cism02-unit 9.pdf

8/15/2019 CISM02-Unit 9.pdf

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Dr Valentina Plekhanova

CISM02: Decision Support for ManagementUnit 9

Forecasting

Unit 9: Learning Outcomes

2CISM02 Decision Support for Management Unit 9

1. To understand the different forecasting methodologies that are applied inpractice

2. To understand the criteria for selection of forecasting methodologies3. To understand the different approaches to forecasting that can be applied in

practice4. To calculate and explain a trend using moving averages5. To carry out exponential smoothing calculations6. To suggest a suitable value of the smoothing constant for a given set of data7. To understand the principles of simple linear regression8. To calculate and interpret the key statistics from a regression equation

9. To use different approaches to forecasting10. To be able to apply forecasting methods to the practical problems11. To be able to explain the limitations of forecasting methods12. To be able to explain the key stages of the forecasting process


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Famous Forecasting Quotes

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"It is far better to foresee even without certainty than not to foresee at all. "

Henri Poincare in The Foundations of Science , page 129

"I have seen the future and it is very much like the present, only longer."Kehlog Albran, The Profit

This nugget of pseudo-philosophy is actually a concise description of statistical forecasting.We search for statistical properties of a time series that are constant in time--levels, trends,seasonal patterns, correlations and autocorrelations, etc. We then predict that thoseproperties will describe the future as well as the present.

"Prediction is very difficult, especially if it's about the future."Nils Bohr, Nobel laureate in Physics

This quote serves as a warning of the importance of validating a forecasting model out-of-sample. It's often easy to find a model that fits the past data well--perhaps too well! - butquite another matter to find a model that correctly identifies those patterns in the past datathat will continue to hold in the future.

CISM02 Decision Support for Management Unit 9

Forecasting in Management

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Forecasting is used in various domains of management, such as:

Personnel management

Resource management

Finance management

Organisational management



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Forecasting (0)

5

All forecasting methodologies can be divided into three broad headings, i.e.forecasts based on:

What people have done :examples – Regression

Analysis, Time Series Analysis

What people say :examples – Surveys,Questionnaires

What people do :examples – TestingMarketing, Reaction Test

Lucey, 2002

The data from past activitiesare cheapest to collect butmay be outdated and pastbehaviour is not necessarilyindicative of future behaviour.

Data derived from surveys are moreexpensive to obtain and needs criticalappraisal – intensions as expressed insurveys and questionnaires are not alwaystranslated into action.

The data derived from recordingwhat people actually do are the mostreliable but also the most expensiveand occasionally it is not feasible forthe data to be obtained.


Forecasting (1)

6

An important use of quantitative models is in the prediction of the future. Inorder to plan and control effectively, management needs estimates of futurelevels of sales, costs, manpower requirements, and a variety of other factors.

Before taking almost any decision, a manager must make a number offorecasts about future conditions and the effects of various courses of action.These forecasts may be made only mentally, even subconsciously, but they area necessary part of decision making.

When forecasts have to be made on the basis of past data, managers has twomain approaches available to them

using intuitionusing a model.

The use of intuition involves experience, knowledge of the market, flair etc. andits importance should not be underestimated.

From Hull, et. al. Model Building Techniquesfor Management, Saxon House, 1977



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Forecasting (2)

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However, when used alone, it does have a number of drawbacks:

Intuitive forecasts tend to be biased. This is partly due to the personality of theforecaster and whether he/she is an optimist or a pessimist, but also to confusionbetween targets and forecasts. If the forecasts is to be used as a target,individuals will set forecasts on the low side. On the other hand, if the forecast isto be used as a basis for budget allocations, individuals will set forecasts on thehigh side to increase their share of the total budget.

It is difficult to forecast the limits of accuracy for an intuitive forecast.

The time of people with the skill and knowledge to make such forecasts isexpensive.

In many forecasting situations, for example, stock control, a very large numberof separate forecasts have to be made and the use of intuitive forecasting can bevery time-consuming.

Model building is a way of overcoming these drawbacks. If the model is chosencorrectly there will be no bias.

Hull, et. al. 1977


Forecasting (3)

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Furthermore, the error is a forecast can be estimated and, generally, if a largenumber of forecasts are required, they can be produced in a routine way byeither a junior clerk or a computer at relatively low cost.

