Time-Series Forecast ModelsTime-Series Forecast Models A time series is based on a sequence of evenly time-spaced data points, such as daily shipments, weekly sales, or quarter- ly earnings.

Forecasting time-series data implies that forecasts are predicted only from the past values of that variable, and that other varia- bles, no matter how potentially valuable, are ignored.

Mo

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Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec

Data Pointor

(observation)

MGMT E-5070

Decomposition of a Time SeriesDecomposition of a Time Series

Analyzing time series means breaking down past data into components and then project- ing them into the future

A time series typically has four components: trend, seasonality, cycles, and random variation

TIME SERIES MODELS ATTEMPT TO PREDICT TIME SERIES MODELS ATTEMPT TO PREDICT THE FUTURE BY USING HISTORICAL DATATHE FUTURE BY USING HISTORICAL DATA

Decomposition of a Time SeriesDecomposition of a Time Series

Trend Trend ( ( TT ) ) is the gradual upward or downward movement of the data over time.

SeasonalitySeasonality ( S ) ( S ) is a pattern of the demand fluc- tuation above or below the trend line that repeats at regular intervals.

CyclesCycles ( C ) ( C ) are patterns in annual data that occur every several years. They are usually tied into the business cycle.

Random variationsRandom variations ( R ) ( R ) are blips in the data that are caused by chance and unusual situations. They follow no discernible pattern.

Time Series & ComponentsTime Series & Components

TREND COMPONENTTREND COMPONENTSEASONAL PEAKSSEASONAL PEAKS

ACTUAL DEMAND LINEACTUAL DEMAND LINE

YEAR 1 YEAR 2 YEAR 3 YEAR 4

TIME

AVERAGE DEMAND OVER 4 YEARSAVERAGE DEMAND OVER 4 YEARS

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Time Series & ComponentsTime Series & ComponentsRANDOM VARIATIONSRANDOM VARIATIONS

Forecasters usually assume that the random variations are averaged out over time.

These random errors are often assumed to be normally distributed with a mean of zero.

IT IS ALSO ASSUMED THAT RANDOM VARIATIONSIT IS ALSO ASSUMED THAT RANDOM VARIATIONS DO NOT HEAVILY INFLUENCE DEMANDDO NOT HEAVILY INFLUENCE DEMAND

TheThe Moving Average Moving Average ModelModel

Assumes demand will stay fairly steady over time.

A two-month moving average forecast is found by summing the demand during the past two periods and dividing by “ 2 ” .

With each passing period, the most recent demand is added to the sum; the earliest demand is dropped. This smooths out short-term irregularities in the data series.

It has no trend, seasonal, or cyclical components.

TheThe Moving Average Moving Average ModelModel

( demands in previous n periods )

nn IS THE NUMBER OF PERIODS IN THE MOVING AVERAGE

Forecast = Σ

TheThe Mo Moving Average ving Average ModelModel

Year Demand Forecast

1 110 -

2 100 -

3 120 105105

4 140 110110

5 170 130130

TWO - PERIOD EXAMPLETWO - PERIOD EXAMPLE

110 + 100 / 2 = 105105100 + 120 / 2 = 110110120 + 140 / 2 = 130130

TheThe Mo Moving Average ving Average ModelModel

Year Demand Forecast

1 110 -

2 100 -

3 120 --

4 140 --

5 170 117.5117.5

6 150 132.5132.5

FOUR - PERIOD EXAMPLEFOUR - PERIOD EXAMPLE

110 + 100 + 120 + 140 / 4 = 117.5117.5100 + 120 + 140 + 170 / 4 = 132.5132.5

Weighted Moving Average ModelWeighted Moving Average Model

Makes the forecast more responsive to changes.

Used when there is a trend or pattern. Weights place more emphasis on recent values.

Deciding the weights requires some experience and good luck!

SEVERAL WEIGHTS SHOULD BE TRIED, AND THE ONES WITHSEVERAL WEIGHTS SHOULD BE TRIED, AND THE ONES WITH THE LOWEST FORECAST ERROR SHOULD BE SELECTEDTHE LOWEST FORECAST ERROR SHOULD BE SELECTED

Weighted MovinWeighted Moving Average Modelg Average Model

∑ ( weight in period i )( actual value in period)

∑ ( weights )

Weighted Moving Average ModelWeighted Moving Average ModelTHREE - PERIOD

88 (120) + 11 (100) + 11 (110)

