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Asian Journal of Dairy and Food Research, volume 40 issue 3 (september 2021) : 279-284

Time Series Analysis of Price of Coffee in Case of Mettu Town, Ilu Ababor Zone, Oromia Regional State, Ethiopia

Dereje Gebeyehu Ababu1,*, Azmeraw Misganaw Getahun1
1Department of Statistics, Faculty of Natural and Computational Science, Mettu University, Ethiopia.
Cite article:- Ababu Gebeyehu Dereje, Getahun Misganaw Azmeraw (2021). Time Series Analysis of Price of Coffee in Case of Mettu Town, Ilu Ababor Zone, Oromia Regional State, Ethiopia . Asian Journal of Dairy and Food Research. 40(3): 279-284. doi: 10.18805/ajdfr.DR-204.

ABSTRACT

Background: Coffee is one of the most important cash crops across the world and major source of export earnings. Coffee has been and remains the leading cash crop and export commodity of Ethiopia. The aim of this study was to estimate and predict the price change of coffee in Mettu town.

Methods: In this study both descriptive and inferential statistics were used to analyze secondary data that were collected from Mettu town of Ethiopian Commodity Exchange office sector. A total of 120 months of price of coffee was included in this study. Time series analysis was used to estimate the parameter and for forecast the future values of price change of coffee.

Result: The original data was not stationary and become stationary after second order differencing. The results showed that the price change of coffee was increasing from time to time. After that the data tested the order MA and AR are identified by using the ACF and PACF. Then the model was selected by using AIC. Since, ARMA (1, 2, 1) for price change of coffee was lower values of AIC found to be the most appropriate model to fit the data of the price change of coffee. After the model was fitted, the diagnostic checking has been applied by using the ACF residual and normality checking. So that the model fitted is appropriate for the price change of coffee. All the forecast values are found between the lower and the upper interval then we can say that forecasted value is accurate.

INTRODUCTION

Coffee is one of the most important cash crops across the world and major source of export earnings (FAO, 2004). In the agricultural sector performance cash crop price remained so high. Coffee is very important staple food crops grown in Ethiopia. A day to day general rise in price is called inflation. Inflation can be defined as by sustained general price; on the other side price change can be defined as deflation. Deflation is a term which can have the following two meanings. The first it is defined as a full in price level and the second slow down rate of growth and output of the economy. There is no exact figure at which inflation becomes higher inflations, but inflation 100 or 200% annually would be demanded to be higher inflation, by most economist.
       
The coffee value chain in Ethiopia is composed of a large number of actors. It includes coffee farmers, collectors, different buyers, processors, primary cooperatives, cooperative unions, exporters and various government institutions (Firdu Gemech and John Struthers, 2007). Ethiopia is the birthplace of coffee Arabica. Coffee has been and remains the leading cash crop and export commodity of Ethiopia. According to Worako et al., (2008), Ethiopian government has been making large investment in agricultural sector such as in the development and extension of coffees.
 
Coffee is critical to the Ethiopian economy with exports of $350 million in 2006. Ethiopian capital city, Addis Ababa, is located near the center of the country. Approximately 2.5 billion cup of coffee drinks every day (Dicum and Luttinger, 1999). Most of us are very familiar and we could not feel comfort without a cup of coffee in the morning. However, some of us have lack ideas about the origin of coffee.
 
Coffee production is concentrated mainly in the Oromia and the Southern Nations, Nationalities and People’s Region (SNNPR). Major and medium growing town as contain an estimated 800,000 coffee farmers with approximately 520,000 ha under coffee which 63.3 per cent is in Oromia, 35.9% in SNNPR and 0.8% in Gambela. Each town (district) is classified as a major, medium and minor coffee grower based on the area covered by coffee trees (FDRE, 2006).
 
The price of the commodity is varying from time to time. Coffee is one of the commodities that face similar problem like any other commodities. Today the price of coffee is the main problem of the buyer part of the population. It is clear that the effect of increment/decrement in the price change of coffees crops and general risk level are does not limited only the living standard of the people and our society. It may be affected by population size, climatic change, labor migration, agro fuel production and so on. Coffee is almost entirely produced in developing countries and mostly consumed in the developed world. A key feature of the world coffee market has been the substantial short term fluctuations in coffee prices, both at the level of international markets as well as markets relevant for coffee producers. Poor price signals in different markets shows that how the agricultural commodity markets are poorly integrated (FAO, 2004).

