ETW3420 Principles of Forecasting and Applications
Principles of Forecasting and Applications
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Topic 5 Pre-tutorial Activity Part 2
In this pre-tutorial activity, you will:
(i) Mathematically derive some ETS models.
(ii) Derive point forecasts from ETS models.
Question 1
Using the component form representation of TS(A,A),
(i) Derive the ETS(A,A,A) innovations state space model.
(ii) Derive the point forecasts for yT +1 and yT +2.
Hint: Assume et = εt = yt − ŷt|t−1, where ŷt|t−1 can be obtained from the forecast equation of
the component form representation.
Question 2
Using the component form representation of TS(A,A),
(i) Derive the ETS(M,A,A) innovations state space model.
(ii) Derive the point forecasts for yT +1 and yT +2.
Hint: Assume εt =
yt−ŷt|t−1
, where ŷt|t−1 can be obtained from the forecast equation of the
component form representation.
Question 1
Question 2
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