Tea is the leading export cash crop and a highly consumed beverage in Kenya. Small scale farmers are more than large scale farmers in Kenya. However, they own small sizes of land which is a limiting factor to tea production. Analysis of trends is an aspect of technical analysis that tries to predict the future movement of stock based on past data. The main objectives of this study is To construct a suitable time series model for the data, To determine the correlation between production and size of land, To forecast tea production Examples of analysis of trends are total monthly sales receipts in a departmental store and total monthly production by company.
This research project was on the trends of tea production and area under tea that are collected annually since 1963 to 2015 and to construct a time series model of a suitable order for the process. The large scale size of land mean is 34882.04 hectares and the average small scale size of land is 4563.25 hectares .For the stationarity of the data the Dickey-Fuller test (ADF); Dickey-Fuller = -1.9254, Lag order = 3, p-value = 0.6045.The correlation of the large scale and small scale holders is; 0.9588537 and 0.9339925 hence strong linear relationship . The best possible models for modelling large scale is ARIMA (2, 1, 0) with Akaike Information Criterion (AIC) of 1885.73 and for Small scale farmers it ARIM(1,1,0) with AIC of 1915.76. The rate of change of the predicted tea production is 0.97 which is a very low rate. These values show that in the next 20 years there will be no significant changes in tea production in Kenya.
TABLE OF CONTENTS
DEDICATION
ACKNOWLEDGEMENT
ABSTRACT
1.0 INTRODUCTION
1.1 BACKGROUND OF STUDY
1.2 STATEMENT OF THE PROBLEM
1.3 OBJECTIVE OF THE STUDY
1.3.1 General objective
1.3.2 Specific objectives
1.4 RESEARCH QUESTIONS
1.5 JUSTIFICACTION
1.6 SIGNIFICANCE OF STUDY
1.7 ASSUMPTIONS OF THE STUDY
2.0 INTRODUCTION
2.1 THEORETICAL LITERATURE REVIEW
2.2 EMPIRICAL LITERATURE REVIEW
2.3 TIME SERIES MODELING REVIEW
RESEARCH METHODOLOGY.
3.0 INTRODUCTION
3.1 DATA
3.2 RESEARCH DESIGN
3.3 Autoregressive model (AR)
3.4 Moving average process (MA)
3.5 Autoregressive moving average (ARMA)
3.6 Autoregressive integrated moving average (ARIMA)
3.7 Box-Jenkins approach.
3.7.1 Autocorrelation function. (ACF)
3.7.2 Partial autoregressive function (PACF)
3.8 SEASONALITY
3.8.1 Multiple seasonal adjustment
3.8.2 Additive seasonal adjustment
CHAPTER 4 RESULTS AND FINDINGS
4.1 Introduction
4.2 Descriptive statistics
4.3 Correlation
4.4 Trend
4.5 Stationarity
4.6 BUILDING BOX JENKINS APPROACH FOR MODELLING TOTAL TEA PRODUCTION.
4.6.1 Identification process .
4.6.2 Estimation
4.6.3 Diagnostic Checks.
4.6.3 Forecast
CHAPTER FIVE
CONCLUSION AND RECOMMENDATION
5.1 INTRODUCTION
5.2 SUMMARY OF FINDINGS AND RESULTS
5.3CONCLUSION
5.4 RECOMMENDATIONS
REFERENCES
DEDICATION
We dedicate this research project to my parents who have always wanted the best for us and have sacrificed almost everything just to see us prosper and our siblings who look up to us as their role models.
ACKNOWLEDGEMENT
We would like to thank the Almighty God for His grace, good health and unity as a group. It is because of His unconditional love that we are writing this paper today. We would also like to express our sincere gratitude to Colleague Dr Oscar Ngesa, Fredrick Muhindi and PollyAnn Wambui for their input throughout the project. We thank my parents for their financial provision and moral support, 1 will forever be grateful for their encouragement.
ABSTRACT
Tea is the leading export cash crop and a highly consumed beverage in Kenya. Small scale farmers are more than large scale farmers in Kenya. However, they own small sizes of land being a limiting factor to tea production. Analysis of trends is an aspect of technical analysis that tries to predict the future movement of stock based on past data. The main objectives of this study is To construct a suitable time series model for the data, To determine the correlation between production and size of land, To forecast tea production Examples of analysis of trends are total monthly sales receipts in a departmental store and total monthly production by company. This research project was on the trends of tea production and area under tea that are collected annually since 1963 to 2015 and to construct a time series model of a suitable order for the process. The large scale size of land mean is 34882.04 hectares and the average small scale size of land is 4563.25 hectares .For the stationarity of the data the Dickey-Fuller test (ADF); Dickey-Fuller = -1.9254, Lag order = 3, p-value = 0.6045.The correlation of the large scale and small scale holders is; 0.9588537 and 0.9339925 hence strong linear relationship . The best possible models for modelling large scale is ARIMA (2, 1, 0) with Akaike Information Criterion (AIC) of 1885.73 and for Small scale farmers it ARIM(1,1,0) with AIC of 1915.76. The rate of change of the predicted tea production is 0.97 which is a very low rate. These values show that in the next 20 years there will be no significant changes in tea production in Kenya.
