Mathematics and Statistics

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Analysis of Volatility of Real Exchange Rate and Exports in Kenya using the Garch Model: 2005:2012
(2015-07) Mustapha, Wasseja; Musundi, Sammy Wabomba; Njoroge, Elizabeth; Ngugi, Mwenda
The real exchange rate has proven to be an important factor in international trade because it is expected that exports respond to real exchange rate movements with respect to the characteristics of the importing and exporting countries. Exchange rate volatility increases uncertainty of profits on contracts denominated in foreign currency and subsequently dampens trade and economic growth. This study investigated how real exchange rate volatility affected exports of key Kenyan commodities to the European Union and United Kingdom, namely; tea, coffee and horticulture to the European Union. The presence of exchange rate volatility was determined using the GARCH model. A Bounds testing and Autoregressive Distributed Lag model was used to establish the presence of a long run relationship between exchange rate volatility and commodity exports. Findings revealed that exchange rate volatility affected tea exports to the UK and horticulture exports to the European Union. Foreign income played an important role in explaining tea and coffee exports to the UK and EU respectively.
Application of Banach space ideal properties in image transmission over wireless network
(2014-04) Musundi, Sammy Wabomba; Ochieng, Ombaka; Njogu, Muriuki; Kinyua, Charles
The Banach space operator ideals and nuclear maps have a large class of morphisms which behave as if they were part of a compact closed category, that is, they allow one to transfer variables between the domain and the codomain. We use the concept of nuclearity in functional analysis to establish application aspect of Banach space ideal properties in the transmission of image over wireless network based on the embedded system.
Application of Principal Component Analysis and Hierarchical Regression Model on Kenya Macroeconomic Indicators
(EJ-MATH, European Journal of Mathematics and Statistics, 2022) Mbaluka, Morris Kateeti; Muriithi, Dennis K.; Njoroge, Gladys G.
The aim of this paper was to apply Principal Component Analysis (PCA) and hierarchical regression model on Kenyan Macroeconomic variables. The study adopted a mixed research design (descriptive and correlational research designs). The 18 macroeconomic variables data were extracted from Kenya National Bureau of Statistics and World Bank for the period 1970 to 2019. The R software was utilized to conduct all the data analysis. Principal Component Analysis was used to reduce the dimensionality of the data, where the original data set matrix was reduced to Eigenvectors and Eigenvalues. A hierarchical regression model was fitted on the extracted components, and R2 was used to determine whether the components were a good fit for predicting economic growth. The results from the study showed that the first component explained 73.605 % of the overall Variance and was highly correlated with 15 original variables. Additionally, the second principal component described approximately 10.03% of the total Variance, while the two variables had a higher positive loading into it. About 6.22% of the overall variance was explained by the third component, which was highly correlated with only one of the original variables. The first, second, and third models had F statistics of 2385.689, 1208.99, and 920.737, respectively, and each with a p-value of 0.0001<5% was hence implying that the models were significant. The third model had the lowest mean square error of 17.296 hence described as the best predictive model. Since component 1 had the highest Variance explained, and model 1 had a lower p-value than other models, Principal component 1 was more reliable in explaining economic growth. Therefore, it was concluded that the macroeconomic variables associated with the monetary economy, the trade and openness of the economy with government activities, the consumption factor of the economy, and the investment factor of the economy predict economic growth in Kenya. The study recommends that PCA should be utilized when dealing with more than 15 variables, and hierarchical regression model building technique be used to determine the partial variance change among the independent variables in regression modeling.
Application of Principal Component Analysis and Hierarchical Regression Model on Kenya Macroeconomic Indicators.
(EJ-MATH, European Journal of Mathematics & Statisctics., 2022) Mbaluka, M. K.; Njoroge, G. G.; Muriithi, D. K.
