FORECASTINGQUAN 21
Filosofo ᴥ Ponciano ᴥ Quisora ᴥ Tagarino
FORECASTING• the process of making statements about events whose
actual outcomes (typically) have not yet been observed.• the term "forecasting" are sometimes reserved for
estimates of values at certain specific future times, while the term "prediction" is used for more general estimates.
• Forecasting can be described as predicting what the future will look like, whereas planning predicts what the future should look like.
Eight Steps to Forecasting1. Determine the use of the forecast.2. Select the items or quantities that are to be forecasted.3. Determine the time horizon of the forecast.4. Select the forecasting model or models.5. Gather the data needed to make the forecast.6. Validate the forecasting model.7. Make the forecast.8. Implement the results.
Types of Forecasting
Types of ForecastingTIME-SERIES MODELS• Attempt to predict the future by using historical data• Look at what has happened over a period of time and use a
series of past data to make a forecast• Relies on Quantitative Data• Includes Moving Average, Exponential Smoothing, and
Trend Projection
Types of ForecastingCAUSAL MODELS• Incorporates the variables or factors that might
influence the quantity being forecasting models• Relies on Quantitative Data
Types of ForecastingQUALITATIVE MODELS• Relies on Qualitative Data• Attempts to incorporate judgmental or subjective factors
into the forecasting model• Especially useful when subjective factors are expected to be
very important or when accurate quantitative data are difficult to obtain
Types of ForecastingQUALITATIVE MODELS1. Delphi Method – allows experts, who may be located in
different places, to make forecasts; three diff. types of participants: decision makers, staff personnel, and respondents.
2. Jury of Executive Opinion – takes opinions of a small high level managers, often in combination with statistical models, and results in a group estimate of demand.
Types of ForecastingQUALITATIVE MODELS3. Sales Force Composite – each salesperson
estimates what sales will be in his or her region.4. Consumer Market Survey – solicits input from
customers or potential customers regarding their future purchasing plans.
Scatter Diagrams• A two-dimensional graph plotted to get a quick idea
if any relationship exists between two variables• Independent variable – horizontal (X) axis• Dependent Variable – vertical (Y) axis
Time-Series Forecasting Models• A time series is based on a sequence of evenly
spaced data points.• Forecasting time-series data implies that future
values are predicted only from past values and that other variables, no matter how potentially valuable, are ignored.
Examples of Scatter Diagrams
MOVING AVERAGE• A forecasting technique that averages the past
values in computing the forecast.• The term moving indicates that as a new
observation becomes available for the time series, it replaces the oldest observation in equation.
MOVING AVERAGE• Mathematically, moving average is expressed as:Moving average = ∑ ( most recent n data values ) nWhere: n = is the number of periods in the moving
average.To use moving average, the number of data value to be
included in the moving average must be selected.
The data below show the number of gallons of gasoline sold by Wallace Company, a gasoline distributor, over past 12 weeks.
Week Sales(000s of galloons) 1 17 2 21 3 19 4 23 5 18 6 16 7 20 8 18 9 22 10 2011 1512 22
MOVING AVERAGE
Given : Computation:Week 1 = 17 Moving Average = (17+21+19) / 3Week 2 = 21 Moving Average = 19Week 3 = 19n = 3• The moving average value is the forecasted sales in week 4.
Summary of 3 –week moving average calculation
MOVING AVERAGE• An important consideration in selecting forecasting method
is the accuracy of the forecast. • The error associated with the forecast is the difference
between the observed value of the time series and the forecast.
• Mean Squared Error (MES), or the average of the sum of squared errors can be used to develop measures of forecast accuracy.
MOVING AVERAGE
MOVING AVERAGEMSE = 16+9+16+1+0+16+0+25+9
9MSE = 10.22
The number of data values that minimized MSE is considered as more accurate.
WEIGHTED MOVING AVERAGE• A moving average forecasting method that places
different weight on past values.• Mathematically, moving average is expressed as:• Weighted Moving average = ∑ (weight for period n)
x (data value in period n) / ∑ weight
ExampleUsing the previous example, find the weightedmoving average for week 4 given the followingweight: Week 1 = 1; Week 2 = 2; and Week 3 = 3.Given: Computation:Week 1 = 17 (3 x 19) + ( 2 x 21 ) (1 x 17)Week 2 = 21 3 + 2 + 1Week 3 = 19 = 19.33
EXPONENTIAL SMOOTHING• A forecasting method that is a combination of last
forecast and last observed value.• Exponential smoothing is expressed as :New Forecast =last period’s forecast +ά (last periods
actual demand – last periods forecast)Where : ά = smoothing constant
EXAMPLE:In January ,a demand for 142 for a certain car model for February was predicted by a dealer. Actual demand for February was 153 autos. Using a smoothing constant of ά = 0.20, what could be the forecast demand for March?Given:last periods actual demand = 153last periods forecast = 142
ά = 0.20Computation: New Forecast = 142 + 0.20(153 – 142)New Forecast = 144.2
SELECTING THE SMOOTHING CONSTANT• The overall accuracy of a forecasting model can be determined by
comparing the forecast value with actual or observed value.• Forecast Error = demand – forecast• Mean Absolute Deviation(MAD) – a technique for determining the
accuracy of a forecasting model by taking the average of the absolute deviations.