CHAPTER 1
INTRODUCTION OF STUDY
1.0 INTRODUCTION
This chapter consists of the background of the study, statement of the problem, objectives of the study, justification, significance and assumption of the study.
1.1 BACKGROUND OF STUDY
Tea was introduced in Kenya in 1903 by GWL Caine and then begun to be grown commercially in the 1920s. (Ongile, 1999) Kenya is Africa’s leading producer of tea and the fourth worldwide after India, China and Sri-Lanka. Black tea is Kenya’s leading agricultural foreign exchange earner. (smartfarmerkenya, 2016) It also states that there is more than 110,000 ha of land under tea in Kenya. Areas where tea is grown are divided into two: the east highlands of rift valley and the west highlands of rift valley. The east highlands are; Nyambene hills in Nyambene, Nyeri, Kiambu, Murang’a and Thika. The west highlands of rift valley are; Kericho, Nandi, Kakamega and Cherengani hills.
Tea growers in Kenya are either large scale farmers (estates) or small scale farmers. The definition of small holders varies from country to country, where in Kenya, small scale farmers are growers that cultivate tea but do not possess their own processing factories. There are a total of over 600,000 small scale farmers cultivating over 130,000 ha, who work under the Kenya Development Tea Agency(KTDA). (Kanampiu, 2017) He also argues that KTDA members produce over 60% of tea produced while the rest is produced by large scale farmers. The estates comprises of large scale farmers that are under the Kenya Tea Growers Association. (KTGA) (John Kipkorir Tanui, 2012)
Time series is a sequence of measurements taken at equally spaced points in time that are successive. An ARIMA model is one of the most traditional methods of time series that is not stationary. The model allows time series to be explained by its past values and stochastic error terms. ARIMA model is a combination of AR (autoregressive) and MA (moving average) where the “I” is integrated referring to the reverse process of differencing. (Abdur Rahman, 2017)
1.2 STATEMENT OF THE PROBLEM
A small size of land is a holdback to efficient agriculture. (Stela Atanasova Todorova, 2005) It is therefore possible that the size of land could affect tea production. Area under tea and tea production has increased significantly over the years. (A.Basu Majumder, 2017) However, pressure on land due to the population growth rate of 3.2% reduces the capacity of food production. This leads to the high and medium potential areas being reduced to small scale farms of up to 10ha. As a result, 81% of the small scale farmers own less than 2ha. (Brussels, 2017) Despite the said government efforts and determination, small scale farmers continue to lag behind the large scale growers thus killing of competition between the two sectors that should be seen which will lead to high tea production in Kenya. In that regard therefore should the effect of size of land on the tea produced in Kenya effect persist, Kenya’s goal in tea production in Kenya and the globe at large will be difficult to achieve. Thus triggered a need to investigate if size of land of small scale farmers affect the tea production in Kenya as a country.
1.3 OBJECTIVE OF THE STUDY
1.3.1 General objective
To analyze the trend of tea production from 1963 to 2015.
1.3.2 Specific objectives
- To construct a suitable time series model for the data.
- To determine the correlation between production and size of land.
- To forecast tea production.
1.4 RESEARCH QUESTIONS
1. Do large scale farmers produce more tea than small scale farmers?
2. Do large scale farmers have larger sizes of land?
3. Will tea have a greater impact on Kenya’s revenue over time?
4. Will the trend be the same for the future of tea production as it has been?
1.5 JUSTIFICACTION
This proposal assumes that an increase in land leads to increase in tea production in Kenya which leads to high revenue. This leads to development and improvement of living standards across the country.
Our data has observations taken over time, from1963-2015. This causes us to propose the time series model that will enable us to know the trend of tea production from the previous observations.
1.6 SIGNIFICANCE OF STUDY
1. It can be used as a source of reference on future researches on related topics by students, teachers and researchers.
2. It will provide important information of how tea industry in Kenya performs to several stakeholders such as KTDA
1.7 ASSUMPTIONS OF THE STUDY
- The study scope represents the whole area under tea in Kenya.
- There is a linear relationship between tea production and the size of land.
CHAPTER 2
LITERATURE REVIEW
2.0 INTRODUCTION
Literature review is analyzing the past to prepare for the future. It involves reviewing the model and reviewing the context. (Webster Jane, 2002) A review facilitates theory development and closes areas where a myriad of research exists. It’s important since one gets to know where research is necessary and guide the researcher on other studies done on the same. This chapter has a review that was conducted based on available publications of tea industry in Kenya.