1010= =

Period Weight Demand

Most recent 8 120

2nd Most recent 1 100

3rd Most recent 1 110

4th

PeriodForecast

117 units

‘10’representsthe sum ofthe weights

Weighted Moving Average ModelWeighted Moving Average ModelTHREE - PERIOD

88 (140) + 11 (120) + 11 (100)

1010= =

Period Weight Demand

Most recent 8 140

2nd Most recent 1 120

3rd Most recent 1 100

5th Period

Forecast134 units

Exponential Smoothing ModelExponential Smoothing Model

THENEW

FORECAST

LAST FORECASTED

DEMANDα 1 - α++==

The new forecast is equal to the old forecast adjusted by a fraction of the error( last period actual demand – last period forecast ) . The smoothing coefficient

( α ) is a weight for the last actual demand.

LASTACTUALDEMAND

First Order or Primary VersionFirst Order or Primary Version

A moving average technique that only requires thelast period actual demand and the last period

forecasted demand for input.

Exponential Smoothing ExampleExponential Smoothing Example

ASSUMING THAT α = .7 , THE NEXT FORECAST IS:

.7 ( 100 units ) + ( 1 - .7 )( 110 units )

70 + 33 = 103 units

LastForecast

Last ActualDemand

Exponential Smoothing ExampleExponential Smoothing Example

ASSUMING THAT α = .7 , THE NEXT NEW FORECAST IS:

.7 ( 120 units ) + ( 1 - .7 )( 103 units )

84 + 30.9 = 114.9 units

LastForecast

Last ActualDemand

The Smoothing CoefficientThe Smoothing Coefficient

The symbol is alpha ( α )

It can assume any value between 0 and 1 inclusive

It places a weight on the last actual period demand The value of alpha resulting in the lowest forecast error is selected for the model.

Smoothing Coefficient SelectionSmoothing Coefficient Selection

This range ( .0 – .3 ) places the heaviest weight on the historical demand periods.

The intent is to make the forecast reflect the long - term stability of the product’s demand, as well as to minimize short-term fluctuations that could distort future forecasts.

It is appropriate for products whose demand patterns are extremely stable over time and expected to remain so.

LOW - RANGELOW - RANGE

Smoothing Coefficient SelectionSmoothing Coefficient Selection

This range ( .4 – .6 ) splits weights between historical and most recent demand periods.

The intent is to make the forecast reflect the importance of each.

It is appropriate for products whose demand patterns are only slightly unstable.

MEDIUM - RANGEMEDIUM - RANGE

Smoothing Coefficient SelectionSmoothing Coefficient Selection

This range ( .7 – 1.0 ) places the heaviest weight on the most recent demand periods.

The intent is to make the forecast largely reflect the most recent demand experience.

It is appropriate for products that are entirely new, and for products whose demand patterns are unstable.

HIGH - RANGEHIGH - RANGE

Trend Projection ModelTrend Projection ModelA REGRESSION MODEL OVER TIMEA REGRESSION MODEL OVER TIME

This technique fits a trend line through a series of historical data points and then projects that trend line into the future forboth medium and long-range forecasting.

WE WILL FOCUS ON STRAIGHT-LINE TRENDS FOR NOWWE WILL FOCUS ON STRAIGHT-LINE TRENDS FOR NOW

Trend Projection ModelTrend Projection ModelA REGRESSION MODEL OVER TIMEA REGRESSION MODEL OVER TIME

TIME ( X )TIME ( X )

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( Y

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Y )

THIS ALSO IMPLIES THAT THE MEAN

SQUARED ERROR (MSE) IS MINIMIZED

MSE IS AMEASURE OF

FORECASTERROR

We identify a straight line that minimizes the sumof the squares of the vertical distances from theregression line to each of the actual observations.

THE THE TREND TREND

LINELINE

Trend Projection ModelTrend Projection Model

Y = a + b X^

Y-AXIS INTERCEPT : THE POINT ON THE VERTICAL

AXIS THAT THE REGRESSION LINE CROSSES

THE SLOPE OF THE LEAST-SQUARES LINE: THE RATE OF CHANGE

IN ‘Y’ GIVEN CHANGE INTIME ‘X’

X AXIS

Y A

XIS

ORIGIN

THE SPECIFIED VALUE OF ‘X’( TIME )

THE PREDICTED VALUE ( FORECAST )

Trend Projection ModelTrend Projection ModelEXAMPLEEXAMPLE

Y = a + b ( X )

Y = 92.6667 + 10.9697 ( 11 ) 213.3333 units = 92.6667 + 120.6667

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11th YEAR FORECAST Y - INTERCEPT SLOPE 11th YEAR

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