1. UNIVERSITY OF NAIROBI
IMPACTS OF OIL PRICE FLUCTUATIONS ON THE
CONSUMER PRICE INDEX IN KENYA.
PROJECT IN B.Sc. STATISTICS BY:-
KANJA SAMUEL - I63/3412/2008
MUSYOKA DANIEL - I63/3407/2008
WAFULA EDGAR -I63/3032/2008
KAHEHO SAMUEL - I63/2967/2008
UNIT: STA 420
SUPERVISOR: DR. MWANIKI
2. Presentation Summary
Background Information
Problem Statement
Objectives
Methodology (Time Series and Linear Modeling)
Model Fitting
Data Analysis and Presentation
Summary of Findings
Recommendations
Conclusions
Questions and Answers Project in Statistics 2012-UON
3. Background Information
Overview of Oil Industry and Pricing in Kenya
Consumer Price Index (CPI)
Literature Review-Hamilton (1983, 1996)
-Basak (2010)
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4. There are in-built inefficiencies in the oil supply chain in
Kenya due to cartels and liberalised market.
Failure to come up with models that can assist in managing
the available oil volumes has led to speculation of prices, thus
giving the oil marketers loopholes to exploit the consumers.
High oil prices has resulted into increased production costs
which are then passed to the consumer, thus influencing the
Consumer Price Index.
Problem Statement
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5. Objectives of the Study
General objective
The general objective of the study is to forecast the prices of the major
oil products and Consumer Price Index in Kenya for the next 6 months
and how this can help in the realization of Vision 2030.
Specific Objectives
i) To forecast Consumer Price Index and the prices of major oil products
in the Kenya for the next 6 months.
ii) To find out if the rate of change in the price of different oil products is
uniform and proportion to the CPI over a period of 6 months.
iii) To determine the correlation of Consumer Price Index (CPI) and the
prices of the different major oil products in Kenya.
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7. Linear Regression
Let Y, X1, X2 represent CPI, Diesel price and petrol price respectively.
Thus
Yi=β0 +β1X1i+β2X2i+єi
Where i=1,2,3,…,n
β j represent the regression coefficients of the jth predictor, for j =1,2
єi is error term at the ith month. єi is independent and identically distributed with mean zero and
constant variance.
The hypothesis to be tested is
H0 : βi= 0, i=0,1,2
versus
H1 : anything different from H0
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8. Correlation
The sample correlation coefficient can be used to estimate the population Pearson
correlation, r between X and Y.
This can also be written as:
the realistic limits on the correlation coefficient are not -1 to +1 but a smaller range.
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9. Time Series Processes
AR
A pth-order autoregressive process {Xt} satisfies the equation
Xt =φ1Xt – 1+φ2Xt – 2+ … + φpXt – p + et
MA Process
A qth-order moving average process {Xt} satisfies the equation :
Xt= εt+β1εt-1+ β2εt-2+ …..+ βqεt-q
ARMA (p, q)
Is a mixed AR and MA process of orders p and q respectively. An ARMA (p, q)
process is normally abbreviated as shown below:
Xt= α1Xt-1+ α 2Xt-2+ ………+ αpXt-p+εt+β1εt-1+ β2εt-2+ …..+ βqεt-q
where εt~iid (0,σ2)
An ARIMA(p,d,q) process
An ARIMA(p,d,q) process expresses this polynomial factorisation property, and is
given by:
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10. Begin
Does a time plot of the data
appear to be stationary
Difference the data
Does the correlogram of
the data decay to zero?
Is there a sharp cut off in
the correlogram?
Is there a sharp cut off in
the partial correlogram?
M.A A. R
Mixed
ARMA
No
No
Yes
Yes
Yes
Yes
The type of data we have is classified as either Moving Average (M.A), Auto-
regressive (A.R) or mixed Auto-regressive Moving average (ARMA) after the
exploration and study of data characteristics.
Model Identification and Fitting
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12. Coefficientsa
Model
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.B Std. Error Beta
1 (Constant) 41.030 12.191 3.365 .001
Prices of
super petrol
(Kshs)
-.024 .692 -.022 -.035 .972
Prices of
diesel (Kshs)
.727 .670 .689 1.086 .282
a. Dependent Variable: Consumer Price Index (CPI)
CPI=41.030-0.024 Super + 0.727 Diesel
Linear Regression
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13. ANOVAb
Model
Sum of
Squares Df Mean Square F Sig.
