1) Triple exponential smoothing was used to analyze monthly bean supply price data for Mbeya and demand data for Kinondoni in Tanzania from 2004-2014.
2) The multiplicative seasonal model best fit the increasing seasonal variations in Mbeya's data. Smoothing parameters of 0.2, 0.1, and 0.1 were applied.
3) Forecasts for 2015 were generated for both locations based on the exponential smoothing models. Accuracy metrics and residual analysis were also calculated.
An index number measures relative changes in price, quantity, or other variables over time or between locations. It expresses these changes as percentages. There are several types of index numbers including price, quantity, and value indexes. Index numbers can be constructed using simple aggregate, simple average of price relatives, or weighted methods. Weighted indexes assign weights to items based on quantities in the base or current period. Common weighted indexes include Laspeyres, Paasche, Fisher ideal, and chain indexes. Index numbers are used to track inflation or deflation, reveal economic trends, and help formulate government policies.
This document discusses various types of index numbers used to measure changes in economic variables over time. It defines an index number as a quantitative measure of the growth of prices, production, or other quantities of economic interest from one period to another. The document then describes different characteristics, uses, problems, classifications, and methods for constructing index numbers, including simple aggregative methods, weighted aggregative methods like Laspeyres and Paasche, and chain index numbers. It provides examples to illustrate how to calculate different index numbers.
Index numbers are used to measure and compare changes in prices, quantities, and values over time. There are several types of index numbers including simple price indexes, quantity indexes, value indexes, and aggregate price indexes. Aggregate price indexes include unweighted, Laspeyres, Paasche, and fixed-weight indexes. The Consumer Price Index is a widely used fixed-weight aggregate price index published monthly by the Bureau of Labor Statistics to measure inflation experienced by urban consumers.
This document discusses key concepts in economic statistics including:
1. The stages of the research process include problem identification, generating hypotheses, conducting research, statistical analysis, and drawing conclusions.
2. Descriptive statistics summarize and describe data while inferential statistics make inferences about a population based on a sample.
3. Data can be qualitative, quantitative, cross-sectional, or time-series. Common descriptive statistics include the mean, median, mode, standard deviation, and range.
This document discusses different types of index numbers used in business statistics. It provides classifications of index numbers including unweighted index numbers, weighted index numbers, simple index numbers, Paasche's Price Index, Fisher Ideal Index, and Laspeyre's Price Index. Unweighted index numbers give equal weight to each stock, while weighted indexes weight stocks based on their market capitalizations. Fisher's Ideal Index Number is defined as the geometric mean of the Laspeyre's and Paasche's index numbers, and is considered ideal as it satisfies tests of time reversal and factor reversal.
This document discusses index numbers, which are statistical values that measure changes in variables like price or quantity over time. It covers simple index numbers calculated for a single item, composite index numbers for multiple items, and weighted index numbers that account for quantities. The most commonly used index in Australia is the Consumer Price Index (CPI), which measures price changes in a fixed basket of consumer goods and services to indicate inflation and cost of living changes. The document provides formulas and explanations for simple, composite, weighted (Laspeyres, Paasche), and Fisher's ideal indexes.
This document discusses index numbers, which are statistical tools used to measure relative changes in variables such as prices or quantities over time. It defines index numbers and outlines their key features and types, including price, quantity, value, simple and composite index numbers. The document also describes several methods for constructing index numbers, such as Laspeyre's method, Paasche's method, Fisher's ideal method and consumer price indexes. Index numbers are expressed as percentages and measure the effect of changes over periods of time.
Multiple Regression worked example (July 2014 updated)Michael Ling
The document describes using regression analysis to predict daily ice cream sales based on temperature and humidity. A base model found temperature and humidity explained 62.9% of sales variance. An interaction model adding a temperature*humidity term explained 77.3%, a significant improvement. Graphs show humidity moderates the temperature-sales relationship, and temperature moderates humidity-sales. The analysis validates both models with adequate sample size and meets statistical assumptions.
An index number measures relative changes in price, quantity, or other variables over time or between locations. It expresses these changes as percentages. There are several types of index numbers including price, quantity, and value indexes. Index numbers can be constructed using simple aggregate, simple average of price relatives, or weighted methods. Weighted indexes assign weights to items based on quantities in the base or current period. Common weighted indexes include Laspeyres, Paasche, Fisher ideal, and chain indexes. Index numbers are used to track inflation or deflation, reveal economic trends, and help formulate government policies.
This document discusses various types of index numbers used to measure changes in economic variables over time. It defines an index number as a quantitative measure of the growth of prices, production, or other quantities of economic interest from one period to another. The document then describes different characteristics, uses, problems, classifications, and methods for constructing index numbers, including simple aggregative methods, weighted aggregative methods like Laspeyres and Paasche, and chain index numbers. It provides examples to illustrate how to calculate different index numbers.
Index numbers are used to measure and compare changes in prices, quantities, and values over time. There are several types of index numbers including simple price indexes, quantity indexes, value indexes, and aggregate price indexes. Aggregate price indexes include unweighted, Laspeyres, Paasche, and fixed-weight indexes. The Consumer Price Index is a widely used fixed-weight aggregate price index published monthly by the Bureau of Labor Statistics to measure inflation experienced by urban consumers.
This document discusses key concepts in economic statistics including:
1. The stages of the research process include problem identification, generating hypotheses, conducting research, statistical analysis, and drawing conclusions.
2. Descriptive statistics summarize and describe data while inferential statistics make inferences about a population based on a sample.
3. Data can be qualitative, quantitative, cross-sectional, or time-series. Common descriptive statistics include the mean, median, mode, standard deviation, and range.
