Chapter 8 (Exponential smoothing)

Question 1

Simple Exponential Smoothing (SES)

Answer 1

forecasting data with no clear trend or seasonal pattern

ETS(A,N,N)
- Error: Additive
- Trend: None
- Season: None

Question 2

Holt’s linear trend method

Answer 2

Allow forecasting of data with a trend

ETS(A,A,N)
- Error: Additive
- Trend: Additive
- Season: None

Question 3

Damped trend method

Answer 3

Forecasting of data that ‘dampens’ the trend so that it approaches a constant some time in the future

0.8 <= Damp value <= 0.98

ETS(A,Ad,N)
- Error: Additive
- Trend: Additive damped
- Season: None

Question 4

ETS methods with seasonality

Additive vs multiplicative

Answer 4

• Additive method: is preferred when the seasonal variations are roughly constant through the series
• Multiplicative method: is preferred when the seasonal variations are changing proportional to the level of the series

Question 5

Holt-Winters’ additive method

Answer 5

ETS(A,A,A)
- Error: Additive
- Trend: Additive
- Season: Additive

Question 6

Holt-Winters’ multiplicative method

Answer 6

ETS(M,A,M)
- Error: Multiplicative
- Trend: Additive
- Season: Multiplicative

If season is multiplicative, error must also be multiplicative.
Having additive error with multiplicative season may result to numeric instability

Question 7

Holt-Winters’ damped method

Answer 7

ETS(M,Ad,M)
- Error: Multiplicative
- Trend: Additive damped
- Season: Multiplicative

Question 8

ETS models - general notation

Answer 8

• Error: Additive (A) or Multiplicative (M)
• Trend: None (N), Additive (A) or Additive damped (Ad)
• Seasonality: None (N), Additive (A) or Multiplicative (M)

Question 9

Model selection

Answer 9

AIC determines which ETS model is most appropriate

AIC only works with same model types

Question 10

Prediction intervals between additive and multiplicative methods

Answer 10

Even if same smoothing parameters, the point forecasts will be the same but prediction intervals will differ

Question 11

Smoothing parameters

Answer 11

• Alpha (α): if close to 1, then level changes rapidly
• Beta (β): if close to 1, then trend changes often
• Gamma (γ): if close to 1, then seasonality updates faster
• Phi (Φ): damping, often between 0.8 to 0.98