1 Regression 5318.896 2 2659.448 22.777 .000a
Residual 6655.309 57 116.760
Total 11974.205 59
a. Predictors: (Constant), Prices of diesel (Kshs), Prices of super petrol (Kshs)
b. Dependent Variable: Consumer Price Index (CPI)
Analysis of Variance
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14. Correlations
Consumer Price
Index (CPI)
Prices of super
petrol (Kshs)
Prices of diesel
(Kshs)
Consumer Price
Index (CPI)
Pearson
Correlation
1 .658** .666**
Sig. (2-tailed) .000 .000
N 60 60 60
Prices of super
petrol (Kshs)
Pearson
Correlation
.658** 1 .988**
Sig. (2-tailed) .000 .000
N 60 60 60
Prices of diesel
(Kshs)
Pearson
Correlation
.666** .988** 1
Sig. (2-tailed) .000 .000
N 60 60 60
**. Correlation is significant at the 0.01 level (2-tailed).
Correlation
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18. Forecast
Model
Jan 2012 Feb 2012 Mar 2012 Apr 2012 May 2012 Jun 2012
Prices of super petrol
(Kshs)-Model_1
Forecast 126.302 127.667 128.578 129.235 129.748 130.179
UCL 134.144 142.702 150.565 157.744 164.330 170.425
LCL 118.810 113.852 109.094 104.779 100.937 97.523
Prices of diesel (Kshs)-
Model_2
Forecast 115.848 116.665 117.179 117.566 117.900 118.212
UCL 125.598 134.126 141.471 147.925 153.731 159.063
LCL 106.679 100.969 96.160 92.140 88.732 85.787
For each model, forecasts start after the last non-missing in the range of the requested estimation period,
and end at the last period for which non-missing values of all the predictors are available or at the end date
of the requested forecast period, whichever is earlier.
Model Description
Model Type
Model ID Prices of super petrol
(Kshs)
Model_1 ARIMA(1,1,0)
Prices of diesel (Kshs) Model_2 ARIMA(1,1,0)
Forecasts for Super and Diesel Prices
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20. Model Description
Model Type
Model
ID
Consumer Price Index
(CPI)
Model_
1
ARIMA(0,1,1)
The CPI data produces an ARIMA (0,1,1) model, which is primarily an MA(1) model, as our best series model.
Consequently, the future CPI values are regressed on only the past value with a small error associated to the approximation.
Forecast
Model
Jan 2012
Feb
2012
Mar
2012
Apr il
2012
May
2012
Jun
2012
Consumer Price
Index (CPI)-
Model_1
Forecas
t
130.991 132.062 133.141 134.230 135.327 136.434
UCL 132.976 135.805 138.095 140.188 142.175 144.096
LCL 129.028 128.396 128.322 128.464 128.731 129.082
For each model, forecasts start after the last non-missing in the range of the requested estimation period, and
end at the last period for which non-missing values of all the predictors are available or at the end date of the
requested forecast period, whichever is earlier.
CPI Forecast
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21. CPI Observed and Forecasted Values
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24. From the findings and analysis of our study, we’ve realized a number of
outcome related to study objectives, they include:
There’s a strong positive correlation between the CPI and the two oil
products of petrol and diesel, and all the three components of our study
exhibit a trend over the whole period of our study.
The rates of change in the oil industry over a span of time are not the same,
not constant.
All the oil products behave in a similar manner in the short-run and/or
long run in terms of pricing and consequently the effects on the CPI.
The prices of the commodities over the next six months will surely keep
increasing and transitively, so will the CPI even if the other components
held constant.
Summary of Findings
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25. The oil products should be given more weight in the
calculation of the CPI due to their positive linear relationship
of 44.4%.
The forecasted values show that the CPI and the oil products
prices have an increasing trend for the next 6months, thus, the
stakeholders should have clear control measures to curb
unnecessary price increases.
There are other stronger factors which affect the CPI
positively and this shows that the government can still control
inflation by sensitizing the stakeholders and general public on
key factors that affect the CPI.
Recommendations
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26. Future research should consider breaking the analysis to
focus on the different classes of people within the economy or
different sectors.
More oil products should be included to develop a
parsimonious and complete model. This may also include the
whole basket.
The next research should consider the emerging trends in
the oil industry.
Recommendation for Further Research
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27. As per the forecasts for CPI using ARIMA (0, 1, 1) and the oil
products using ARIMA (1, 1, 0). This shows that diesel and petrol
has the same model as explained by the high correlation.
For a period of 6 months, the rates of change in the prices of the
oil products are 63.6and 69.9 for diesel and petrol respectively.
The rate of change of CPI over the same period is 70.8. It’s
slightly higher considering that the predictors we are using are
only subsets of the many components of the CPI.
The CPI and the various oil products are directly related with both
sets showing uptrend all through the study period.
Conclusions
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