This document discusses different types of index numbers used in business statistics. It provides classifications of index numbers including unweighted index numbers, weighted index numbers, simple index numbers, Paasche's Price Index, Fisher Ideal Index, and Laspeyre's Price Index. Unweighted index numbers give equal weight to each stock, while weighted indexes weight stocks based on their market capitalizations. Fisher's Ideal Index Number is defined as the geometric mean of the Laspeyre's and Paasche's index numbers, and is considered ideal as it satisfies tests of time reversal and factor reversal.
This document discusses index numbers, which are statistical values that measure changes in variables like price or quantity over time. It covers simple index numbers calculated for a single item, composite index numbers for multiple items, and weighted index numbers that account for quantities. The most commonly used index in Australia is the Consumer Price Index (CPI), which measures price changes in a fixed basket of consumer goods and services to indicate inflation and cost of living changes. The document provides formulas and explanations for simple, composite, weighted (Laspeyres, Paasche), and Fisher's ideal indexes.
This document discusses index numbers, which are statistical tools used to measure relative changes in variables such as prices or quantities over time. It defines index numbers and outlines their key features and types, including price, quantity, value, simple and composite index numbers. The document also describes several methods for constructing index numbers, such as Laspeyre's method, Paasche's method, Fisher's ideal method and consumer price indexes. Index numbers are expressed as percentages and measure the effect of changes over periods of time.
Multiple Regression worked example (July 2014 updated)Michael Ling
The document describes using regression analysis to predict daily ice cream sales based on temperature and humidity. A base model found temperature and humidity explained 62.9% of sales variance. An interaction model adding a temperature*humidity term explained 77.3%, a significant improvement. Graphs show humidity moderates the temperature-sales relationship, and temperature moderates humidity-sales. The analysis validates both models with adequate sample size and meets statistical assumptions.
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The document provides an overview of time series analysis, including definitions, components, and methods for measuring trends, seasonal variations, cyclical variations, and irregular variations in time series data. It discusses adjusting raw time series data, measuring linear and nonlinear trends, converting annual trends to monthly trends, and different methods for measuring seasonal, cyclical, and irregular variations, including indexes and averages. Examples are provided to illustrate calculating seasonal variations using the monthly average method.
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Dear students, get latest Solved NMIMS assignments and case study help by professionals.
Mail us at : help.mbaassignments@gmail.com
Call us at : 08263069601
The headline CPI (for all urban areas) annual inflation rate in September 2015 was 4,6%. This rate was the same as the corresponding annual rate of 4,6% in August 2015. On average, prices were unchanged between August 2015 and September 2015.
How do your campaigns perform against the rest of the industry? Laurence Kite from Dovetail gives you the benchmarks to compare just how you're doing.
You'll find more data and a complete write-up of the presentation here:
http://www.dovetailservices.com/guides/christmas-benchmarking-report-2014/
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This is my scorecard, what I infer from my simplified worksheet (...)Giuseppe Piazzolla
(...) crossing balance sheet, income and cash flow statements.
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° A really high Altman's Z-score and a very robust history of positive and growing operating income;
° No debt - interest expenses;
° Piotroski score is very robust;
° A recent (relatively) high fcfy due to lower market cap;
° Slowing sales growth (now negative) and pressure in assets turnover and gross margin (high competition in the growing craft beer category);
° Roic, has been particularly subdued recently, BUT never under low 20s
° Tangible book value per share growth has been outstanding.
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This document provides an overview of time series forecasting techniques. It discusses the components of time series data including trends, cycles, seasonality and irregular fluctuations. It also covers stationary and non-stationary time series. Forecasting techniques covered include naive methods, smoothing techniques like moving averages and exponential smoothing, and decomposition methods. Regression models for trend analysis and measuring forecast accuracy are also discussed.
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The document discusses capital requirements for small and medium-sized entities (SMEs) and other retail asset classes under Basel II. It provides formulas for calculating capital requirements based on probability of default, loss given default, maturity, and firm size. It also examines methods for determining probability of default using migration matrices and cohort or hazard rate approaches based on historical credit rating data. Transition probabilities are presented for one, five, and ten year time periods based on these methods.
Time series analysis is conducted on daily views of Wikipedia article. The data set contains individual Pages and daily views of the pages.
The total number of pages in the data set is 145k. The training data set 1 contains daily views from July 1st 2015 to Dec 31st 2016 with a total number of 550 days.
Testing of forecast model is based on data from January, 1st, 2017 up until March 1st, 2017, which is 60 days including 1st march 2017.
This document provides an analysis of audience trends for Food Network and its competitors from 2006 to 2016. It finds that while Food Network's average audience has declined slightly, the rate of decline is slowing. Predictive analysis indicates audiences for Food Network and competitors like HGTV and AMC will likely increase in upcoming quarters. Sentiment analysis on Twitter finds Food Network has more positive sentiment than competitors. Program diagnostics examine minute-by-minute ratings for Chopped Junior and Cooks vs Cons, finding ratings grow steadily or remain stable for most episodes.
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This document analyzes trends in non-performing assets (NPAs) of major commercial banks in India from 2003-2013. It finds that gross and net NPAs as a percentage of total assets declined over time for State Bank of India, Punjab National Bank, and Central Bank of India. Priority sector lending, especially to small and medium enterprises, accounted for the largest portion of NPAs, though this varied by bank. The document examines reasons for NPAs and the regulatory framework around classifying and provisioning for problematic loans.
The document provides an overview of time series analysis, including definitions, components, and methods for measuring trends, seasonal variations, cyclical variations, and irregular variations in time series data. It discusses adjusting raw time series data, measuring linear and nonlinear trends, converting annual trends to monthly trends, and different methods for measuring seasonal, cyclical, and irregular variations, including indexes and averages. Examples are provided to illustrate calculating seasonal variations using the monthly average method.
