forecasting (quan21)

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