Research

Research

LIST OF TABLES

Table 4. 1. Showing unit root test results at level. 6

Table 4. 2. Showing unit root test results at level. 7

Table 4. 3. Showing AR (3) model estimation output results. 9

Table 4. 4. Showing AR (2) model estimation output results. 10

Table 4. 5. Showing AR (1) model estimation output results. 10

Table 4. 6. Showing 2017 milk production forecasts. 11

LIST OF FIGURES

Figure 4. 1. Showing the trend for milk production in Uganda. 4

Figure 4. 2. Showing the correlogram plot of the series at level. 6

Figure 4. 3. Showing the correlogram plot of the series at first difference. 7

Figure 4. 4. Showing the partial correlogram plot of the series at first difference. 7

Figure 4. 5. Showing the correlogram plot of the series at first difference. 8

METHODOLOGY.

3.1. Introduction

This chapter presents and discusses the methodology used in the study.

3.2. Data and its source.

The study utilized a secondary univariate time series data set from Sameer Dairy Company on litters of milk produced monthly from January 2015 to December 2016 in (000) litters.

3.3. Data analysis.

Trend Examination.

A time plot for the data was used to examine the trend of milk production in Uganda. It involved plotting the series against the time variable.

Stationarity test

Test for stationarity was conducted the Augmented Dickey Fuller unit root test and examination of the correlogram plot for the series.

ARIMA model estimation.

Model estimation and diagnostic testing were conducted to fit and select the best model to be used in the forecast of milk production in the country. The partial correlogram and the correlogram plots of the stationary series were used to estimate the p part for the Autoregressive (AR) process and the q part for the Moving Average (MA) process respectively.

Forecasting.

Using the selected model, a 12 months forecast for 2017 was made for milk to be produced in (000) litters.

CHAPTER FOUR

4.1. Introduction

This chapter presents and discusses the findings of the study. It is composed of a time plot explaining the trend of milk production for month of January 2015 to December 2016, stationarity tests at different levels; using the correlogram plot and the Augumented Dickey-Fuller unit root test, model estimation and fitting and lastly a 12 months milk production forecast for the year 2017.

4.2. Trend for Milk production in Uganda.

Figure 4. 1. Showing the trend for milk production in Uganda.

The time plot above revealed a cyclical kind of trend in milk production between January 2015 and December 2016. The highest amount of milk was seen to be produced in March 2015. Thisincrease was attributed to the growing cattle population in the country. The cattle  population  increase  is  said  to  be  as  a  result  of  Cattle restocking,  support  by  government  and  Non-governmental organizations  (NGOs),  disease  control,  training  and  delivery  of advisory  services  to  cattle  farmers,  increasing  market  and improved peace and stability in the country are among others. (Kabwanga Ismail Tijjani & Atila Yetişemiyen, 2015). Between the September 2016 and October 2016, a decline in the supply of milk was recorded in the country. This fall in supply was attributed to drought in many parts of the country. The ongoing drought in many parts of Uganda has caused a drop of more than 25% in milk supplies and rising farm gate prices. Processors have been forced to limit the range of products and to mark up prices. Daily supplies are running out in both big and small outlets(Boylan, 2017).

4.3. Stationarity test

This was executed using the Augmented Dickey Fuller unit root test technique and examination of the partial correlogram plots at different levels.

4.3.1. Unit root test of the series at level.

The test was guided by the following hypotheses below and the results rejected at a 5% level of significance.

Ho: Milk production has a unit root.

Ha: Milk production has no unit root.

Table 4. 1. Showing unit root test results at level.

Results from the table above show that the absolute vale of the ADF t-statistics is less than that of the 5% critical value. the pvalue for the ADF t-statistic was also found to be greater than 0.05, thus failing to reject the null hypothesis and concluding that Milk production has a unit root at level and therefore not stationary.

4.3.2. Examination of the series correlogram plot at level.

Figure 4. 2. Showing the correlogram plot of the series at level.

The correlogram plot above revealed a clear uniform up and down pattern in the spikes with the first spike falling on the first lag and outside the confidence band. Hence a sign of non-stationarity of the series.

4.3.3.Unit root test of the series at first difference.

Ho: Milk production has a unit root.

Ha: Milk production has no unit root.

Table 4. 2. Showing unit root test results at level.