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The document discusses various time series forecasting models that can be used to predict the number of nurses needed each quarter in a hospital's surgical division. It provides historical data on the number of nurses needed from 1997 to 1999. The document then demonstrates forecasts for 2000 using three different models: 1) a 3-period simple moving average, 2) exponential smoothing with alpha=0.2, and 3) a linear trend model that incorporates both trend and seasonality. The linear trend model is found to have the lowest mean squared error and mean absolute deviation, indicating it provides the most accurate forecasts.
Dear students, get latest Solved NMIMS assignments and case study help by professionals.
Mail us at : help.mbaassignments@gmail.com
Call us at : 08263069601
The headline CPI (for all urban areas) annual inflation rate in September 2015 was 4,6%. This rate was the same as the corresponding annual rate of 4,6% in August 2015. On average, prices were unchanged between August 2015 and September 2015.
How do your campaigns perform against the rest of the industry? Laurence Kite from Dovetail gives you the benchmarks to compare just how you're doing.
You'll find more data and a complete write-up of the presentation here:
http://www.dovetailservices.com/guides/christmas-benchmarking-report-2014/
Multiple regression model of sale prediction based on the information about day of the weeks, holidays, and sales promotions
elena-tulainova@yandex.ru
looking opportunity to work as an analyst in retail/food industry
This document describes a study that used Bayesian statistics to analyze the relationship between average total payroll and average winning percentage in Major League Baseball teams from 2004 to 2012. Data on payroll and winning percentage for each team was collected and averaged over the time period. Bayesian linear regression with both non-informative and informative priors was used to assess the linear relationship between average payroll and winning percentage. The results of the Bayesian regression models are presented along with descriptive statistics of the data.
AP Statistics - Confidence Intervals with Means - One SampleFrances Coronel
The document discusses how to construct confidence intervals for means using z-scores and t-scores. It outlines the assumptions, calculations, and conclusions for one-sample confidence intervals. The key steps are to check assumptions about the population distribution and sample size, then use the appropriate formula to calculate the confidence interval with either z-critical values if the population standard deviation is known, or t-critical values if the population standard deviation is unknown.
The document discusses risk management in commercial lending portfolios with small time series datasets. It aims to show that time series models are more accurate than expected loss models for forecasting portfolio losses. It also proposes a methodology to develop time series models with less than 50 observations. The methodology involves disaggregating quarterly loss data into simulated monthly observations to increase the dataset size. Time series models are then used to forecast monthly losses up to Q4 2015, which are aggregated to obtain quarterly and 12-month loss forecasts. The results are compared to expected loss model forecasts to evaluate accuracy.
This is my scorecard, what I infer from my simplified worksheet (...)Giuseppe Piazzolla
(...) crossing balance sheet, income and cash flow statements.
We are checking the health of SAM - The Boston Beer Company, Inc.
° A really high Altman's Z-score and a very robust history of positive and growing operating income;
° No debt - interest expenses;
° Piotroski score is very robust;
° A recent (relatively) high fcfy due to lower market cap;
° Slowing sales growth (now negative) and pressure in assets turnover and gross margin (high competition in the growing craft beer category);
° Roic, has been particularly subdued recently, BUT never under low 20s
° Tangible book value per share growth has been outstanding.
- The SOHO Package was launched in October 2017 to target small businesses and is the only hybrid package that converts to prepaid after postpaid incentives are used.
- As of September 2018, 49,000 packages had been sold with an active customer base of 36,816. Most customers only remain active for 3 months or less.
- Revenue from the postpaid component totaled 22.6 million Pakistani rupees through September with an additional 7.7 million from prepaid usage. However, bill recovery is only around 75% with most customers not paying monthly bills.
July 2015 - Market Snapshot - General OverviewMLSListings Inc
This document contains market data comparing July 2015 to previous months and years for several counties in California. The key points are:
- Single family and condo/townhouse inventory increased in July 2015 compared to July 2014 across most counties. Santa Clara county saw the largest year-over-year inventory growth at 31%.
- Closed sales were up in July 2015 compared to the previous year for most counties. Santa Clara county again saw the largest increase, with closed sales rising 31% from July 2014 to July 2015.
- Median and average sales prices rose from July 2014 to July 2015 in most counties, with increases ranging from 3% to 14% depending on the county and property type.
Hindustan Unilever Limited (HUL) is the largest fast moving consumer goods (FMCG) company in India. It has a presence in over 20 consumer product categories through brands like Lux, Lifebuoy, and Surf Excel. The document analyzes HUL's revenues and profits over 12 years using various forecasting methods like time series analysis, linear and exponential modeling to predict future trends. Different analysis techniques like PivotTables, histograms and correlation are applied to HUL product sales data to gain insights.
Multi Objective Optimization of PMEDM Process Parameter by Topsis Methodijtsrd
In this study, MRR, SR, and HV in powder mixed electrical discharge machining PMEDM were multi criteria decision making MCDM by TOPSIS method. The process parameters used included work piece materials, electrode materials, electrode polarity, pulse on time, pulse off time, current, and titanium powder concentration. Some interaction pairs among the process parameters were also used to evaluate. The results showed that optimal process parameters, including ton = 20 µs, I= 6 A, tof = 57 µs, and 10 g l. The optimum characteristics were MRR = 38.79 mm3 min, SR = 2.71 m, and HV = 771.0 HV. Nguyen Duc Luan | Nguyen Duc Minh | Le Thi Phuong Thanh ""Multi-Objective Optimization of PMEDM Process Parameter by Topsis Method"" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-4 , June 2019, URL: https://www.ijtsrd.com/papers/ijtsrd23169.pdf
Paper URL: https://www.ijtsrd.com/engineering/manufacturing-engineering/23169/multi-objective-optimization-of-pmedm-process-parameter-by-topsis-method/nguyen-duc-luan
This document provides an overview of time series forecasting techniques. It discusses the components of time series data including trends, cycles, seasonality and irregular fluctuations. It also covers stationary and non-stationary time series. Forecasting techniques covered include naive methods, smoothing techniques like moving averages and exponential smoothing, and decomposition methods. Regression models for trend analysis and measuring forecast accuracy are also discussed.