2.1 THEORETICAL LITERATURE REVIEW
Theories are formulated to predict, elaborate and understand a phenomena and may be used to challenge and existing knowledge. It is a structure that holds a theory of a research study. The theoretical literature review introduces the theory that explains why a research problem exists. Shen Nung, a Chinese emperor discovered tea in Circa 2700 B.C.In 1805 A.D Dengo Daishi, a Buddhist patron saint of Japanese tea introduced tea growing in Japan. However, in 1191 after centuries of neglect the cultivation of tea in Japan was revived by the Buddhist Abbot Yesai, who subsequently published the first Japanese tea book. (EATTA, 2008)
Chinese Emperor Shen Nung discovered tea in circa 2700 B.C. (East African Tea Trade Association, 2008) Tea is one of the cheapest and most consumed beverage in the world. It is majorly produced in Asia where China, India and Sri-Lanka are major producers. They are known to account for 77% of world’s production and 80% of global exports. In Africa, it is mainly grown around tropical regions such as; Tanzania, Uganda, Kenya, Malawi and Rwanda which are major producers. Tea is cultivated in 3691938 ha of land with an annual production of 4066596 thousand kilograms all over the world. (A.Basu Majumder, 2017)
Tea is one of the cheapest and most consumed beverage in the world. It is majorly produced in Asia where China, India and Sri-Lanka are the major producers. In Africa it is mainly grown around the tropical regions such as Rwanda, Tanzania, Uganda, Kenya and Malawi. (A.Basu Majumder, 2017)
Tea is a major cash crop and is wealth to AFA as stated in their vision. (AFA, 2014) The AFA has put effort to ensure increased consumption and efficient production to the realization of their vision to come true.
There is a total of over 600,000 small scale farmers cultivating 130,000 Ha in 17 counties and 66 factories across Kenya which work and are managed by KTDA. KTDA members produce over 60% of tea produced while the rest is produced by large scale farmers. Tea in Kenya grows in regions that are climatically endowed ideally; tropical, volcanic red soils and rainfall ranging between 1200mm to 1400mm per year. Tea covers an area of over 157,720 Ha and produces approximately 345,817 metric tons. About 70% of the produced tea is exported earning revenue for the Kenyan government. (Kanampiu, 2017)
2.2 EMPIRICAL LITERATURE REVIEW
Empirical review is based on previously observed, measured and mathematical phenomena from actual experiences instead of beliefs and assumptions. (Cahoy, 2017)
In the 20th century, tea was grown in 2563.75 thousand Ha of land which then increased to 2661.88 thousand ha with a growth rate of 0.42%.In the 21st century, production increased slowly where in 2001 tea area was 2727.42 thousand Ha that increased with a growth rate of 3.42% to 3691.89 in 2010. (A.Basu Majumder, 2017)
2.3 TIME SERIES MODELING REVIEW
Time is an important and actually the most important factor that enables success in any business. Time series modeling is a vital method of prediction and forecasting and it is all about working on time; days, hours, minutes, months, years and many other measurements of time. (Srivastava, 2015)
The ARIMA model is a standard statistical time series model. The Box Jenkins method for time series analysis was developed by George Box and Gwilym Jenkins who also suggested a process for identifying, estimation and for a specific time series dataset, checking models. Hence it is known as Box-Jenkins method. It involves ARIMA and 3 steps of the Box-Jenkins and it is the best way for selecting p, d and q model for configuration of an ARIMA model. (Brownlee, 2017)
To determine an appropriate ARMA (p, q) model in representing a stationary observed time series consists a number of inter related problems. He further states that these problems include the choices of p’s and q’s and in estimation of the remaining parameters which are mean/average, the coefficients like Abbildung in dieser Leseprobe nicht enthalten and the white noise Abbildung in dieser Leseprobe nicht enthaltensquared for values of p and q. (Peter J Brockwell, 2010)The final selection of the most appropriate time series depends on the goodness of fit tests using either the Akaike Information Criteria (AIC) or Bayesian information criterion (BIC).
P is the number of lags observed included in the model, d is the times that the observations have been differenced and q is the order of moving average. (Brownlee, 2017) The Box-Jenkins method consists 3 steps which are identification, estimation and diagnostic checks. Identification involves using the data and its information to help select a subclass of model that may summarize the data best. Estimation uses the data to train the coefficients of the model. Diagnostic checks involves evaluating the fitted model in the context of the data available and check for areas to be improved in the model.
It is possible to have both cyclic and seasonal behavior in an ARMA model but long period cyclicity is not handled very well in an ARMA framework. (Hyndman, 2011)
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