At first difference, absolute of the ADF t-statistic was found to be greater than that of the 5% critical value. Its pvalue was also found to be less than 0.05, thereby rejecting the null hypothesis and concluding that milk production has no unit root at first difference and is therefore stationary.

4.3.4.Examination of the series correlogram plot at first difference.

Figure 4. 3. Showing the correlogram plot of the series at first difference.

The correlogram plot above reveled no clear pattern in its spikes thereby concluding that the series was indeed stationary at first level of differencing.

 4.4. Model estimation.

This put to use the partial-correlogram and the correlogram plots of the stationary data to predict the p and q parts of the Autoregressive (AR) and Moving Average (MA) respectively.

Predicting the p for the AR.

Figure 4. 4. Showing the partial correlogram plot of the series at first difference.

The partial correlogram plot above revealed 3 seemingly significant spikes, thus suggesting p to be 3. Hence an AR (3) model.

Predicting the q for the MA.

Figure 4. 5. Showing the correlogram plot of the series at first difference.

The correlogram plot for the stationary series revealed no significant spikes that were falling outside the confidence band, there by suggesting q to be zero. Hence MA(0) process.

4.4.1. Model diagnostic testing

The AR (3) model was taken up and subjected to diagnostic testing and compared with an AR (2) and AR (1) model.

AR (3) model

Table 4. 3. Showing AR (3) model estimation output results.

The output from the AR (3) model revealed a significance in only the first lag of the series while the second and third lags were not significant since they had a pvalue<0.05. The R² value was found to be 0.571 as shown in the table above, implying 57.1% of the variations in milk production at a given time t can be explained by the first, second and third lags of the series (i.e. milk production in the previous three periods).

AR (2) model

Table 4. 4. Showing AR (2) model estimation output results.

The AR(2) results revealed that the fist lag was still significant and the second lag was not. The R² value was found to be 0.525, implying 52.5% of the variations in milk production at time t can be explained by the first and second lags of the series (i.e. milk production in the previous two periods).

AR (1) model

Table 4. 5. Showing AR (1) model estimation output results.

Fitting the AR (1) model still found the first lag to be significant. The R² value was found to be 0.458, implying 45.8% of the variations in milk production at time t can be explained by the first lag of the series (i.e. milk production in the previous one period).

Model comparison.

the AR(1) model had its lag significant lag compared to the AR(2) whose second lag was not significant and the AR(3) model whose second and third lags were not significant. This implied that a true relationship existed between the series and its first lag while the same couldn’t be said about the second and third lags. For this reason, the AR (1) model was taken up, despite it having a low R² value.

The model was specified as:

MP_t=21065.62 + 0.6266116MP _t-1

Where;

MP_{t =} Milk production at time t.

MP _t-1= Milk production in the previous period.

This model implied that the total litters of milk produced at a given time t, depend on the total number of litters that were produced in the previous period.

Without considering the total number of litters of milk produced in the previous period, the total number of litters that would be produced at a time t would be 21065.62 litters.

A unit increase the number of milk produced in the previous period would lead to an increase in the total amount of milk produced at a given time t by 0.6266116 litters.

 4.5. Forecast for Milk production for 2017.

Table 4. 6. Showing 2017 milk production forecasts.

The forecasts revealed a steady increase in milk production.

CHAPTER FIVE.

SUMMERY, CONCLUSION AND RECOMMENDATION.

5.1. Summery

The main emphasis of this study was to conduct a time series analysis for the milk production in Uganda in (000) litters from January 2015 to December 2016. The study used a secondary univariate time series data set from Sameer dairy company.

A time plot was used to examine the trend of the series. Stationarity of the series was conducted by using the Augmented Dickey Fuller unit root test and the correlogram plot at level and first difference.

An AR (1) model was selected as the best model to make forecasts for milk production. The model was later on used to make a 12 months forecast for the year 2017.

5.2. Conclusion.

The time plot revealed a cyclical kind of trend in the series.  The unit root test and the correlogram plots revealed that the series was stationary at the first level of differencing.

The estimated AR (1) model was specified as;

MP_t=21065.62 + 0.6266116MP _t-1

The forecasts made using the estimated model revealed a future increase in milk production in (000) litters.

5.3. Recommendation.

Since estimates in milk production show an increase in milk production, there is need for policymakers to foresee the requirements of milk storage, import and/or export of milk thereby allowing them to take appropriate measures and avoid wastage of the available resources.

APPENDICES.