cycles and exponential smoothing models materials for this lecture lecture 4 cycles.xls lecture 4...

Cycles and Exponential Smoothing Models

• Materials for this lecture• Lecture 4 Cycles.XLS• Lecture 4 Exponential Smoothing.XLS• Read Chapter 15 pages 18-30• Read Chapter 16 Section 14

How Good is Your Forecast?

• Can your forecast beat a Moving Average?

• Business forecasters use Moving Average as a point of comparison– MAPE for MA model– MAPE for your model

• Example of two Data Series– X with a Moving Average MAPE of 23%

• Your model’s MAPE of 15%– Y with a Moving Average MAPE of 12%

• Your model’s MAPE of 10%

Cycles, Seasonal Decomposition and Exponential Smoothing Models

• Business cycle• Beef cycle• Hog cycle• Weather cycle?

• Cycles caused by over correction of an economic system– The Cob Web Theorem in action

Cycles and Exponential Smoothing Models

• Cyclical analysis involves analyzing data for underlying cycles – Estimate length of cycle– Forecast variable based on cycle length

• Exponential Smoothing most often used forecasting method in industry– Easy to use and update, very flexible– Only forecasts a few periods ahead is

major disadvantage

Cyclical Analysis Models

• Harmonic regression model estimated with OLS regression estimates cycle length – Sin and Cos using CL variable

• Need enough observations to see several cycles in the data series

• Two considerations in estimating cycle length and specifying the OLS model– Annual data can easily exhibit a cycle– Monthly data can show a seasonal pattern

about a multiple year cycle


• If you are using Annual data– Define CL = Number of years for a possible

cycle length, as CL = 5 to test for a 5 year cycle

• If you are using Monthly data– Define CL = SL * No. Years for cycle length

where SL = 12 number of months in a year• If you are using Quarterly data

– Define SL = 4 number of quarters in a year


• OLS regression model for annual dataŶ = a + b1T + b2 Sin(2*ρi*T/CL) + b3 Cos(2*ρi*T/CL)where: CL is the number of years for a cycle

• Estimate the best cycle length– Enter CL in a cell– Refer to the cell with CL to calculate the Sin() and

Cos() values in the X matrix– Estimate regression model in Simetar for a CL– Change the value for CL, observe the MAPE – Change the value for CL, observe the MAPE – Repeat process for numerous CL values and find

the CL with the lowest MAPE


• OLS regression model for monthly dataŶ = a +b1T+ b2 Sin(2*ρi*T/SL) + b3 Cos(2*ρi*T/SL)

+ b4 Sin(2*ρi*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

• Estimate the best cycle length– Enter the No. Years in a cell– Calculate CL in a cell with CL = SL * Years– Refer to the cell with CL to calculate the second Sin() and

Cos() values in X matrix– Estimate regression model in Simetar for No. of Years– Change the CL value for no. of years in cycle, observe the

MAPE – Repeat process for different CL values for No. of years and

pick the CL for the lowest MAPE


• Part of the Y and X matrix for annual data

• Sin and Cos functions refer to CL in C49


• Y and X matrix for a monthly data series

• Sin and Cos functions refer to CL and SL

in C11 and F11

Lecture 4


• Sample table of R2 and MAPE for CL’s • CL = 9 for the chart and regression

shown here, based on maximum MAPE

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 observations

• Level for period TLT = a YT + (1-a) LT-1

where a is the smoothing constantŶT+1 = LT = a YT + (1-a) LT-1


• Different forms of ES models1. 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 next two slides– Numbers in ()’s match Simetar ES option settings


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)


• Select the type of model to fit based on the presence of – Trend – additive or multiplicative, dampened or not– Seasonal variability – additive or multiplicative

• Do this prior to the estimation. With Simetar you can experiment with different specifications after model is estimated– Can 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)

Exponential Smoothing Forecasts

• Using the Forecasting Icon for ES– Data on the Excel toolbar to get Data Ribbon

• Select Solver• Close Solver

– Select the “Exponential Smoothing” tab in Simetar• Specify the data series to forecast• Provide initial guesses for

– Dampening Factor (0.5), – Trend Factor (0.5), and – Season Factor (0.5)

• Indicate the Optional Seasons per Period as 12 • Forecast Periods of 1 or 6


• Simetar estimates all forms of ES models – Provides deterministic

forecasts– Provides probabilistic

forecasts• Parameters for ES model

estimated by Solver to minimize MAPE for residuals– PRIOR to running ES MUST

open Solver and close it – Provide starting guesses for

parameters 0.25 to 0.50– Enter no. of periods/year


• Initial Parameters for ES– Dampening Factor is required

for all models – good guess is 0.25

– Optional Trend factor entered as 0.5 if the data have any trend

– Optional 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 12

• Indicate cycle length if using annual data, say 9 years


Lecture 4

• ES Options• Season Method

– 0 No seasonal effects– 1 Additive seasonal effect– 2 Multiplicative seasonal

effect• Trend Method

– 0 No trend dampening– 1 Dampened Additive– 2 Dampened

Multiplicative• Stochastic Forecast

– TRUE– FALSE


• Experiment with alternative settings for the Trend and Seasonal Smoothing variables to see which combination is best

• Look for the lowest MAPE


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)


• Select the type of model to fit based on the presence of – Trend – additive or multiplicative, dampened or not– Seasonal variability – additive or multiplicative

• Do this prior to the estimation. With Simetar you can experiment with different specifications after model is estimated– Can 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)

cycles and exponential smoothing models materials for this lecture lecture 4 cycles.xls lecture 4...

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