However, a forecast which is produced by model building is sometimes no morethan an extrapolation of past data . It may ignore the effects of changes someexternal important factors such as government policy, increases in the number ofcompetitors and any other events which are not reflected in the past data.

Hull, et. al., 1977



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Available Forecasting Methodologies (1)

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There are several dimensions that can be used in grouping existing forecasting

methodologies. Many of these are technical in their orientation.For example, the distinction between statistical methods and non-statistical methods might be considered, or that between time series methods and causalmethods.

Still another technical distinction can be made between those methods that are quantitative in their orientation and those that are qualitative .

The most general distinction is between informal forecasting approaches and formal forecasting methods.

The informal forecasting methodologies are based largely on intuitive feel andlack systematic procedures that would make them easily transferable forapplication by others.

The formal forecasting methodologies seek to overcome this weakness bysystematically outlining the steps to be followed so that they can be repeatedlyapplied to obtain suitable forecasts in a range of situations.


Available Forecasting Methodologies (2)

10

Formal forecasting methodologies can be divided into those that are qualitativeand those that are quantitative .

Qualitative forecast methodssubjective

Quantitative forecast methodsbased on mathematical formulas

The quantitative methods , in turn, can be subdivided into the categories of time series techniques and causal or regression techniques.

The qualitative segment also includes two categories:

Techniques based on subjective assessment (the judgement of managers)Techniques based on the forecasting of technological developments.

???



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Criteria for Selection ofForecasting Methodologies

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A number of different criteria have been suggested as a basis formaking a selection decision for an appropriate forecastingmethodology. These include:

AccuracyThe time horizon of forecastingThe value of forecastingThe availability of dataThe type of data patternThe experience of the practitioner at forecasting


Forecasting: Framework

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Data (time series, or historical data)Forecasting method (e.g. Moving average, Trend analysis)ForecastForecast Evaluation (i.e. Forecast accuracy measurement)



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Forecasting Situation & Methodology

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In the very short-term, randomness (i.e. where it is not seasonality,trends, or cyclicality) is usually the most important.

As the time horizon is lengthened, seasonality takes on increasingimportance, followed by cyclicality. For the every long-term timehorizon, seasonality becomes less important, and trend plays a primaryrole.

Time horizon reflect such correlated characteristics as the value ofaccuracy in forecasting, the cost of various methodologies, thetimeliness of their results, and the types of data patterns involved in the

forecasting situation.


Forecasting Methods

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Qualitative: Delphi method, Surveys, Forecast by analogy, Scenariobuilding

use management judgment, expertise, and opinion to predict futuredemand

Time seriesstatistical techniques that use historical demand data to predict futuredemand

Causal/ Econometric methods: Regression methodsattempt to develop a mathematical relationship between demand andfactors that cause its behavior

Other Methods: Simulation



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Categories of Forecasting Methods

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Time series methods:Time Series methods use historical data as the basis of estimating futureoutcomes.

Moving AverageExponential SmoothingExtrapolationLinear predictionTrend EstimationGrowth Curve



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Causal / econometric methods

Some forecasting methods use the assumption that it is possible to identify theunderlying factors that might influence the variable that is being forecast. Forexample, sales of umbrellas might be associated with weather conditions. If thecauses are understood, projections of the influencing variables can be madeand used in the forecast.

Regression Analysis using linear regression or non-linear regression Autoregressive Moving Average (ARMA) Autoregressive Integrated Moving Average (ARIMA)



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Judgmental methods

Judgmental forecasting methods incorporate intuitive judgments, opinions andprobability estimates.

Composite ForecastsSurveysDelphi MethodScenario BuildingTechnology ForecastingForecast by Analogy

Other methods

Simulation

Prediction MarketProbabilistic Forecasting and Ensemble ForecastingReference Class Forecasting


Qualitative Methods

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Management, marketing, purchasing, and engineering are sources forinternal qualitative forecasts

Surveys, Forecast by analogy, Scenario building

Delphi method: involves soliciting forecasts about technological advancesfrom experts



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Quantitative Methods

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Time Series Models: Assumes the future will follow same patterns as the pastRelate the forecast to only one factor - timeInclude

moving averageexponential smoothinglinear trend line

Causal / Econometric Models:Explores cause-and-effect relationshipsUses leading indicators to predict the future,

e.g. housing starts and appliance sales


Quantitative Forecasting:Time-Series Models

20

Two factors are important in a time-series model: the series we want toforecast (such as weekly supermarket sales) and the period of time towhich we are referring.