The aim of this paper was to apply Principal Component Analysis (PCA) and hierarchical regression model on Kenyan Macroeconomic variables. The study adopted a mixed research design (descriptive and correlational research designs). The 18 macroeconomic variables data were extracted from Kenya National Bureau of Statistics and World Bank for the period 1970 to 2019. The R software was utilized to conduct all the data analysis. Principal Component Analysis was used to reduce the dimensionality of the data, where the original data set matrix was reduced to Eigenvectors and Eigenvalues. A hierarchical regression model was fitted on the extracted components, and R2 was used to determine whether the components were a good fit for predicting economic growth. The results from the study showed that the first component explained 73.605 % of the overall Variance and was highly correlated with 15 original variables. Additionally, the second principal component described approximately 10.03% of the total Variance, while the two variables had a higher positive loading into it. About 6.22% of the overall variance was explained by the third component, which was highly correlated with only one of the original variables. The first, second, and third models had F statistics of 2385.689, 1208.99, and 920.737, respectively, and each with a p-value of 0.0001<5% was hence implying that the models were significant. The third model had the lowest mean square error of 17.296 hence described as the best predictive model. Since component 1 had the highest Variance explained, and model 1 had a lower p-value than other models, Principal component 1 was more reliable in explaining economic growth. Therefore, it was concluded that the macroeconomic variables associated with the monetary economy, the trade and openness of the economy with government activities, the consumption factor of the economy, and the investment factor of the economy predict economic growth in Kenya. The study recommends that PCA should be utilized when dealing with more than 15 variables, and hierarchical regression model building technique be used to determine the partial variance change among the independent variables in regression modeling.
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.
Assessment of Water Quality in Boreholes and Wells in Waa Location, Kwale County –Kenya”.
(CODEN (USA), 2017) Kilwake, J. Wanjala1; Mwakio, Tole1; Musundi, Sammy 2*
Water from boreholes and dug wells is extensively used in Kwale County, especially by rural communities living away from established market centers, where piped water is commonly available. The study aimed to assess the quality of water in boreholes and dug wells found in Waa location of Kwale County – Kenya. Selection of the boreholes and dug wells was carried out using purposive sampling and simple random sampling. All the seventy one boreholes and wells in Waa location were visited and inspected to determine their sanitary condition and functionality. Twenty eight samples of water that were collected in duplicate from 14 boreholes and dug wells (30% of total number) were analyzed for faecal coliform (Escherichia. coli), total coliform count, pH, total dissolved solids, turbidity, colour, total hardness, salinity, chloride content, electrical conductivity, total alkalinity, Ca2+ and Mg2+ using 3M Petrifilm™ method, pH meter, HACH digital titrator, Total dissolved solids/Conductivity meter, and DR 2000 (HACH) spectrophotometer at KIMAWASCO laboratory. The study revealed that 32% of the boreholes and dug wells have either permanently or temporarily failed to discharge good quality drinking water to the local community reliably. This state has been attributed to negligence from the relevant authorities and agencies in terms of water quality monitoring and low level of community involvement in the development of these water projects. The County government of Kwale and water resource providers should build the capacity of the community in water resource management, introduce desalination and water treatment plants to provide safe drinking piped water.
The Banach Numerical Range for Finite Linear Operators
(Modern Scientific Press, Florida, USA, 2019-01) Ohuru, Priscah M.; Musundi, Sammy Wabomba; Ombaka, Ochieng
The numerical range has been studied extensively in Hilbert spaces. Properties of the numerical range such as non-emptiness, containment of the spectrum and in particular, convexity have been proved and results have been given in these spaces. Furthermore, comparison of the numerical ranges with the spectra have been established. In this study, we consider the Banach space numerical range for a linear operator based on the definition by Lumer (1961) and establish its properties in relation to the above stated. Properties of the corresponding Banach numerical radius and spectrum are also discussed.
The Banach Numerical Range for Finite Linear Operators
(Modern Scientific Press Company, 2020-02-14) M. Ohuru, Priscah; W. Musundi, Sammy
The numerical range has been a subject of interest to many researchers and scholars in the recent past. Based on the research outputs, many results have been obtained. Besides, several generalizations of the classical numerical range have also been made. The recent developments have focused on the theory of operators on Hilbert spaces. The determination of the numerical ranges of linear and nonlinear operators have been given in both the Hilbert and Banach spaces. In addition, results of these numerical ranges have been extended to the case of two operators in both spaces. It is important to note that more generalizations have been made in Hilbert spaces as compared to those that have been made in the Banach spaces. The Banach space has two major numerical ranges which are: the spatial and algebraic numerical ranges. This research focuses on determining the numerical range for a finite number of linear operators in the Banach space based on the classical definition. Properties which hold for the classical numerical range have been shown to hold for the Banach space numerical range. The property of convexity has been established using the Toeplitz-Hausdorff theorem under the condition that the Banach space is smooth. Furthermore, the numerical radius and the spectrum of these operators have also been determined.
