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Forecasting NoTrend Time Series II: Moving Averages

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Can lead to misleading forecasts attempting to model 'random noise' ... Accept other defaults and click O.K. to obtain forecasts in new sheet ... – PowerPoint PPT presentation

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Title: Forecasting NoTrend Time Series II: Moving Averages


1
Forecasting No-Trend Time Series II Moving
Averages Exponential Smoothing
Topics Moving Average Method Smoothing Effect of
Span/Period Assessment of Forecast with Holdout
Sample Exponential Smoothing Method Effect of
Smoothing Constant Implementation in StatTools
2
Moving Average Method
  • Apply when time series does not have a pronounced
    trend
  • Takes average of past k observations to forecast
    value of the next observation
  • Ftk (Yt Yt1Ytk-1)/k

3
Moving Average Calculation with k 3
131 (128 135 130)/3 130.7 (135 130
127)/3
4
Smoothing Effect of Span Value, k 3
  • Small values of k lead to light smoothing
    forecast series closely mirrors original series
  • Can lead to misleading forecasts attempting to
    model random noise
  • Use small k when movements believed to be true
    pattern

5
Smoothing Effect of Span Value, k gt 7
  • Large values of k lead to heavy smoothing
    forecast series tracks overall basic movement
  • Can lead to misleading forecasts if series
    fluctuations are part of true pattern and not
    random
  • Use large k when movements believed to be random

6
Graph of Smoothing with Small Span Value, k 3
7
Graph of Smoothing with Large Span Value, k 12
8
Assessment of Forecast
  • Use MAE, RMSE, MAPE
  • Choose k that yields smaller values of error
    metrics
  • Calculations based on historical values do not
    guarantee better forecasts
  • Better based on holdout sample

9
Assessment of Forecast Small Span, k 3
10
Assessment of Forecast Large Span, k 12
11
Simple Exponential Smoothing Method
  • Apply when time series does not have a pronounced
    trend

Starting at the end until power equals zero
12
Simple Exponential Smoothing vs. Moving Avg.
  • Improves on Moving Avg. since no series
    observations are lost due to averaging
  • In forecast, it gives weight to all past
    observations but weight depends on smoothing
    constant, a

13
Simple Exponential Smoothing Calculation with a
0.1
L1 Y1 to start off process L2 128.7 0.1135
0.9128 L3 128.83 .1130
.1.9135.9.9128
14
Effect of Small Smoothing constant, a 0.1
  • Small values of a lead to heavy smoothing because
    distant series observations continue to have
    large influence
  • Effect is similar to that of moving average with
    large k
  • Use small a when series swings believed to be
    random

15
Effect of Large Smoothing constant, a 0.9
  • Large values of a lead to light smoothing
    forecast series mimics original series
  • Only very recent observations influence next
    forecast
  • Use large a when swings believed to be true
    pattern

16
Graph of Simple Exponential Smoothing with Small
a (0.1)
17
Graph of Simple Exponential Smoothing with Large
a (0.9)
18
Assessment of Forecast
  • Use MAE, RMSE, MAPE
  • Choose a that yields smaller values of error
    metrics
  • StatTools can find optimal a
  • Calculations based on historical values do not
    guarantee better forecasts consider holdout
    sample

19
Assessment of Forecast Small Smoothing Constant
20
Assessment of Forecast Large Smoothing Constant
21
Simple Exponential Smoothing with Optimal a
(0.264)
22
Assessment of Forecast Optimal Smoothing Constant
Optimization based on RMSE
23
Forecasting with Moving Averages in StatTools
  • After naming data set, place cursor anywhere in
    spreadsheet and click on the Time Series
    Forecasting icon (4th from right)
  • Select Forecast from drop down menu
  • Select variable of interest by clicking in the
    box next to it

24
Forecasting with Moving Averages in StatTools
  • Accept defaults for Number of Forecasts and
    Method ( Moving Avg.) then enter desired
    number of holdouts and span value
  • Check defaults under Time Scale and adjust if
    necessary
  • Click O.K. for output in new sheet

25
Forecasting with Simple Exponential Smoothing in
StatTools
  • After naming data set, place cursor anywhere in
    spreadsheet and click on the Time Series
    Forecasting icon (4th from right)
  • Select Forecast from drop down menu
  • Select variable of interest by clicking in the
    box next to it

26
Forecasting with Simple Exponential Smoothing in
StatTools
  • Accept default for Number of Forecasts then
    enter desired number of holdouts
  • Click radio button for Expon. Smoothing
    (Simple) then enter parameter value (a) or check
    optimize box
  • Accept other defaults and click O.K. to obtain
    forecasts in new sheet
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