Advantage of time-series models is that the basic rules of accountingare oriented toward sequential time period. This means that in mostfirms data is readily available on the basis of these time periods andcan be used in the application of a time-series forecasting technique.



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Quantitative Forecasting:Time-Series Models – Time Horizon

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Medium/long range forecasts deal with more comprehensive issuesand support management decisions regarding planning and products,plants and processes.

Short-term forecasting usually employs different methodologies thanlonger-term forecasting.

Short-term forecasts tend to be more accurate than longer-termforecasts.


Time Series Data Composition

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Data = historic pattern + random variation

Historic pattern to be forecasted:Level (long-term average)

Trend

SeasonalityCycle

Random Variation cannot be predicted



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Time Series Components

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Trend : Long-term upward or downward change in a time seriesSeasonal : Periodic increases or decreases that occur within one

yearCyclical : Periodic increases or decreases that occur over more than

a single yearIrregular : Changes not attributable to the other three components;

non-systematic and unpredictable


Moving Average

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Naive forecastdemand the current period is used as next period ’s forecast

Simple moving averagestable demand with no pronounced behavioral patterns

Weighted moving averageweights are assigned to most recent data



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Forecasting: Naïve Methods

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One of the simplest time series methods is Naïve I . This method uses the most

recently observed value as a forecast. Thus, if product demand for the comingweek were to be predicted, the observed value of demand for the most recentweek would be used as that forecast. This is equivalent to giving a weigh of 1.0 to the most recent observed value and a weight of 0.0 to all other observations.

An important application of Naïve methods is to use their forecasting accuracy asa basis for comparing alternative approaches . It is not uncommon to find that oneof the Naïve methods may provide adequate accuracy for certain situations. Itmay also be the case that more sophisticated methods (which are usually muchmore costly) do not give sufficient improvement in accuracy over these methodsto justify their use.

We sold 532 pairs of shoes lastweek, I predict we ’ ll

sell 532 pairs this week.


Forecasting: Moving Averages (1)

26

Let us consider example that introduces the way in which model building can beused in short term forecasting (i.e. in situations where a forecast is beingproduced two to three months in advance).

The simplest approach to forecasting using past data is to assume that in theshort run the underlying mean is constant with the actual data being subject torandom fluctuations about the mean.

We might choose to average the previous six values in an attempt to estimatethis underlying mean and use it as our forecast. This procedure is called the moving average method .

The length of time over which a moving average is taken will vary according tochoice and circumstances, and three month and twelve month average are allrelatively common. The method by which a moving average can be calculated isshown in Table below.

From Hull, et. al. Model Building Techniquesfor Management, Saxon House, 1977



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Forecasting: Moving Averages (1.2)

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Notes:

It is called “moving ” because as new demand data becomes available,the oldest data is not used.

Updated (recomputed) for every new time periodMay be difficult to choose optimal number of periodsMay not adjust for trend, cyclical, or seasonal effects


Simple Moving Average

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MAn =

n

i = 1Di

n where

n = number of periods in the moving averageDi = demand in period i



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Simple Moving Average: Example

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Jan 120Feb 90Mar 100Apr 75May 110June 50July 75Aug 130Sept 110

Oct 90

Nov -

ORDERSMONTH PER MONTH

– – – – –

99.085.082.088.095.0

91.0

MOVINGAVERAGE

MA 5 =

5

i = 1D i

5

=90 + 110 + 130+75+50

5

= 91 orders for November

Calculations:



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Suppose that it is now the end of month 6. The total of the previous sixmonths

’

demands is: 31+29+30+33+34+29=186 .

