Cycles and Exponential Smoothing Models - PowerPoint Presentation

Slide1

Cycles and Exponential Smoothing Models

Materials for this lectureLecture 10 Cycles.XLSLecture 10 Exponential Smoothing.XLSXRead Chapter 15 pages 18-30Read Chapter 16 Section 14

Slide2

How Does Regression Work?

Y

t

= a + b1 X1t + b2 Tt + b3 Yt-1 + b4 SIN()t + b4 COS()t

Slide3

A Score for Your Forecast?

MAPE -- Mean absolute percent errorStatistic often used to determine how good your forecast is at forecasting the historical periodMAPE = ∑ [ (Ai – Fi) / Ai ] * (100/N)Where A

i

is the actual value in period

i and Fi is the forecasted value in period iN is the number of historical periodsMAPE is the average percentage error for a forecast

Slide4

How Good is Your Forecast?

Can your forecast beat a Moving Average?Business forecasters use Moving Average as a reference forecast. They compare the:MAPE for MA modelMAPE for your modelExample of two Data SeriesX with a Moving Average MAPE of 23%Your structural model’s MAPE of 15%Y with a Moving Average MAPE of 12%

Your structural model’s MAPE of 10%

Which is the better model?

Slide5

Cycles, Seasonal Decomposition and Exponential Smoothing Models

Business cycleBeef cycleHog cycleWeather cycle?Cycles caused by over correction of an economic systemThe Cob Web Theorem in action

Slide6

Cycles and Exponential Smoothing Models

Cyclical analysis involves analyzing data for underlying cycles Estimate the length of an average cycleForecast Y variable in part based on cycle length, may still include trend, seasonal, and structural variables

Exponential Smoothing

is the most

often used forecasting method in industryEasy to use and update, very flexibleOnly forecasts a few periods ahead is its major disadvantage

Slide7

Cyclical Analysis Models

Harmonic regression model estimated with OLS regression used to estimate cycle length Sin and Cos use CL variableRecall Seasonal analysis used SLLength of data needed: Enough observations to observe several cycles

Two

considerations in estimating cycle length and specifying the OLS model

Annual data can easily exhibit a cycleMonthly data can show a seasonal pattern around a multiple year cycle

Slide8

Cyclical Analysis Models

Define CL = Number of years in the cycleCL is used in both the Sin and Cos functionsIf you are using A

nnual data

CL equals the number of years for the cycle

If you are using Monthly dataDefine CL = SL * No. Years for cycle length where SL = 12 number of months in a yearIf you are using Quarterly dataDefine CL = SL * No. Years for cycle length where SL = 4 number of quarters in a year

Slide9

Cyclical Analysis Models

OLS regression model for annual data Ŷ = a + b1T + b2 Sin(2*

ρ

i

()*T/CL) + b3 Cos(2*ρi()*T/CL) where: CL = possible number of years for a cycleSteps to estimate best cycle length with SimetarEnter CL in a cellReference the cell with CL to calculate all of the Sin() and Cos() values in the X matrixEstimate regression model

Change the value for CL, observe the

F ratio or MAPE Change the value for CL, observe the F ratio or MAPE Repeat process for numerous CL values and find the CL associated with the largest F ratio or the lowest MAPE

Slide10

Cyclical Analysis Models

OLS regression model for Monthly data Ŷ = a +b1

T+

b

2 Sin(2*ρi*T/SL) + b3 Cos(2*ρi*T/SL) + b4 Sin(2*ρ

i

*T/CL) + b5 Cos(2*ρi*T/CL) where: SL = No. months (quarters, or weeks) in a year and CL = SL * No. years for a cycle to TestSteps to estimate the best cycle length with SimetarEnter the

SL value in a cellCalculate a value for CL where: CL = SL * YearsRefer to the cell with SL to calculate the first Sin() and Cos() values in your X matrixRefer to the cell with CL to calculate the second Sin() and Cos() values in your X matrixEstimate regression model in Simetar Change the no. of years used to calculate CL, record F or MAPE Repeat process for different CL values for no. of years and pick the CL associated with the highest F or the lowest MAPE

Slide11

Cyclical Analysis Models with Annual Data

Part of the Y and X matrix for annual data Sin and Cos functions refer to CL in C49

Slide12

Cyclical Analysis Models with Monthly Data

Y and X matrix for a monthly data series Sin and Cos functions refer to CL and SL in C11 and F11

Lecture 4

Slide13

Cyclical Analysis Model Results

Sample table of R2 and MAPE for CL’s CL = 9 for the chart and regression shown here, based on maximum MAPE