Also influences the fixed income group people such as workers, teachers, students and work shippers. Some cash crop based pilot study showed that, In Ilu Ababor Zones price of coffee increase from time to time. To best of our knowledge, no study has been conducted in Buno-Bedele and Ilu Ababor Zones regarding time to treatment dropout in TB patients.  As a result, the study was intended to address research question, such as: What is the amount of estimates for price of coffee? Is there price change of coffee from time to time? What will be the prices of coffee looks like in the future?

MATERIALS AND METHODS

The study area
 
The study area was conducted in Mettu town. Mettu is the capital city of Ilubabor zone of Oromia National Regional State, which is located about 600km from the capital city (Addis Ababa) of the country.
 
Source of data and study design
 
Secondary data source was used and it was obtained from Mettu town of ECX office sector from 2000 to 2010 E.C.
 
Method of statistical analysis
 
Both descriptive statistics and inferential statistics used for data analysis to answer the research question and to meet the objectives of the study.
 
Trend analysis
 
Trend is general tendency to increase or decrease during a long period of time. In order to measure trend we try to eliminate seasonal components from the time series data.
 
Test of stationary
 
Stationarity is a fundamental property underlying almost all time series statistical models. The time series under consideration should be checked for stationary before one can attempt to fit a model. It has played a major role in time series analysis. This can be checked through time series plot and Augmented Dickey Fuller Test (ADF).
 
Model identification and estimation
Box-Jenkins methodology
 
The Box-Jenkins methodology refers to a set of procedure for identifying and estimating time series models with the class of Autoregressive process (AR), Moving Average (MA), Autoregressive Moving Average (ARMA) and Autoregressive Integrated Moving Average (ARIMA) models.
 
Model identification and selection criterion
Autocorrelation function (ACF)
 
It refers the way the observations in a time series are related to each other. Simply, it is the correlation between current observations (Yt) and previous observations (Yt-p). For a given sample y1, y2, y3………….yn of n observation we define the sample autocorrelation as follow.
 
 
Where:
rk- the autocorrelation function, gk- the covariance of sample at lag k and g0- the variance of sample.
 
Partial autocorrelation function (PACF)
 
PACF is used to identify a tentative ARIMA model. It is the correlation between current observations (Yt) and previous observations (Yt-p) when the effects at other time lags p-1 are removed and it can be computed using the following formula (where j takes on values from 1 to k - 1):
 
 
 
Where
rk = The autocorrelation coefficient for k lags apart.
rkk = Sample partial autocorrelation.
rj  = Partial autocorrelation of jth sample observation.
rk-j = The partial autocorrelation coefficient for k lags apart.
 
Model selection criterion
 
Given a set of model for the data, the preferred model is the one with the minimum AIC and BIC value.
 
Estimating the model parameter
 
After selecting the most appropriate model, the model parameters are estimated by using several estimation procedures. These are: Least square methods and Maximum likelihood estimation.
 
Diagnostics checking
Examine the ACF for residuals
 
Autocorrelation Function (ACF) pick best model with well-behaved residuals. Once we have identified a tentative model the next step is to determine the adequacy of the models.
 
Method of analyzing the residuals
 
If an ARMA (p, q) model is an adequate representation of the data generating process, then the residuals should be uncorrelated. To determine whether the error are random or not, we use the modified Ljung Box Pierce statistic.
 
Box - jenkins method of forecasting
 
The last step of the ARIMA modeling process is forecasting. In forecasting, the goal is to predict future values of a time series variable, yt + k, k =1, 2... based on the data collected to the present, x = yt, yt-1... y1. Throughout this section, we would assume Yt is stationary and the model parameters are known.
 
Measure of accuracy
 
A measure of accuracy refers to goodness of fit. The three measure of accuracy are MAPE (Mean absolute % age error), MSD (Mean Square deviations) and MAD (Mean Absolute Deviation) for each the forecasting and smoothing models.
 
Study variables
 
There are two types of variable in this study; such are dependent (response) and independent (explanatory) variables.
 
Dependent variable
 
the dependent variable is Prices change (in birr) of coffee is the dependent variable.
 
Independent variable
 
The independent variable of this research is consecutive time interval from 2001-2010 E.C.

RESULTS AND DISCUSSION

Descriptive statistics
 
The average price coffee was 22.62 ETB with standard deviation of 3.315 ETB per kilogram. The minimum and maximum average price of 1KG of coffee was 14.000 and 34.000 ETB, respectively (Table 1).
 

Table 1: Descriptive Statistics: price.


 
Trend analysis
 
Trend is general tendency to increase or decrease during a long period. In order to measure trend we have to eliminate seasonal time series data. As one can observe from the figure, price of coffee was increased by 3.72E-0.028 ETB for a unit change of time (in months). The best model was a model with minimum value of MAD which was 2.5536. Fig 1
 

Fig 1: Trend analysis of price of coffee.