Month DemandTotal demand

in last 6months

6 monthmovingaverage

Forecast

(1) (2) (3) (4) (5)

1 31

2 29

3 30

4 335 34

6 29 186 31

7 31

The 6 month average is: 186/6=31 .From Hull, et. al. Model Building Techniquesfor Management, Saxon House, 1977



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Note that we use the moving average as the forecast of the next demand inmonth 7, as shown in column 5 of the table. When we know the demand in

month 7, the moving average is updated to forecast month 8.Suppose the actual demand in month 7 is thirty-seven units. We could updatethe 6 month moving average by re-calculating for what, after month 7, would bethe previous six month, i.e. 2,3,4,5,6 and 7, and proceed as before. This wouldbe correct, but there is an easier way.

The previous total was 186 . If we subtract from this the earliest demand whichoccurred in that total and add the latest demand we have:

New total = 186-31+37=186+6 = 192 . This gives the same result as adding thedemand figures for months 2,3,4,5,6 and 7.

The new moving average is 192/6=32 .

Month Demand Total demand inlast 6 month

6 month movingaverage

Forecast

7 37 192 32

8 32



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Suppose the demand in month 8 in fact proves to be 33 units. Proceeding inthe same way, the new total demand for six months 3,4,5,6,7 and 8 is then:192 – 29 + 33 = 196 .

Month DemandTotal demand

in last 6months

6 monthmovingaverage

Forecast

(1) (2) (3) (4) (5)

7 37 192 32

8 33 196 32.67 32

9 32.67

Note that it is not essential to have both columns 4 and 5;both have been shown here only for

the purpose of explanation.



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6 period moving average

Sales

Time (month)

100

200

300

400

1 2 3 4 5 6 7 8

o

o

o

o

o

o

o

forecast



34

When the time horizon for forecasting is fairly short, it is usually therandomness element that is major concern.

One way to minimize the impact of randomness on individual forecastsis to average several of the past values rather than using only a singlevalue.

The Moving Average approach is one of the simplest ways to reducethe impact of randomness. This method consists of weighting N of the

recently observed values by 1/N . (Note that the N most recent termsare thereby included in the average.)



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Forecasting: Moving Averages – Formal Representation (7)

35

In simple terms the technique of forecasting with moving average canbe represented as follows:

S t+1 = (x t + x t-1 + … + x t-N+1 )/ N

where S t = the forecast for time txt = the actual value at time tN = the number of values included in the average.

S t = (x t-1 + x t-2 + … + x t-N)/ N(should be updated for each period)

S t+1 = x t/ N - x t-N/N + S t

It is obvious that each new forecast based on a moving average is anadjustment of the preceding moving average forecast.It is easy to see why the smoothing effect increases as N becomes largerbecause a much smaller adjustment is being made between each forecast.


Weighted Moving Average

36

Adjusts moving average method to more closely reflect data fluctuations

WMAn = i = 1W i D i

where

W i = the weight for period i, between 0 and 100 percent

W i = 1.00



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Weighted Moving Average:Example

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Month Weight Data

August 17% 130September 33% 110October 50% 90

WMA3 =3

i = 1W i D i

= (0.50)(90) + (0.33)(110) + (0.17)(130)

= 103.4 orders

November Forecast:


Forecasting withSmoothing Techniques (1)

38

One type of problem that managers frequently face is that of preparing short-term forecast for a number of different items. As a result of the nature of thesesituations, the variable to be forecast can generally be assumed to change onlyslightly during each subsequent time period.

Obviously there can be occasions on which it might change a considerableamount in a single period, but generally speaking many of these items exhibit afairly stable series of values over a short time horizon.

In the government sector forecasting situations would include predictingunemployment figures for each of several industries on a short-term basis andperhaps changes in the price index for each of several commodities.

The techniques that are used most often in the above situations are referred toas

“

smoothing methods”

.



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The historical data is used to obtain a“

smoothing”

value for the serieswhich becomes the forecast for some future period.

In applying a smoothing techniques there are two steps :

1. In the first some kind of smoothing values is computed based onhistorical data.

2. In the second that value is used as a forecast for some future time.

(Forecasts are obtained by smoothing/averaging past values in, e.g. a

liner or exponential manner.)



40

The basic notion inherent in some smoothing techniques such asmoving average, exponential smoothing and other forms is that there issome underlying pattern in the values of the variables to be forecast andthat the historical observations of each variable represent theunderplaying pattern as well as random fluctuations.