MAD = ∑|forecast errors | n
EXAMPLE:The port of Baltimore has unloaded large quantities of grain from ships during the past eight quarters. The ports' operation manager wants to test the use of exponential smoothing to see how well the technique works in predicting tonnage unloaded. He assumes that the forecast of grain unloaded in the first quarter was 175 tons. Two value of ά are examined ά = 0.10 and ά = 0.50.
Absolute Deviation and MADs for Port of Baltimore
Sum of the absolute deviation :For ά=0.10 = 84 For ά=0.50 = 100
MAD(ά=0.10 ) = 84 / 8= 10.5
MAD(ά=0.50) = 100 / 8 = 12.50
* Smoothing constant, ά=0.10 , is preferred to ά=0.50 because its MAD is smaller.
TIME SERIES REGRESSION• Time Series- is a set of data collected at regular
intervals such as every week , every month, or every week.
• Regression – in statistics is a term used to describe the process of estimating the relationship between two variables , in this case the time and sales.
LEAST SQUARE METHOD
Where Ft = estimated or forecast value of sales for t a = intercept , or the point at which the trend line
intercepts . The x axis (sales) b = slope of the trend line , or the rate of the change in
sales. t = time , in this case the months from 1 to 6 any series
of number can be used as long
as they are consecutive.
LEAST SQUARE METHOD• Two equations are used to find the slope and
intercept of the best fitting trend line. The slope is always computed as follows:
where b = slope
t = time
x= dependent variable of sales = mean of the value of x
LEAST SQUARE METHOD• Second the intercept is calculated as follows:
SMOOTHING LINEAR TRENDS• Simple smoothing continually adjusts the forecasts according
to the errors. To start a forecast for a period 1 (F1) is selected. A fraction of error in period 1 is added to F1 to get F2 , A fraction of in period 2 to get F3 and so on..
• Smoothing the linear trend works the same way except that the errors are used to continually adjust to things : the intercept and the slope of the trend line.
• The adjustments are made with sequence of equations repeated each period.
SMOOTHING LINEAR TRENDSSmoothed level of t = forecast for t + a1 x error in t
Smoothed trend at the end of t = smoothed trend at the end of t + a2 x error in t
Forecast for t + 1 = smoothed level at the end of t + smoothed trend at the end of t• The smoothing equations for a linear trend compute a new trend line at the end
of each period . The intercept of the trend line is called smoothed level• This is not quiet the same as the regression intercept of a . In regression trend
line starts at period 1 in smoothing the trend line starts at current period.• The slope of a new trend line is called smoothed trend and is similar to the
slope b in regression.
SMOOTHED LINEAR TRENDS• To see how model works, we will put the equations into symbols and then
smooth the Computer land sales. The equations are:
Where = is the smoothed level = is the smoothed trend
= regression forecastThere are two smoothing parameters: for the level and for the trend.
SMOOTHING NON-LINEAR TRENDSNON LINEAR TRENDS
• Exponential Trends– A model in which the amount of growth increases
continuously in the future.
• Damped Trends– A model used for long-range forecasting in which the
amount of trend declines each period.
EXPONENTIAL SMOOTHING MODELS
Trend Modification Parameter (φ)
The effect of φ is to accelerate or decelerate the trend.• Φ > 1 - exponential trend• 0 < Φ < 1 - damped trend• Φ = 1 - nonlinear is same as linear
Forecasting More Than One Step Ahead
Damped Forecasting• The Damped version is more likely similar to the
Exponential version. The only difference is the φ value which is made over the range 0 < φ < 1.
NONLINEAR TRENDS
• Asymptote– Limiting the value of the forecasts using a
damped trend. When sales reach asymptote, growth disappears.
• Selecting Trend Alternative• Limitation of Data
DECOMPOSITION OF SEASONALIZED DATA
• Classical Decomposition– A method which attempts to separate a time
series into as many as four components.
FOUR COMPONENTS OF A TIME SERIES
• Trend - gradual movement of the data• Seasonality – pattern of demand fluctuation• Cycle – patterns in data• Random Variation – blips in data caused by chance
Questions to Verify SeasonalityAre the peaks and the troughs consistent?Is there an explanation for the seasonal
pattern?
If the answer is no, we should decomposed the seasonal data.
DecompositionRemoving of the seasonal pattern from the dataDeseasonalized data will be forecastedForecast will be seasonalized
Steps in forecasting Seasonal Data1. Centering the Moving Average2. Ratios are approximate indices3. The mean ratios4. Norminalization5. The final indices6. Deseasonalizing the data
Steps in forecasting Seasonal Data
7. Forecasting the deseasonalized data8. Seasonalizing the forecast9. The seasonalized MSE
Limitation• Two seasons of data are needed• Equal weights• Storage
Advantage• Simplicity• Accuracy
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