Materials for this lecture Lecture 4 CyclesXLS Lecture 4 Exponential SmoothingXLS Read Chapter 15 pages 1830 Read Chapter 16 Section 14 How Good is Your Forecast Can your forecast beat a Moving Average ID: 808049
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Slide1
Cycles and Exponential Smoothing Models
Materials for this lectureLecture 4 Cycles.XLSLecture 4 Exponential Smoothing.XLSRead Chapter 15 pages 18-30Read Chapter 16 Section 14
Slide2How Good is Your Forecast?
Can your forecast beat a Moving Average?Business forecasters use Moving Average as a point of comparisonMAPE for MA modelMAPE for your modelExample of two Data SeriesX 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%
Slide3Cycles, 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
Slide4Cycles and Exponential Smoothing Models
Cyclical analysis involves analyzing data for underlying cycles Estimate length of cycleForecast variable based on cycle lengthExponential Smoothing most often used forecasting method in industryEasy to use and update, very flexibleOnly forecasts a few periods ahead is major disadvantage
Slide5Cyclical Analysis Models
Harmonic regression model estimated with OLS regression estimates cycle length Sin and Cos using CL variableNeed enough observations to see several cycles in the data seriesTwo considerations in estimating cycle length and specifying the OLS modelAnnual data can easily exhibit a cycleMonthly data can show a seasonal pattern
about
a multiple year cycle
Slide6Cyclical Analysis Models
If you are using Annual dataDefine 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
Slide7Cyclical Analysis Models
OLS regression model for annual data Ŷ = a + b1T + b2
Sin(2*
ρ
i
*T/CL) + b
3
Cos(2*
ρ
i
*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 CLChange 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
Slide8Cyclical Analysis Models
OLS regression model for monthly data Ŷ = a +b1
T+
b
2
Sin(2*
ρ
i
*T/SL)
+ b
3
Cos(2*
ρ
i
*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 cycleEstimate the best cycle lengthEnter the No. Years in a cellCalculate CL in a cell with CL = SL * YearsRefer to the cell with CL to calculate the second Sin() and Cos() values in X matrixEstimate regression model in Simetar for No. of YearsChange 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
Slide9Cyclical Analysis Models
Part of the Y and X matrix for annual data Sin and Cos functions refer to CL in C49
Slide10Cyclical Analysis Models
Y and X matrix for a monthly data series Sin and Cos functions refer to CL and SL in C11 and F11
Lecture 4
Slide11Cyclical Analysis Models
Sample table of R2 and MAPE for CL’s CL = 9 for the chart and regression shown here, based on maximum MAPE
Slide12Exponential 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 T
L
T
= a Y
T
+ (1-a) L
T-1
where a is the smoothing constant
Ŷ
T+1
= L
T
= a Y
T
+ (1-a) L
T-1
Exponential Smoothing Models
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
Slide14Exponential 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)
Slide15Exponential 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 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)
Slide16Exponential Smoothing Forecasts
Using the Forecasting Icon for ESData on the Excel toolbar to get Data RibbonSelect SolverClose 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
Slide17Exponential Smoothing Models
Simetar estimates all forms of ES models Provides deterministic forecastsProvides probabilistic forecastsParameters for ES model estimated by Solver to minimize MAPE for residualsPRIOR to running ES MUST open Solver and close it Provide starting guesses for parameters 0.25 to 0.50Enter no. of periods/year
Slide18Exponential 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 12
Indicate cycle length if using annual data,
say 9 years
Slide19Exponential Smoothing Models
ES OptionsSeason Method0 No seasonal effects1 Additive seasonal effect2 Multiplicative seasonal effectTrend Method
0 No trend dampening
1 Dampened Additive
2 Dampened MultiplicativeStochastic Forecast
TRUE
FALSE
Slide20Exponential Smoothing Models
Experiment with alternative settings for the Trend and Seasonal Smoothing variables to see which combination is bestLook for the lowest MAPE
Slide21Exponential 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)
Slide22Exponential 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 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)