Combined Effects of Hall Current, Rotation and Inclined Magnetic Field on a Free Convection Fluid Flow over an Exponentially Accelerated Vertical Plate with Heat and Mass Transfer
(2019-05) Kirimi, Jacob 1; Okong’o, Mark 2; Musundi, Sammy 3; Ombaka, Ochieng 4
Many natural phenomena and technological applications undergo Magneto hydrodynamics (MHD). Applications such as the drawing of continuous strips of polymers through a die are carried out through a stagnant cooling fluid. The quality of the strips is found to depend on the rates of heat and mass transfer on the stretching surface. To assure quality, it is vital to understand how heat and mass transfer are affected by Hall current, rotation and inclined magnetic field for a free convection fluid flow. Due to wide applications of MHD in science and technology, many scholars have studied a wide variety of flow situations including those that combine Hall current, rotating systems and inclined magnetic field. However, no such studies have incorporated the effects on heat and mass transfer. In this study, we investigate the combined effects of Hall current, rotation and inclined magnetic field on a free convection fluid flow with heat and mass transfer for a fluid flowing over an exponentially accelerated vertical plate. A strong, steady and inclined magnetic field is applied into the fluid region. The coupled non-linear partial differential equations governing the flow are first expressed in dimensionless form then solved using the finite difference method. The skin friction and the rates of heat and mass transfer at each of the boundaries are computed using the least squares approximation method. Numerical values are simulated from the model equations using the MATLAB program. The profiles for velocity, temperature and concentration at various distances from the plate are demonstrated graphically for various parameters values. This study shows that increase in the angle of application of the magnetic field decreases the primary velocity while it increases the secondary velocity. The secondary velocity decreases when the Hall parameter is increased. It however increases when the rotation parameter is increased.
Correlation Between Electromagnetic Wave Equation and Einstein Theory of Relativity in Derivation of Schrödinger Equation and Hilbert Space Operators "
(2020-03) Mbatha, M. Elizabeth; Musundi, Sammy Wabomba; Kamweru, Paul
Operators in Hilbert space have properties which are useful in the study of mathematical abstract areas such as approximation theory, Banach Fixed point theory, the spectral theory as well as Quantum Mechanics. Schrödinger equation is a fundamental entity with many applications in Quantum Mechanics. This equation was initially derived by applying the knowledge of electromagnetic wave function and Einstein theory of relativity. Later, it was derived by applying the knowledge of Newtonian mechanics. It was also derived by extending the wave equation for classical fields to photons and simplified using approximations consistent with generalized non-zero rest mass. However, from the existing literature no study has been done on deriving Schrödinger equation using properties of Hilbert space operators. In this study, Hilbert space operators that include unitary operators, self adjoint operators and compact operators, norms of linear operators, Hilbert Schmidt operator, normal operators together with Lebesque Integral, Neumann Integral and spectrum are used in place of the existing concepts of electromagnetic wave function, Einstein theory of relativity and approximation consistent with generalized non zero mass to derive the Schrödinger equation. The derivation of Schrödinger equation and its application using Hilbert space operators enhances a better understanding of the concept of Schrödinger equation. The results of this work can further find use in quantum mechanics as well as in mathematical operator theory.
Demystifying Mathematics: handling learning difficulties in Mathematics among low achievers in Kenyan schools
(Journal of Language, Technology & Entrepreneurship in Africa, 2022) Njoroge, Gladys Gakenia
Mathematics is a compulsory subject in both primary and secondary schools in Kenya. However, learners’ poor performance in the subject in Kenya national examinations year in year out remains a serious concern for teachers of Mathematics, parents, curriculum developers, and the general public. This is particularly worrying because of the importance attached to the subject in national development hence the need to find out what could be affecting learning of Mathematics in Kenyan schools. The research on which this paper is based sought to examine the factors that influence performance in Mathematics in Kenyan schools; identify the characteristics of Mathematics learning disabilities; determine how the learners with such learning disabilities can be assessed and identified and interventions for these difficulties implemented. A case study was undertaken on class six learners in a primary school in Nairobi County. The tools used for the research were: classroom observations and an Individualized Education Program (IEP) developed by the teachers with the help of the researcher. This paper therefore highlights the findings from the research, discusses the implications of the findings and suggests the way forward as far as teaching, learning and assessment of Mathematics in Kenyan schools is concerned. Perhaps with the application of the right interventions, poor performance in Mathematics in the national examinations in Kenya will be a thing of the past.