This document shows monthly progress percentages from January 2011 to October 2015 for a four-laning highway project in Bihar, India. It includes the original project timeline, revised monthly targets, actual monthly progress achieved, and cumulative percentages completed. Several notes list factors that could impact the project schedule such as delays in land acquisition, design approvals, and equipment availability. The project met three contractual milestones, with the final completion of outstanding items by April 2015.
The document discusses capital requirements for small and medium-sized entities (SMEs) and other retail asset classes under Basel II. It provides formulas for calculating capital requirements based on probability of default, loss given default, maturity, and firm size. It also examines methods for determining probability of default using migration matrices and cohort or hazard rate approaches based on historical credit rating data. Transition probabilities are presented for one, five, and ten year time periods based on these methods.
1. 1
Analysis of Data Using Triple Exponential Smoothing and Commentary Treating Mbeya
As Supply Region For Beans And Kinondoni As The Market Region For Beans.
By: MAWDO GIBBA
3. 3
Introduction
The objective of the assignment is to analyze the data and give comment on the analysis of the
data. Several methods were used to approach the data analysis and all approaches cannot be
presented. As per the requirement of the assignment question, we resorted in reporting the
HoltWinters exponential smoothing to be specific, the triple exponential smoothing.
The HoltWinters seasonal method otherwise the triple exponential smoothing comprises the
forecast equation and three smoothing equations one for the level, one for trend, and one for the
seasonal component, with smoothing parameters α, β and γ. We use m to denote the period of the
seasonality, m=12, for this case, because we are dealing with monthly data.
There are two variations to this method that differ in the nature of the seasonal component. The
additive method is preferred when the seasonal variations are roughly constant through the
series, while the multiplicative method is preferred when the seasonal variations are changing
proportional to the level of the series. With the additive method, the seasonal component is
expressed in absolute terms in the scale of the observed series, and in the level equation the
series is seasonally adjusted by subtracting the seasonal component. Within each year the
seasonal component will add up to approximately zero. With the multiplicative method, the
seasonal component is expressed in relative terms (percentages) and the series is seasonally
adjusted by dividing through by the seasonal component. Within each year, the seasonal
component will sum up to approximately m.
The objectives of using this method is analyse the data for both Mbeya and Kinondoni include
the following:
Estimate the HoltWinter Model using either the seasonal multiplicative or seasonal
additive methods whichever of the two methods that best fits or describes the data.
Calculate the Level, Trend and Seasonality in order to generate the fitted values or
predicted values of the model used for both Mbeya and Kinondoni.
Do a forecast for the whole period of year 2015 for both Mbeya and Kinondoni.
Do residual analysis and forecast measurement accuracy analysis to test the fit and
accuracy of the fitted time series model using the techniques of MAD, MSE, MAPE,
THEIL’s U and error scatter plot.
4. 4
The chart below shows the plot of the Supply prices of beans for Mbeya and as can be seen from
the seasonal variation from the plot, there is an increasing variation of supply price of bean over
the period. For this kind of seasonal variation, the multiplicative method of the HoltWinter triple
exponential smoothing is preferred, that is when the seasonal variations are changing
proportional to the level of the series. Therefore we used the seasonal multiplicative approach of
triple exponential smoothing to analyse the supply price of beans for Mbeya.
The table below shows the smoothing parameters that were used in fitting the models. An alpha
level of 0.2, beta level of 0.1 and gamma level of 0.1 were used to smoothen the multiplicative
seasonal variation by using the HoltWinters triple exponential smoothing for Supply price of
bean in Mbeya. Since the selection of the smoothing parameters is objective, thus we selected the
parameters that will give the best smoothing to the model.
Smoothing Parameters
Alpha 0.2
Beta 0.1
Gamma 0.1
Time
Supply
2 4 6 8 10 12
4000080000120000
5. 5
The table below shows the coefficients generated from the model, “a” which is the first or initial
smoothed level value and “b” which is the first smoothed trend value and seasonal indices “S”.
Since there are twelve seasons in the given data, so we expect to have seasonal indices from
to . The trend and level are initialized at period S. These initialization values are estimated as:
( )
( )
Coefficients
a 1.23059E-05
b -0.0458759
S1 1.152692
S2 1.123397
S3 1.005243
S4 0.88383
S5 0.9451797
S6 0.938037
S7 0.9013298
S8 0.8973297
S9 0.9244399
S10 0.9754336
S11 1.087385
S12 1.129305
The table below gives the fitted or predicted values of the HoltWinters Triple Exponential
smoothing for the supply price of beans for Mbeya.