The goal of these forecasting methods is to distinguish between therandom fluctuation and the basic underlying pattern by

“

smoothing”

thehistorical values. This amounts to eliminating the extreme values foundin the historical sequence and basing a forecast on some smoothingintermediate values.



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Forecasting: Moving Averages- Characteristics (6)

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Can provide reasonably good forecasts over the short-term period.The variable to be forecast can generally be assumed to change only

slightly during each subsequent time periodThe different moving averages produce different forecasts.The greater the number of periods in the moving average, the greater

the smoothing effect.In the underlying trend of the past data is thought to be fairly constant

with substantial randomness, then a greater number of periods shouldbe chosen.


Forecasting: Moving Averages- Characteristics (7)

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Limitations of moving averages :

When there are changes in the basic pattern of the variable being forecastmoving averages may not adapt rapidly to the changes. Two common types ofchange can help to illustrate this limitation. The first, referred to as a step change.The second is the ramp change or trend.

Equal weighting (or importance) is given to each of the values used in themoving average calculation, whereas it is reasonable to suppose that the mostrecent data is more relevant to current conditions. (Note: no weight is given tovalues observed before that period.)

The moving average calculation takes no account of data outside the period ofaverage, so full use is not made of all the data available. An n period moving average requires the storage of n -1 values to which is

added the latest observation. This may not seem much of a limitations when onlya few items are considered, but it becomes a significant factor when, for example,a company carries a number of thousands stock items each of which requires amoving average calculation involving say 6 months of usage data to be recorded.



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Geometric Progression

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In mathematics, a geometric progression , also known as a geometric sequence ,is a sequence of numbers where each term after the first is found by multiplyingthe previous one by a fixed non-zero number called the common ratio .

For example, the sequence 2, 6, 18, 54, ... is a geometric progression withcommon ratio 3 and 10, 5, 2.5, 1.25, ... is a geometric sequence with commonratio 1/2. The sum of the terms of a geometric progression is known as ageometric series .

Thus, the general form of a geometric sequence is a , ar , ar 2 , ar 3 , ar 4 ,…

and that of a geometric series is

a + ar + ar 2 + ar 3 + ar 4 + …

where r ≠ 0 is the common ratio and a is a scale factor, equal to the sequence'sstart value.


Effect of Smoothing Constant

48

0.0 1.0

If = 0.20 , then F t +1 = 0.20 Dt + 0.80 F t

If = 0 , then F t +1 = 0 Dt + 1 F t 0 = F t Forecast does not reflect recent data

If = 1 , then F t +1 = 1 Dt + 0 F t = Dt Forecast based only on most recent data



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Exponential Smoothing ( α=0.30)

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Period Month Demand

1 Jan 372 Feb 403 Mar 414 Apr 375 May 456 Jun 507 Jul 438 Aug 479 Sep 56

10 Oct 5211 Nov 5512 Dec 54

F 2 = D1 + (1 - )F 1= (0.30)(37) + (0.70)(37)

= 37

F 3 = D2 + (1 - )F 2= (0.30)(40) + (0.70)(37)

= 37.9 ….

F 13 = D12 + (1 - )F 12= (0.30)(54) + (0.70)(50.84)

= 51.79


Exponential Smoothing

50

FORECAST, F t + 1 Period Month Demand ( = 0.3) ( = 0.5)

1 Jan 37 – – 2 Feb 40 37.00 37.003 Mar 41 37.90 38.504 Apr 37 38.83 39.755 May 45 38.28 38.376 Jun 50 40.29 41.687 Jul 43 43.20 45.848 Aug 47 43.14 44.429 Sep 56 44.30 45.71

10 Oct 52 47.81 50.8511 Nov 55 49.06 51.4212 Dec 54 50.84 53.2113 Jan – 51.79 53.61



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Exponential Smoothing

51

.