Derivation of Fixed-Point Theorem Using Expansive Mapping Approach
(Asian Research Journal of Mathematics, 2023-06-07) Koech Vincent a , Musundi W. Sammy a* and Kinyanjui Jeremiah
Application of Fixed-Point Theorem has tremendously increased in different areas of interest and research. Fixed Point Theorem presents that if is a contraction mapping on a complete metric space then there exists a unique fixed point in . A lot has been done on application of contraction mapping in Fixed Point Theorem on metric spaces such as Cantor set with the contraction constant of , the Sierpinski triangle also with contraction constant of . On the other hand, a mapping on such that is called an expansive mapping. There are various types of expansive mappings such as; isometry expansive mapping, proper/strict expansive mapping and anti-contraction expansive mapping. From the available literature, Fixed Point Theorem has been derived using contraction mapping approach. In this paper, we establish that it is also possible to derive Fixed Point Theorem using expansive mapping approach.
Distribution of Spectrum in a Direct Sum Decomposition of Operators into Normal and Completely Non normal parts;
(Modern Scientific Press Company, Florida, USA, 2014-09-05) Mwenda, E.1; Musundi, S. W.2*; Nzimbi, B. M. 1; Marani, V. N. 3; Loyford, N. 4
We discuss the distribution of spectra of a direct sum decomposition of an arbitrary operator into normal and completely non normal parts. We utilize the fact that any given operator 𝑇∈𝐵(𝐻) can be decomposed into a direct summand 𝑇=𝑇1⊕𝑇2 with 𝑇1 and 𝑇2 are the normal and completely non normal parts respectively. This canonical decomposition is preferred to other forms of decomposition such as Polar and Cartesian decompositions because these two do not transfer certain properties (for instance the spectra, numerical range, and numerical radius) from the original /decomposed operator to the constituent parts. This is presumably done since these parts are simpler to deal with.
An Empirical analysis of Commercialization of Small holder Farming: Its inclusive household Welfare Effects
(2916-04-18) Wasseja, Mustapha M.; Mwenda, Samwel N.; Musundi, Sammy; Jerobon, Josephine; Ochieng, Pascal *
This paper assesses the potential impact of commercialization of agriculture on household welfare of farmers in eastern Kenya under the Mwea rice scheme. The study consists of cross-sectional data collected with structured survey questionnaires. Stratified sampling was adopted with each of the four zones in the District forming a stratum. The number of respondents was 368 selected conveniently with the help of the National agriculture advisory services officers. The causal relationship and impact of commercialization on welfare were estimated using Pearson’s correlation coefficient and regression analysis. The analysis results revealed significant positive relationship between commercialization and household welfare, with key variables of market access and internal farming activities positively and significantly contributing to improved household incomes and farm outputs. The regression result further predicted a 16.9% improvement in household welfare if farmers actively worked on improving market access and internal farm activities like fertilizers and pesticides. It’s therefore recommended that farmers work on all aspects that can improve on their farm outputs and also get links to both nearby and far markets. Formation of saving schemes will help them pool resources to buy inputs like tractors, lobbying central and local governments for infrastructure in the districts and negotiating better output prices. All this will help improve farmers’ household welfare and standards of living in this area.
Equilibrium Equity Premium in a Semi Martingale Market When Jump Amplitudes Follow a Binomial Distribution
(Scientific Research Publishing Inc., 2018-08-20) Mukupa, George M.; Offen, Elias R.
This paper studies equilibrium equity premium in a semi martingale market when jump amplitudes follow a binomial distribution. We take n to be the number of times. An investor is trading in this market with p being the probability that there is a shift in the price at the trading time t. We find significant variations in the equilibrium equity premium for the martingale and semi martingale markets in terms of wealth value, volatility and other parameters under study. In this market, the equilibrium equity premium remains constant regardless of volatility and wealth value.