The whole of year 2004 is without fitted or predicted values that is from January 2004 through
December 2004. Fitted values begin from period two that is from January 2005 down to the
December 2014. For the Winter’s multiplicative method, the level, trend and seasonality are
generated as:
( )( )
( ) ( )
6. 6
( )
( )
Fitted Values
period Month Level Trend Season
2005 Jan 40058.46 34271.17 663.889423 1.1466548
2005 Feb 39469.93 35862.38 756.620803 1.0778538
2005 Mar 34363.64 37387.95 833.515721 0.8990665
2005 Apr 31003.04 38807.93 892.162411 0.7809312
2005 May 39331.74 40083.47 930.500201 0.958984
2005 Jun 41373.23 41153.34 944.437012 0.9827889
2005 Jul 39337.16 42003.3 934.989904 0.9161322
2005 Aug 39857.94 43628.77 1004.037687 0.8930189
2005 Sep 43859.48 45336.5 1074.407021 0.9450253
2005 Oct 47260.87 45555.59 988.875264 1.0153917
2005 Nov 55662.1 45709.74 905.402713 1.1940776
2005 Dec 53423.46 44224.5 666.337831 1.1900751
Month Level Trend Season
2006 Jan 51470 43863.93 563.64748 1.1585146
2006 Feb 48228.41 43871.69 508.059077 1.086721
2006 Mar 41657.92 45441.96 614.279369 0.9045012
2006 Apr 38263.25 48001.41 48001.41 0.7839189
2006 May 50390.34 51406.08 1068.384095 0.9602831
2006 Jun 52982.86 52853.03 1106.240877 0.9819047
2006 Jul 50714.21 53907.56 1101.070027 0.9219318
2006 Aug 49470.54 54049.95 1005.201584 0.8985633
2006 Sep 51496.56 54004.46 900.132983 0.9379281
2006 Oct 55079.06 53848.75 794.547849 1.0079747
2006 Nov 63574.17 53716.08 701.826096 1.1682583
2006 Dec 63411.8 53206.84 580.719909 1.1789307
7. 7
Month Level Trend Season
2007 Jan 62229.11 53442.03 546.166482 1.152643
2007 Feb 59420.78 53659.19 513.266245 1.0968818
2007 Mar 49058.32 52978.93 393.913683 0.9191626
2007 Apr 42885.99 53243.09 380.938379 0.7997532
2007 May 53592.31 55118.99 530.434716 0.9630343
2007 Jun 54243.12 54816.79 447.170595 0.981528
2007 Jul 49983.25 54256.73 346.447617 0.9153909
2007 Aug 48896.06 54505.9 336.719567 0.8915705
2007 Sep 51999.3 55478.56 400.313902 0.9305718
2007 Oct 56680.81 56191.73 431.599978 1.0010151
2007 Nov 66047.57 56622.97 431.563822 1.1576218
2007 Dec 68849.72 58023.15 528.424932 1.1758817
Month Level Trend Season
2008 Jan 71844.71 61645.81 837.848602 1.1498161
2008 Feb 73486.23 66377.55 1227.237617 1.0869975
2008 Mar 68546.69 72891.97 1755.955908 0.9182666
2008 Apr 69699.21 83567.62 2647.925858 0.8084297
2008 May 92625.78 93402.51 3366.622505 0.9571831
2008 Jun 97426.16 96647.78 3354.487217 0.9742395
2008 Jul 90730.27 96211.79 2975.439512 0.9147374
2008 Aug 88995.64 96642.4 2720.956218 0.8956585
2008 Sep 93754.66 97946.38 2579.258568 0.9326443
2008 Oct 102617.9 99988.53 2525.547575 1.0010125
2008 Nov 120585.1 101091.94 2383.334083 1.1653517
2008 Dec 121682.8 99463.25 1982.131764 1.1994904
8. 8
Month Level Trend Season
2009 Jan 117518.8 97948.16 1658.114675 1.1767966
2009 Feb 111198.9 97948.16 1466.597666 1.1185354
2009 Mar 95078.44 97978.61 1322.982676 0.9574715
2009 Apr 85206.43 100779.56 1470.7794 0.833312
2009 May 101772.8 104666.37 1712.383315 0.9567024
2009 Jun 102705 105485.52 1623.0596 0.9588866
2009 Jul 95255.81 103937.2 1305.921391 0.9051024
2009 Aug 95985.17 106372.1 1418.818997 0.8904755
2009 Sep 102292.8 108433.45 1483.072885 0.9306403
2009 Oct 110933.7 109961.07 1487.526778 0.9953797
2009 Nov 128120.5 110365.25 1379.192864 1.1465491
2009 Dec 127957.9 107180.75 922.823472 1.1836601
Month Level Trend Season
2010 Jan 121507.4 103594.7 471.935752 1.1675927
2010 Feb 112672.3 101146.19 179.891379 1.1119773
2010 Mar 95582.76 99271.67 -25.549884 0.9630882
2010 Apr 83277.83 99065.29 -43.632623 0.8410062
2010 May 96244.45 100807.18 134.919506 0.9534619
2010 Jun 94260.31 99523.39 -6.951818 0.9471834
2010 Jul 89508.68 98576.32 -100.963413 0.908945
2010 Aug 86833.57 97483.29 -200.170245 0.8925862
2010 Sep 90155.04 97079.09 -220.573175 0.9307911
2010 Oct 95972.64 97004.19 -206.005851 0.9914715
2010 Nov 107315.8 95551.42 -330.681903 1.1270214
2010 Dec 107471.4 92961.19 -556.636939 1.163053
9. 9
Month Level Trend Season
2011 Jan 103713.4 90601.47 -736.944953 1.1541077
2011 Feb 97704.02 89383.58 -785.040032 1.1027724
2011 Mar 88044.4 91936.85 -451.209049 0.962385
2011 Apr 86234.52 101287.04 528.930849 0.8469646
2011 May 106448.4 110851.88 1432.521777 0.9480252
2011 Jun 110988.1 115837.8 1787.861676 0.9435701
2011 Jul 110106.1 119641.82 1989.477855 0.9052449
2011 Aug 111458 122863.21 2112.668578 0.8918358
2011 Sep 120587.5 127146.24 2329.704862 0.9313502
2011 Oct 130095.6 129564.53 2338.564126 0.9862968
2011 Nov 153065.9 134545.18 2602.772616 1.1160638
2011 Dec 160353.9 136446.94 2532.671356 1.1537945
Month Level Trend Season
2012 Jan 161859.1 138103.56 2445.066251 1.1516237
2012 Feb 159713.9 140332.56 2423.459561 1.1187895
2012 Mar 145969.2 143522.22 2500.079271 0.9996364
2012 Apr 128568.1 144643.36 2362.184954 0.8745802
2012 May 139024.2 142915.32 1953.162765 0.9596577
2012 Jun 134037.6 139669.3 1433.244931 0.9499303
2012 Jul 127151.1 138705.83 1193.572769 0.9088755
