Spectrum Analysis (SSA) is data-adaptive; hence do not necessarily consider these restrictive assumptions as in classical methods. The current study employed a longitudinal research design to evaluate how SSA fist Kenya’s monthly industrial inputs price index from January 1992 to April 2022. Since 2018, reducing the costs of industrial inputs has been one of Kenya’s manufacturing agendas to level the playing field and foster Kenya’s manufacturing sector. It was expected that Kenya’s Manufacturing Value Added hit a tune of 22% by 2022. The study results showed that the SSA (L = 12, r =7) (MAPE = 0.707%) provides more reliable forecasts. The 24-period forecasts showed that the industrial inputs price index remains high above the index in 2017 before the post-industrial agenda targeting a reduction in the cost of industrial inputs. Thus, the industrial input prices should be reduced to a sustainable level.
Singular Spectrum Analysis: An Application to Kenya’s Industrial Inputs Price Index
(Springer, 2022-01) Kimutai, Emmanuel K.; Wagala, Adolphus; Muriithi, Dennis K.
Time series modelling and forecasting techniques serve as gauging tools to understand the time-related properties of a given time series and its future course. Most financial and economic time series data do not meet the restrictive assumptions of normality, linearity, and stationarity of the observed data, limiting the application of classical models without data transformation. As non-parametric methods, Singular Spectrum Analysis (SSA) is data adaptive; hence do not necessarily consider these restrictive assumptions as in classical methods. The current study employed a longitudinal research design to evaluate how SSA fist Kenya’s monthly industrial inputs price index from January 1992 to April 2022. Since 2018, reducing the costs of industrial inputs has been one of Kenya’s manufacturing agendas to level the playing field and foster Kenya’s manufacturing sector. It was expected that Kenya’s Manufacturing Value Added hit a tune of 22% by 2022. The study results showed that the SSA (L = 12, r =7) (MAPE = 0.707%) provides more reliable forecasts. The 24-period forecasts showed that the industrial inputs price index remains high above the index in 2017 before the post-industrial agenda targeting a reduction in the cost of industrial inputs. Thus, the industrial input prices should be reduced to a sustainable level.
TRIPLE EXPONENTIAL SMOOTHING TECHNIQUES: APPLICATION TO KENYA’S INDUSTRIAL INPUTS PRICE INDEX
(Chuka University, 2021) Koech, Emmanuel K.; Wagala, Adolphus; Muriithi, Dennis K.
A move towards industrialization is an active ingredient in achieving sustainable economic development owing to the derived benefits of the creation of employment opportunities and enhanced international trade. Through its big four agenda launched on December 12, 2017, Kenya aims to foster the manufacturing sector. One of the industrial- agenda is reducing the costs of industrial inputs. Thus, an accurate predictive model that can be used to gauge the cost of manufacturing inputs ought to be developed. The current study compared the pertinence of two Holt-Winter Exponential Smoothing (HWES) techniques in forecasting Kenya's industrial inputs price data. Unlike simple moving average, where past values are weighted equally, exponential functions assign exponentially decaying weights, over time. The study used secondary data on Kenya's monthly industrial inputs price index from January 1980 to June 2018 extracted from the OECD website. The data had 450 observations and was analyzed using R software. The findings indicated that a hybrid of both the additive and multiplicative HWES model efficiently captures the nonlinearity or seasonality of industrial inputs price index series. Specifically, the “optimal” model was a specification of the multiplicative error, additive trend, and multiplicative seasonality (“MAM”) with a performance accuracy of 2.3% in terms Mean Absolute Percentage Error (MAPE) in making 24 months step-ahead forecasts. The model outperformed the purely additive (2.44%) or multiplicative HWES model (2.55%). The estimated smoothing of alpha, beta and gamma were; 0.9647, 0.1378, and 0.0004, respectively. The prediction future prices movement is beneficial to producers, consumers and policymakers. The 24-period forecast of the industrial inputs the price index indicates a falling trend, and indication that the industrial agenda shows some prospects in the reduction of the cost of inputs
Volatility Modelling of the Nairobi Securities Exchang
(2012-03) Wagala, Adolphus; Nassiuma, Dankit K.; Islam, Ali S.; Mwangi, Jesse W.
In this paper we identify the most efficient ARCH-type model that can be applied to the Nairobi stock exchange data for forecasting and prediction of volatility which in turn is important in pricing financial derivatives, selecting portfolios, measuring and managing risks more accurately. The establishment of an efficient stock market is indispensable for an economy that is keen on utilizing scarce capital resources to achieve its economic growth. The purpose of this study was to determine the most efficient model from the symmetric and the asymmetric GARCH models. The models were evaluated by use of the Shwartz Bayesian Criteria (SBC), Akaike Information Criteria (AIC) and the Mean Squared Error (MSE). The results show that the AR-Integrated GARCH (IGARCH) models with student’s t-distribution are the best models for modelling volatility in the Nairobi Stock Market data.