 
Test of stationary
 
Time series plot
 
As it observed from Fig 1, there was increase or decrease in price change of coffee from the 2001 to 2010 year (i.e. not stationary). Therefore, we have to change non-stationary time series in to stationary time series by taking the differences. The following graph showed that approximately stationary time series plot. Stationary time series would have no predictable patterns (no growth or decline in the data) in the long-term (Fig 2).
 

Fig 2: Stationary time series plot.


 
Augmented duchy fuller test (ADF)
 
The test result showed that the null hypothesis that the series in level contain unit root could not rejected because p-value was greater than α (5%) and there is a unit root in the data series. This means, there is no stationary time series data in levels (Table 2).
 

Table 2: Unit root test result (at level).


       
The test result Table 3 also showed that the null hypothesis that the series in level contain unit root be rejected because p-value was less than α (5%) and there is no unit root in the data series. This means, there is stationary time series data in 2nd difference.
 

Table 3: Unit root test result (at 2nd difference).


 
ARIMA model
 
We have the stationary time series after second order differencing. Now, the model that we are looking at is ARIMA (p, 2, q). We have to identify the model, estimate suitable parameters, diagnostic checking for residuals and finally achieve our objective of forecasting the future price change of coffee in Mettu town.
 
Model identification
 
After suitably transforming of the data, the next step Firstly, we compute ACF and PACF of the stationary series which consists of the sample ACF and PACF values. The parameters of ARIMA consist of three components: p (Autoregressive parameter), d (number of difference) and q (moving average parameters). From these analyses it is possible to identify the order of AR (p) process and MA (q) process by plotting a correlogram (is the plot of the ACF against lag k) and partial correlogram, using R statistical software and the following graph was obtained. The graph showed that ACF to cut off  to  zero after lag 2 in moving average so it show statinarity of time series data after differencing (Fig 3).
 

Fig 3: The ACF of price change of coffee.


       
The following (Fig 4) graph shows that the model identification is based on recognizable pattern of ACF and PACF. PACF is used to identify a tentative ARIMA model. The behavior of the partial autocorrelation coefficients (PACF) for the stationary time series, along with the corresponding ACF, is used to identify an uncertain ARIMA model.
 

Fig 4: PACF of price change of coffee.


 
Parameter estimation and model identification
 
The best model, using OLS method, was identified by using AIC which shows ARIMA (1,2,1) model was the best model because the value of AIC  ARIMA (1,2,1) is minimum (622.5) as compared to other candidate model (Table 4).
 

Table 4: model identification and parameter estimation.


 
Model diagnostics checking
 
ACF of residuals plot
 
A first step in diagnostic checking of fitted model is to observing residual plot and their ACF diagrams. The figure showed that the ACF plot of Residuals for price change of coffee which shows that neither of values break the confidence interval (95%); this implies the fixed mean with constant variance (Fig 5).
 

Fig 5: ACF of residual of price.


 
Normality checking
 
Normal probability plot is also one of the technique which checking diagnostic modeling of a given data. This indicate that the most of the residuals are not much far from the line showing randomness so, this implies that the fitted model ARIMA (1,2,1)  was an appropriate (Fig 6).
 

Fig 6: Normal probability plot of the residuals of price.


 
Analysis of residual
 
From the following test statistic (Ljung-Box statistic), since all the p-values of lag are less than 5%, so the residual is independent and uncorrelated. This implies that, the selected model ARIMA (1, 2, 1) is an appropriate model for price change of coffee in study area (Table 5).
 

Table 5: Residual analysis.


 
Forecasting
 
Forecasting is prediction which is used to determining what might happen to one particular item of interest such as price of coffee. ARIMA model for price we can check the accuracy of the forecasted value by using the above 95% confidence interval (CI) described as follows. All the forecast values are found between the lower and the upper interval then we can say that forecasted value is accurate (Table 6).
 

Table 6: Forecasts from period 120 (for 10 months).

CONCLUSION

Based on the result of the study, the price of coffee was changed or increased from month to month. As we have seen from the time series plot of original data, there was a prices fluctuation from month to month (not stationary). But, by differencing the price of coffee is become insignificant from month to month (stationary). Therefore time series analysis is necessary for the analysis of price change of coffee. After differencing the series was stationary, therefore any analysis was made now. After that the data tested the order MA and AR are identified by using the ACF and PACF. Then the model was selected by using AIC. Since, ARMA (1,2,1) for price change of coffee  was  lower values of AIC found to be the most appropriate model to fit the data of the price change of coffee After the model was fitted the diagnostic checking have been applied by using the ACF residual and normality checking. So that the model fitted is appropriate for the price change of coffee.

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