70 –

60 –

50 –

40 –

30 –

20 –

10 –

0 – | | | | | | | | | | | | |1 2 3 4 5 6 7 8 9 10 11 12 13

Actual

O r d e r s

Month

= 0.30

= 0.50


Exponential SmoothingForecasting Method

52

Most frequently used time series method because ofease of use and minimal amount of data needed

Need just three pieces of data to start:Last period ’s forecast ( F t)Last periods actual value ( Dt)

Select value of smoothing coefficient, between 0 and 1.0

If no last period forecast is available, average the last fewperiods or use naive methodHigher values (e.g. 0.7 or 0.8) may place too much

weight on last period ’s random variation



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Forecasting: Trend Estimation- Linear Trend Line (0)

53

Moving average: forecasting error due to presence of trend

Number of Orders

Time (weeks)

220

240

260

280

1 2 3 4 5 6 7 8

oo o

o o

X

Trend Line

Error

Forecast based on 5 period moving average

200


Forecasting: Trend Estimation (1)

54

To obtain a forecast we can fit a regression line to the past data andproject this forward. The equation of the regression line is:

y – y”

= b (x – x”

)where

y = the value of the item to be forecast, in this case sales, during aparticular time period;

x = the corresponding time period;

b = the trend, in this case average increase in sales per month;

y”

= the mean of the y values for which data are available; x

”

= the mean of the x values for which data are available.



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55

where n = number of pairs of values available.The best estimate of the trend is given by

" x xn

" y yn

22 ( )

x y xy

nb x

xn

and

As the trend is likely to change over time, only the more recent data can beused to estimate the trend. Table below shows a calculation of the regressionline for example which considers sales figures for the last five months.



56

x”

=15/5=3.0 ; y”

= 245/5=49.0 ;

b= {751-(15 x 245)/5} / {55 – (15 x 15)/5}= {751-735} / {55-45}=1.6

The equation of the regression line is: y – 49.0 = 1.6 ( x – 3.0) , i.e.y = 44.2 + 1.6 x

Month Sales

x y xy

1 46 46 12 47 94 4

3 52 156 9

4 45 180 16

5 55 275 25

=15 =245 =751 =55 x y xy 2 x

2 x

Regressionanalysis

using previous five

months’

sales

To obtain a forecast of sales for nest month we just substitute x = 6 in theabove equation, i.e. forecast = 44.2 + 1.6 x 6 = 53.8



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Measure Forecast Accuracy

57

The goal of any measurement instrument is to have high accuracy (matchingreality as close as possible) and to also have a high precision (being able toconsistently replicate results and to measure with as many significant digits asappropriately possible).

Accuracy is defined as, "The ability of a measurement to match the actual value ofthe quantity being measured". If in reality it is 34.0 F outside and a temperaturesensor reads 34.0 F, then than sensor is accurate.

In order to benefit from the value of forecasting it is necessary to keepperformance metrics that measure its effectiveness .

While all forecasts will be incorrect, the degree of error should be minimized . Forexample, a forecast with +/- 10% variability is much better than a forecast with +/-50% variability.

By measuring and monitoring the forecast errors, new learning may be applied tofuture forecasts, further reducing forecast errors.


Measurement: Remarks

58

Measuremen t is the determination of the size or magnitude of something.

Measurement is not limited to physical quantities, but can extend to quantifyingalmost anything imaginable.

In physics and engineering, measurement is the process of comparing physicalquantities of real-world objects and events. Established standard objects andevents are used as units, and the measurement results in at least two numbersfor the relationship between the item under study and the referenced unit ofmeasurement, where at least one number estimates the statistical uncertainty inthe measurement, also referred to as measurement error (in a philosophicaldistinction). Measuring instruments are the means by which this translation ismade.

In scientific research, measurement is essential. It includes the process ofcollecting data which can be used to make claims about learning. Measurementis also used to evaluate the effectiveness of a program or product (known as anevaluand).“

A measurement is a comparison to a standard.”

-- William Shockley



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Absolute Error

61

Absolute error - absolute uncertainty. Compare with relative error.

The uncertainty in a measurement, expressed with appropriate units.

For example, if three replicate weights for an object are 1.00 g , 1.05 g ,and 0.95 g , the absolute error can be expressed as ± 0.05 g .

Absolute error is also used to express inaccuracies; for example, if the"true value " is 1.11 g and the measured value is 1.00 g , the absoluteerror could be written as 1.00 g - 1.11 g = -0.11 g .

Note that when absolute errors are associated with indeterminate errors,they are preceded with " ± "; when they are associated with determinateerrors, they are preceded by their sign.


Relative Error

62

Relative error - relative uncertainty.

Compare with absolute error.