2012 Aug 123548.3 136717.64 875.396308 0.8979252
2012 Sep 130356.4 138918.7 1007.962946 0.9316049
2012 Oct 140794 140565.69 1071.866233 0.994044
2012 Nov 157620.1 140555.72 963.682559 1.1137703
2012 Dec 162203.2 140116.58 823.400369 1.1508669
10. 10
Month Level Trend Season
2013 Jan 160793.5 139072.67 636.668776 1.1509145
2013 Feb 157352.6 139709.08 636.642716 1.1211785
2013 Mar 138818.6 138907.84 492.854597 0.9958245
2013 Apr 118785.6 137127.48 265.533046 0.864568
2013 May 128954.1 136254.5 151.681846 0.9453685
2013 Jun 124662.8 132396.29 -249.306777 0.9433647
2013 Jul 114458.8 127801.73 -683.832417 0.9004148
2013 Aug 113019.1 126167.26 -778.896059 0.9013527
2013 Sep 116227 125319.33 -785.799931 0.933299
2013 Oct 121177.4 123199.12 -919.24098 0.9909836
2013 Nov 131594.2 119794.8 -1167.74864 1.1093099
2013 Dec 131516.4 116294.04 -1401.04978 1.1446859
Month Level Trend Season
2014 Jan 130183.4 114548.55 -1435.493801 1.1509136
2014 Feb 125230.9 113551.77 -1391.621809 1.1165363
2014 Mar 111478.7 113910.05 -1216.632018 0.9892212
2014 Apr 100564.6 117448.93 -741.080478 0.8616784
2014 May 116537.9 124723.69 60.503161 0.9339155
2014 Jun 120143.5 128663.8 448.46345 0.930535
2014 Jul 118929.3 131768.05 714.042382 0.897701
2014 Aug 121370.9 133834.59 849.292067 0.9011541
2014 Sep 124499.6 133269.93 707.897217 0.9292555
2014 Oct 130511.4 132264.28 536.542137 0.9827606
2014 Nov 143784.2 130370.85 293.544642 1.1004082
2014 Dec 145003.2 126909.57 -81.937301 1.1433091
The table below gives the forecasted values for the whole of year 2015 that is from January 2015
to December 2015. The forecasted value of supply price of beans at the beginning of the year
2015 is 141320.8 with confidence level of one percent error, as this forecasted value must lie
between its corresponding upper and lower bound. The same applies to the rest of the other
months down to December 2015 with forecasted value of 100803.96 as it also lies between its
corresponding upper and lower bounds of one percent error.
11. 11
Forecast For Supply For The Whole Of Year 2015
Confidence Bound
period Month Forecasted Values Upper Bound Lower Bound
2015 Jan 141320.8 148543.9 134097.75
2015 Feb 137213.9 146311.4 128116.32
2015 Mar 122321.1 132670.7 111971.46
2015 Apr 107141.7 118422 95861.46
2015 May 114145.2 127922.7 100367.71
2015 Jun 112852.3 128417.8 97286.78
2015 Jul 108022.7 124925.8 91119.55
2015 Aug 107131.6 125875.1 88388.11
2015 Sep 109944.2 131180.8 88707.54
2015 Oct 115561.4 139964 91158.78
2015 Nov 128325.7 157652.2 98999.12
2015 Dec 132754.7 164705.4 100803.96
The chart below depicts the smoothened seasonal multiplicative forecast for the supply price of
beans for Mbeya. The line with dots is the smoothened line.
Time
Supply
2 4 6 8 10 12
4000080000120000
16. 16
Measurements of forecast accuracy were determined using the techniques of MAD, MAPE, MSE, THEIL’s U and residual plot. As
the Measurement of forecast accuracy table shows large values for MAD and MSE, the MAPE is about 10 percent which is acceptable
and the Theil’s U, which is slightly larger than zero. Since the Theil’s U is different than one and it is fairly close to zero then we can
conclude that the multiplicative triple exponential smoothing forecast produced are better than the naïve forecast.
Measurement of Forecast Accuracy
MAD 9486.243991
MAPE 9.985910844
MSE 172610906.8
Theil’s U 0.131246765
18. 18
ANALYSIS FOR KINONDONI
The plot shows the demand prices of beans (100Kg) for Kinondoni. As can be seen from the
plot, there is an increasing seasonal variation in the demand price for beans, but the increase in
the demand price for beans looks stable as indicated by the oscillations. In this situation it is
appropriate to use the additive seasonal HoltWinters triple exponential smoothing. Also due to
the presence of zero demand prices for beans in some months in the data set, the additive
seasonal method will do better than the multiplicative seasonal method of triple exponential
smoothing. The plotted data has almost shown constant variability. Hence the choice of additive
seasonal triple exponential smoothing. The demand price for beans for Kinondoni is analyzed
using the seasonal additive triple exponential smoothing.
In this regard also the smoothing parameters as shown in the table below are an alpha level of
0.2; beta level of 0.1 and gamma level of 0.1, were use in smoothing the forecast. Since the
choice of these smoothing parameters is subjective, we choose the parameters that give the best
smoothing forecast.
SMOOTHING PARAMETERS
Alpha 0.2
Beta 0.1
Gamma 0.1
Time
Demand
2 4 6 8 10 12
050000100000
19. 19
The table below gives the initialization values and initial seasonal indices for the seasonal
additive triple exponential smoothing model for demand price for beans for Kidondoni. The
value “a” which is the initial level value, “b” which is the initial trend value and to are
the initial seasonal indices, as shown in the table. These initial seasonal indices are computed as:
…………….