Slide14

Exponential Smoothing Models

ES is the most popular forecasting method Very good for forecasting a few periods Like moving average, but greater weights placed on more recent observationsMA assumes equal weights for each lagged value, i.e., X

T+I

=(X

T-3 + XT-2 + XT-1 ) / 3ES assumes weights are different i.e., XT+I =((1-β) * XT-2 + β * XT-1 ) / 3

Slide15

Exponential Smoothing Models

1. No trend and additive seasonal variability (1,0)2. Additive seasonal

variability

with an additive trend (1,1)

3. Multiplicative seasonal variability with an additive trend (2,1)

4. Multiplicative seasonal variability with a multiplicative trend (2,2)

Slide16

Exponential Smoothing Models

Select the type of model to fit based on the presence of Trend – additive or multiplicative, dampened or notSeasonal variability – additive or multiplicativeDo this prior to the estimation if not using Simetar. With Simetar you can experiment with different specifications after

the model

is estimated

Can select 3 seasonal effects: none, additive, multiplicativeCan select 3 trend effects: none, additive, multiplicative5. Dampened trend with additive seasonal variability (1,1)6. Multiplicative seasonal variability and dampened trend (2,2)

Slide17

Exponential Smoothing Models

Different forms of ES models (options in Simetar)1. Simple exponential smoothing, additive seasonal and no trend (1 seasonal ,0 trend)2. Additive seasonal and additive trend (1,1)3. Additive trend and multiplicative seasonal variability (2,1)

4. Multiplicative trend and multiplicative

seasonal

variability (2,2)5. Dampened trend ES with additive seasonal variability (1,1)6. Dampened trend ES with multiplicative seasonal variability (2,2)Numbers match chart numbers in last two slidesNumbers in ()’s match Simetar ES option settings

Slide18

Exponential Smoothing Forecasts

Using the Forecasting Icon for ESData on the Excel toolbar to get Data RibbonSelect SolverClose Solver

Select the “Exponential Smoothing”

tab in the menu

Specify the data series to forecast (see next slide for the menu)Provide initial guesses for Dampening Factor (0.25), Optional Trend Factor (0.5), and Optional Season Factor (0.5) if monthly or quarterly data Indicate the Optional Seasons per Period as 12 if monthly dataForecast Periods of 1 to 6

Slide19

Exponential Smoothing Models

Simetar estimates many different forms of ES models Provides deterministic forecastsProvides probabilistic forecastsParameters for ES model estimated by Solver to minimize MAPE for residualsPRIOR to running ES, You MUST open Solver and close it

so Simetar can Optimize Parameters

Provide starting guesses for parameters 0.25 to 0.50

Enter no. of periods/year if monthly or quarterly data

Slide20

Exponential Smoothing Models

Initial Parameters for ESDampening Factor is required for all models – good guess is 0.25Optional Trend factor entered as 0.5 if the data have any trendOptional Seasonal factor, 0.5, if the data are monthly or you have >30 years annual data (with annual data you have a cycle)Optional Seasons per Period

Indicate

the number of months

for seasonal effect as 12Indicate cycle length if using annual data, say 9 years

Slide21

Exponential Smoothing Models

ES OptionsTrend Method0 No trend dampening1 Dampened Additive2 Dampened MultiplicativeSeason Method

0 No seasonal effects

1 Additive seasonal effect

2 Multiplicative seasonal effectStochastic ForecastTRUEFALSE

Slide22

Exponential Smoothing Models

Experiment with alternative settings for the Trend and Seasonal Smoothing variables to see which combination is bestAll possible combinations are listed belowLook for the model formulation with the lowest MAPE

Slide23

Exponential Smoothing Models

1. No trend and additive seasonal variability (1,0)2. Additive seasonal

variability

with an additive trend (1,1)

3. Multiplicative seasonal variability with an additive trend (2,1)

4. Multiplicative seasonal variability with a multiplicative trend (2,2)

Slide24

Exponential Smoothing Models

Select the type of model to fit based on the presence of Trend – additive or multiplicative, dampened or notSeasonal variability – additive or multiplicativeDo this prior to the estimation. With Simetar you can experiment with different specifications after model is estimatedCan select 3 seasonal effects: none, additive, multiplicative

Can select 3 trend effects: none, additive, multiplicative

5. Dampened trend with additive seasonal variability (1,1)

6. Multiplicative seasonal variability and dampened trend (2,2)