Forecasting with Exponential Smoothing Adjusted for Trend and Seasonality

1
Forecasting with Exponential Smoothing Adjusted
for Trend and Seasonality
Topics Trend only Adjustment in Holts
Model Comparing Holts with Simple Trend
Seasonality Adjustment in Winters
Model Implementation in StatTools
2
Exponential Smoothing Adjusted for Trend Only

• Apply when time series does have a pronounced
  trend
• Holts model includes a trend term and a
  corresponding smoothing constant.
• This new smoothing constant, b, controls how
  quickly the model reacts to perceived changes in
  the trend.

3
Choice of Smoothing Constants for Holts Model

• Trial Error begin with small a (0.1 or 0.2)
  and put b a
• Settle on values that minimize error metrics
  (MAE, RMSE, MAPE)
• Utilize optimization option in StatTools software

4
Problem Scenario

• A company wants to forecast sales ( units sold)
  based on monthly time series data collected over
  the last 5 years. They believe sales have been
  growing by a constant percentage
• Is there a good trend model?

5
Exploring the Best Trend Model with Excel
6
Interpreting Forecast Error for Exponential Model

• In each of the past 60 months the exponential
  model forecast the Sales with a mean error of
  8.3
• The monthly forecast was off by 1103 units on
  average

7
Simple Exponential Smoothing with Optimal a
(0.957)
8
Assessment of Forecast Optimal Smoothing Constant
Holdout period 4 Improvement on Trend only
9
Holts Exponential Trend Model with Small a b
(0.1)
10
Assessment of Forecast Holts Model, small a b
Improvement on simple smoothing
11
Assessment of Forecast Holts Model, Increased a
b
Worse than for small a and b
12
Assessment of Forecast Holts Model, Optimal a
b
Optimized on RMSE for Est. Period Worse holdout
than for small a, b
13
Graph of Holts Model with Optimal a, b
b 0 implies no update of slope
14
Winters Forecast Model for Trend Seasonality

• Similar to Holts model - has level and trend
  terms and smoothing constants a, b - but also
  seasonal indexes and a corresponding smoothing
  constant.
• New smoothing constant g controls how quickly the
  model reacts to perceived changes in the pattern
  of seasonality.

15
Seasonality Scenario

• A company wants to forecast sales ( units sold)
  based on monthly time series data collected over
  the last 5 years. They believe sales have been
  growing at a constant rate but sales tend to be
  high in the summer and low in the winter

16
Sales with Seasonality and Trend
17
Choice of Smoothing Constants based on Observed
Series

• Trend appears to be constant let b 0
• Seasonal variation appears to be fairly constant
  let g 0.1
• Apart from trend and seasonality changes in level
  appear random let a 0.1

18
Winters Model with Intuitive Estimates for a, b,
and g
19
Assessment of Forecast Winters Model with
Intuitive Smoothing Constants
Holdout period 4 Very good Forecasts
20
Winters Model with Optimal Estimates for a, b,
and g
21
Assessment of Forecast Winters Model with
Optimal Smoothing Constants
Forecasts very similar to Intuitive model
22
Forecasting with Holts Winters 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

23
Forecasting with Holts Winters in StatTools

• Accept default for Number of Forecasts then
  enter desired number of holdouts
• Click radio button for Holts or Winters
  smoothing then enter parameter values a, b, (g)
  or check optimize box
• Accept other defaults and click O.K. to obtain
  forecasts in new sheet