COEFFICIENTS
a 124873.5843
b -3254.0222
S1 6258.4307
S2 6081.4272
S3 -488.5466
S4 -5026.8528
S5 130.885
S6 1076.7557
S7 -5911.6547
S8 -5914.4704
S9 -3857.1757
S10 -2569.8874
S11 1451.726
S12 -7447.197
The table below shows the fitted or predicted values of the seasonal additive triple exponential
smoothing model of demand price for beans for Kidondoni. There are no predicted or fitted
values for the year 2004 that is from January 2004 down to December 2004. The predicted
values commenced from January 2005 to December 2014. The various components and the
predicted values are computed using;
( ) ( )( )
( ) ( )
( ) ( )
20. 20
Fitted Values
period Month Level Trend Season
2005 Jan 54430.42 45988.98 800.118 7641.326
2005 Feb 53521.18 48175.81 938.7896 4406.576
2005 Mar 55556.24 50201.36 1047.466 4307.41
2005 Apr 44586.25 52001.18 1122.701 -8537.63
2005 May 53021.85 53506.63 1160.976 -1645.76
2005 Jun 57400.81 54763.24 1170.539 1467.035
2005 Jul 47758.52 55770.22 1154.183 -9165.88
2005 Aug 50738.91 57103.5 1172.093 -7536.67
2005 Sep 58170.46 58018.81 1146.414 -994.757
2005 Oct 58615.16 57667.53 996.6451 -49.0069
2005 Nov 59604.61 56657.74 796.0018 796.0018
2005 Dec 65706.48 56999.42 750.5696 7956.493
period Month Level Trend Season
2006 Jan 64465 55721.29 547.7 8196.013
2006 Feb 61030.09 55698.19 490.6199 4841.282
2006 Mar 63881.12 58546.39 726.378 4608.351
2006 Apr 54060.77 61496.55 948.7556 -8384.53
2006 May 67493.18 67633.15 1467.54 -1607.51
2006 Jun 72127.1 69243.65 1481.837 1401.61
2006 Jul 61178.38 68966.67 1305.955 -9094.24
2006 Aug 63089.91 69500.55 1228.747 -7639.39
2006 Sep 68965.25 69457.51 1101.569 -1593.83
2006 Oct 68744.98 68682.63 913.9239 -851.58
2006 Nov 70693.22 67972.56 751.5244 1969.139
2006 Dec 74433.11 66735.44 552.6599 7145.015
21. 21
period Month Level Trend Season
2007 Jan 73183.17 64901.48 313.9976 7967.692
2007 Feb 69863.51 63897.04 182.1542 5784.315
2007 Mar 69459.24 63806.49 154.884 5497.861
2007 Apr 42525.84 50069.53 -1234.3 -6309.39
2007 May 36694.92 40330.06 -2084.82 -1550.32
2007 Jun 43795.57 44551.66 -1454.18 698.0819
2007 Jul 37551.13 47925.57 -971.367 -9403.07
2007 Aug 43756.67 52337.78 -433.01 -8148.1
2007 Sep 54346.26 56649.23 41.4368 -2344.41
2007 Oct 57338.25 58606.42 233.0117 -1501.18
2007 Nov 64948.79 63114.58 660.5266 1173.681
2007 Dec 75283.45 68009.15 1083.931 6190.365
period Month Level Trend Season
2008 Jan 80480.97 71696.39 1344.262 7440.319
2008 Feb 83430.34 76104.46 1650.642 5675.234
2008 Mar 84104.51 82080.23 2083.156 -58.8782
2008 Apr 81022.09 88242.49 2491.066 -9711.46
2008 May 96053.86 92421.73 2659.884 972.2462
2008 Jun 98250.71 93154.25 2467.146 2629.317
2008 Jul 89668.12 94557.05 2360.712 -7249.64
2008 Aug 92917.26 96816.94 2350.63 -6250.31
2008 Sep 101663.3 100734.1 2507.285 -1578.11
2008 Oct 105701.7 103008.7 2484.019 208.8816
2008 Nov 110689.7 105352.4 2469.986 2867.298
2008 Dec 117207.4 107534.5 2441.192 7231.69
22. 22
period Month Level Trend Season
2009 Jan 122109.6 110909.2 2534.545 8665.841
2009 Feb 121879.5 112076.4 2397.813 7405.287
2009 Mar 115341.4 111652.9 2115.682 1572.761
2009 Apr 104090.8 111261.9 1865.015 -9036.19
2009 May 115003.2 112954.2 1847.74 201.2971
2009 Jun 116414.3 112584.7 1626.015 2203.58
2009 Jul 104402.6 110443.3 1249.269 -7289.97
2009 Aug 107978.4 112292.8 1309.298 -5623.69
2009 Sep 112475 112906.4 1239.73 -1671.18
2009 Oct 113985.9 112734.6 1098.57 152.75
2009 Nov 115111.2 111494.4 864.6926 2752.121
2009 Dec 119291.9 110961.8 724.9693 7605.101
period Month Level Trend Season
2010 Jan 118636.5 109964.8 552.7716 8118.915
2010 Feb 116895.4 110106.9 511.7018 6276.765
2010 Mar 110508.8 109535.3 403.3749 570.0908
2010 Apr 102055.7 110683.1 477.8193 -9105.29
2010 May 113093.8 113107 672.4261 -685.602
2010 Jun 114890.9 113545.3 649.0093 696.5969
2010 Jul 107275.8 113723.7 601.9516 -7049.86
2010 Aug 108094.2 113478.9 517.2756 -5901.97
2010 Sep 111258.6 113069.7 424.6314 -2235.82
2010 Oct 110393.6 111001.1 175.3004 -782.76
2010 Nov 110716.7 108605.2 -81.8115 2193.227
2010 Dec 113092 106463.5 -287.805 6916.31
23. 23
period Month Level Trend Season
2011 Jan 111237.3 103807.3 -524.645 7954.635
2011 Feb 106129.3 101035.2 -749.39 5843.458
2011 Mar 101376.8 101170 -660.975 867.8686
2011 Apr 83391.29 93118.2 -1400.05 -8326.86
2011 May 95282.75 96939.89 -877.878 -779.269
2011 Jun 102822.5 102543.9 -229.693 508.3664
