Resumo:
This study presents a nonlinear multi-objective optimization method for defining optimal
weights for combining time series forecasting methods used to estimate annual natural gas
demands. The weight allocation approach employs mixed experimental arrangements to model
the relationship between various predictive performance metrics, and the weights assigned to
the prediction residuals of the individual time series methods chosen for the combinations. The
Double Exponential Smoothing (DES) method, the Holt-Winters additive (WA) method, and
the multiplicative (WM) method were used in this study. Various performance metrics related
to location, dispersion, and diversity were modeled using canonical polynomials for mixtures,
which were then individually optimized to form a Payoff matrix for the individual solutions.
These were then grouped according to the minimum distance between optimal points and the
Jolliffe criterion, defined by the Principal Component Analysis (PCA), and applied to each
group identified for non-redundant metric first selection (Payoff-Jolliffe Criteria). Factor
analysis (FA) was applied to the remaining metrics, via principal component extraction and
varimax rotation, storing the rotated factor scores. After modeling these scores with the same
canonical polynomial mixture class, the Normal Boundary Intersection (NBI) optimization
method was used, modified by adding an auxiliary elliptic constraint class. The set of results
was compared with results from the best individual forecasting methods, results from traditional
combination methods, results from the FA-NBI method, and its variants according to the 3
applied Jolliffe rules, in order to verify the reasonableness of the data treatment. The results for
all methods were compared with a test set not used in the modeling and optimizing stages, i.e.,
an out-of-sample set, which verified the remarkable efficiency of the method proposed in this
paper, relative to the other methods. Although the results are limited to the studied series alone,
the adequacy of the methods presupposes that all other types of time series, or combinations of
methods, might result in similar significant improvements in forecast assertiveness.
