Title: Forecasting NoTrend Time Series II: Moving Averages
1Forecasting 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
2Moving 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
3Moving Average Calculation with k 3
131 (128 135 130)/3 130.7 (135 130
127)/3
4Smoothing 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
5Smoothing 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
6Graph of Smoothing with Small Span Value, k 3
7Graph of Smoothing with Large Span Value, k 12
8Assessment 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
9Assessment of Forecast Small Span, k 3
10Assessment of Forecast Large Span, k 12
11Simple Exponential Smoothing Method
- Apply when time series does not have a pronounced
trend
Starting at the end until power equals zero
12Simple 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
13Simple 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
14Effect 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
15Effect 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
16Graph of Simple Exponential Smoothing with Small
a (0.1)
17Graph of Simple Exponential Smoothing with Large
a (0.9)
18Assessment 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
19Assessment of Forecast Small Smoothing Constant
20Assessment of Forecast Large Smoothing Constant
21Simple Exponential Smoothing with Optimal a
(0.264)
22Assessment of Forecast Optimal Smoothing Constant
Optimization based on RMSE
23Forecasting 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
24Forecasting 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
25Forecasting 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
26Forecasting 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