2011 Jul 99145.96 106359.7 174.8563 -7388.56
2011 Aug 106904 112413.7 762.7771 -6272.54
2011 Sep 116496.1 118440.1 1289.138 -3233.14
2011 Oct 121577.2 121883.8 1504.596 -1811.21
2011 Nov 130672.8 127398 1905.551 1369.255
2011 Dec 141768.4 133476.6 2322.855 5968.95
period Month Level Trend Season
2012 Jan 147153.9 137595.8 2502.488 7055.653
2012 Feb 147291.8 138729.1 2365.57 6197.117
2012 Mar 139725.3 139597.9 2215.895 -2088.44
2012 Apr 137107.2 141191.7 2153.688 -6238.17
2012 May 147659 143660.4 2185.183 1813.471
2012 Jun 146357 142390.7 1839.703 2126.563
2012 Jul 138873.1 142266.6 1643.323 -5036.88
2012 Aug 141084.1 143635.3 1615.862 -4167.1
2012 Sep 146083.3 146694.4 1760.18 -2371.31
2012 Oct 149952.3 148404.5 1755.174 -207.385
2012 Nov 153144.7 148515.4 1590.748 3038.472
2012 Dec 158454.2 150169.7 1597.095 6687.48
24. 24
period Month Level Trend Season
2013 Jan 159511.9 151439.5 1564.371 6507.981
2013 Feb 160365.8 153184.9 1582.474 5598.417
2013 Mar 155719.6 156319.2 1737.658 -2337.27
2013 Apr 155128.3 159371.4 1869.106 -6112.18
2013 May 163463 161169.4 1862.001 431.5504
2013 Jun 163695.7 160723.4 1631.202 1341.043
2013 Jul 156009.3 159782.1 1373.948 -5146.72
2013 Aug 157657.5 159990 1257.342 -3589.83
2013 Sep 157236.9 158632.4 995.8526 -2391.33
2013 Oct 157983.6 158014.3 834.4538 -865.09
2013 Nov 160240.7 156570.2 606.601 3063.86
2013 Dec 162637 155628.7 451.7876 6556.582
period Month Level Trend Season
2014 Jan 160482.5 153689.5 212.6868 6580.393
2014 Feb 159448.6 153097.2 132.1961 6219.154
2014 Mar 151171.4 152885.1 97.76448 -1811.47
2014 Apr 150578.1 156290.2 428.4964 -6140.61
2014 May 159718.4 159503.1 706.9347 -491.646
2014 Jun 162940.9 161766.3 862.5674 312.0305
2014 Jul 159981.3 164540.7 1053.749 -5613.15
2014 Aug 161191.5 164848.2 979.1224 -4635.79
2014 Sep 160253.2 162630.6 659.4516 -3036.92
2014 Oct 159917.3 161239.4 454.3887 -1776.5
2014 Nov 162411 159710.4 256.0422 2444.607
2014 Dec 163092.2 157484.2 7.821917 5600.179
25. 25
The table below shows the forecasted values for demand price for beans in Kidondoni for the
entire period of year 2015. That is from January 2015 to December 2015. The forecasted demand
price for beans is all presented in the table, with confidence level of one percent error. This
means that the forecasted demand values for beans for the whole of year 2015 must fall within
the specified upper and lower bounds for each month.
Forecast Values for the whole of Year 2015
CONFIDENCE BOUNDS
period Month Forecast Values Upper Bound Lower Bound
2015 Jan 127877.99 168578.2 87177.77
2015 Feb 124446.97 166120.5 82773.43
2015 Mar 114622.97 157426 71819.95
2015 Apr 106830.64 150922.3 62738.94
2015 May 108734.36 154275 63193.73
2015 Jun 106426.21 153575.3 59277.14
2015 Jul 96183.77 145098.6 47268.94
2015 Aug 92926.94 143761.5 42092.37
2015 Sep 91730.21 144634.2 38826.18
2015 Oct 89763.48 144881.9 34645.09
2015 Nov 90531.07 148003.5 33058.66
2015 Dec 78378.12 138338.8 18417.42
The chart below shows the smoothened seasonal additive triple exponential forecast for demand
price for beans for Kidondoni. The red line depicts the smoothened line for the demand price for
beans.
Time
Demand
2 4 6 8 10 12
050000100000
30. 30
Measurement of Forecast Accuracy
MSE 430478559.1
MAD 11803.53433
MAPE CAN NOT BE COMPUTED
Theil U 0.184349811
For the measurement of forecast accuracy of the seasonal additive triple exponential smoothing, we made use of the techniques of
MAD, MSE, MAPE, THEIL’S U and the residual plot to check for the best fit of the model. From the measurement of forecast
accuracy table, MSE and MAD are extremely large; MAPE is undefined and could not be computed as a result of the presences of
zero demand prices for some months in Kidondoni. Basing our argument or conclusion on the THEIL’S U statistics which is barely
close to zero; we can then conclude that the forecast using the seasonal additive triple exponential smoothing is better than the naïve
forecast.
31. 31
From the residual plot, the errors are not random and still visible pattern exist. This problem
could be attributable to the existence of zero demand prices for some months in the data set.
Presence of outliers in a data set can distort the analysis of a data.
-200000
-150000
-100000
-50000
0
50000
0 20 40 60 80 100 120 140
Residual
Time
Residual Analysis