The uncertainty in a measurement compared to the size of themeasurement.

For example,

if three replicate weights for an object are 2.00 g , 2.05 g , and 1.95 g ,

the absolute error can be expressed as ± 0.05 g and the relative error is± 0.05 g / 2.00 g = 0.025 = 2.5% .



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Types of Errors & Mistake

63

Systematic errors have an identifiable cause and affect the accuracy of results.

Random errors are errors that affect the precision of a set of measurements.Random error scatters measurements above and below the mean, with smallrandom errors being more likely than large ones.

A mistake is a measurement which is known to be incorrect due to carelessness,accidents, or the ineptitude of the experimenter. It's important to distinguishmistakes from errors: mistakes can be avoided. Errors can be minimized but notentirely avoided, because they are part of the process of measurement. Data thatis mistaken should be discarded. Data that contains errors can be useful, if thesizes of the errors can be estimated.


Gross Error

64

Compare with systematic error, random error and mistake.

Gross errors are undetected mistakes that cause a measurement to be verymuch farther from the mean measurement than other measurements.

Errors that occur when a measurement process is subject occasionally to large

inaccuracies.



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Standard Statistical Measuresto Estimate Errors

67

The evaluation of Naive Forecasting Techniques relies primarily on thecomparison of the forecasts with the corresponding actual values .

To preliminary evaluate a forecast and suitability of a method, variousstatistical measures may be used.

In evaluating forecasts obtained by means of the moving averagemethod, the following measures may be used:

Mean Error (ME)Mean Absolute Error (MAE)Mean Squared Error (MSE)Mean Percentage Error (MPE)Mean Absolute Percentage Error (MAPE)


Mean Error (ME)

68

The ME can be very misleading.

A ME value of zero can mean that the method forecasted the actual valuesperfectly (unlikely) or that the positive and negative errors cancelled eachother out.

It tends to Understate the error in all cases.

1

/n

t t

i

ME A F n



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Mean Absolute Error (MAE)

69

MAE is a way of dealing with the Understatement of ME.

By using the Absolute values of the error, the mean gives a betterindication of the model ’s fit.

1

( ) /n

t t i

MAE A F n


Mean Squared Error (MSE)

70

The MSE eliminates the positive/negative problem by squaring theerrors.

The result tends to place more emphasis on the larger errors and,therefore, gives a more conservative measure than the MAE.

2

1

/n

t t

i

MSE A F n



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Measures: Remarks

71

The previous three measures are “series specific; ” i.e., they only allowevaluation of the series that generated the errors.

The next two measures, by using the percentage of the error relative tothe actual , are designed to allow comparison of the results with differentmodels.


Mean Percentage Error (MPE)

72

The MPE is a relative measure of the forecasting error.

It is subject to the “averaging ” of the positive and negative errors.

1

100 /n

t t

t t

A F MPE n

A



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Mean Absolute PercentageError (MAPE)

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MAPE is a comparative measure that does not have the problem ofaveraging the positive and negative errors.

It is relatively easy to use to communicate a model ’s effectiveness.

1

100 /n

t t

t t

A F MAPE n

A


Mean Absolute Deviation

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Dt - F t n

MAD =

where

t = period number

Dt = demand in period t F t = forecast for period tn = total number of periods = absolute value



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MAD: Example

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1 37 37.00 – – 2 40 37.00 3.00 3.003 41 37.90 3.10 3.104 37 38.83 -1.83 1.835 45 38.28 6.72 6.726 50 40.29 9.69 9.697 43 43.20 -0.20 0.208 47 43.14 3.86 3.869 56 44.30 11.70 11.70

10 52 47.81 4.19 4.1911 55 49.06 5.94 5.9412 54 50.84 3.15 3.15

557 49.31 53.39

PERIOD DEMAND, Dt F t ( =0.3) ( Dt - F t ) | Dt - F t |

Dt - F t n MAD =

=

= 4.85

53.3911

R o b e r

t a R

u s s e

l l & B e r n a r d

W . T

a y l o r ,

I I I


Other Accuracy Measures

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Mean absolute percent deviation (MAPD)

MAPD =|D t - F t |

D t Cumulative error

E = e t Average error

E =e t n



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cism02-unit 9.pdf

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