Equivalent Banach operator ideal norms’’
(2012-01) Musundi, S. Wambomba; Shem, Aywa; Fourie, Jan
Let X, Y be Banach spaces and consider the w'-topology (the dual weak operator topology) on the space (L(X, Y) of bounded linear operators from X into X with the uniform operator norm. L w' (X, Y) is the space of all T ∈ L(X, Y) for which there exists a sequence of compact linear operators (Tn) ⊂ K(X, Y) such that T = w' - lim nT n. Two equivalent norms, on L w'(X, Y) are considered. We show that and Banach operator ideals.
Features Selection in Statistical Classification of High Dimensional Image Derived Maize (Zea Mays L.) Phenomic Data
(Science and Education Publishing, 2022) Gachoki, Peter; Muraya, Moses; Njoroge, Gladys
Phenotyping has advanced with the application of high throughput phenotyping techniques such automated imaging. This has led to derivation of large quantities of high dimensional phenotypic data that could not have been achieved using manual phenotyping in a single run. Hence, the need for parallel development of statistical techniques that can appropriately handle such large and/or high dimensional data set. Moreover, there is need to come up with a statistical criteria for selecting the best image derived phenotypic features that can be used as best predictors in modelling plant growth. Information on such criteria is limited. The objective of this study is to apply feature importance, feature selection with Shapley values and LASSO regression techniques to find the subset of features with the highest predictive power for subsequent use in modelling maize plant growth using highdimensional image derived phenotypic data. The study compared the statistical power of these features extraction methods by fitting an XGBoost model using the best features from each selection method. The image derived phenomic data was obtained from Leibniz Institute of Plant Genetics and Crop Plant Research, -Gatersleben, Germany. Data analysis was performed using R-statistical software. The data was subjected to data imputation using 𝑘𝑘 Nearest Neighbours technique. Features extraction was performed using feature importance, Shapley values and LASSO regression. The Shapley values extracted 25 phenotypic features, feature importance extracted 31 features and LASSO regression extracted 12 features. Of the three techniques, the feature importance criterion emerged the best feature selection technique, followed by Shapley values and LASSO regression, respectively. The study demonstrated the potential of using feature importance as a selection technique in reduction of input variables in of high dimensional growth data set.
Features Selection in Statistical Classification of High Dimensional Image Derived Maize (Zea Mays L.) Phenomic Data
(Science and Education Publishing, 2022) Gachoki, Peter; Muraya, Moses; Njoroge, Gladys
Phenotyping has advanced with the application of high throughput phenotyping techniques such automated imaging. This has led to derivation of large quantities of high dimensional phenotypic data that could not have been achieved using manual phenotyping in a single run. Hence, the need for parallel development of statistical techniques that can appropriately handle such large and/or high dimensional data set. Moreover, there is need to come up with a statistical criteria for selecting the best image derived phenotypic features that can be used as best predictors in modelling plant growth. Information on such criteria is limited. The objective of this study is to apply feature importance, feature selection with Shapley values and LASSO regression techniques to find the subset of features with the highest predictive power for subsequent use in modelling maize plant growth using highdimensional image derived phenotypic data. The study compared the statistical power of these features extraction methods by fitting an XGBoost model using the best features from each selection method. The image derived phenomic data was obtained from Leibniz Institute of Plant Genetics and Crop Plant Research, -Gatersleben, Germany. Data analysis was performed using R-statistical software. The data was subjected to data imputation using 𝑘𝑘 Nearest Neighbours technique. Features extraction was performed using feature importance, Shapley values and LASSO regression. The Shapley values extracted 25 phenotypic features, feature importance extracted 31 features and LASSO regression extracted 12 features. Of the three techniques, the feature importance criterion emerged the best feature selection technique, followed by Shapley values and LASSO regression, respectively. The study demonstrated the potential of using feature importance as a selection technique in reduction of input variables in of high dimensional growth data set.
Forecasting Commodity Price Index of Food and Beverages in Kenya Using Seasonal Autoregressive Integrated Moving Average (SARIMA) Models
(Springer, 2021-12) Wanjuki, Teddy Mutugi
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.
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.

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