TimeSeriesAnalysis
Initialize
initialize an exponential smoothing model
Calling Sequence
Parameters
Description
Examples
References
Compatibility
Initialize(model, ts)
model
-
Exponential smoothing model
ts
Time series consisting of a single data set
The Initialize command initializes the optimization process run by Optimize for finding suitable parameters and initial conditions for a specialized Exponential smoothing model.
It returns a table, indexed by the names of parameters or initial conditions. The value corresponding to an index is the number that that parameter or initial condition will be initialized to during the optimization process.
Parameters that are fixed beforehand are not given in the resulting table.
withTimeSeriesAnalysis:
Consider the following time series.
ts≔TimeSeries1.8,3.4,2.1,2.9,2.4,2.9,2.5,3.1,period=2
ts≔Time seriesdata set8 rows of data:2016 - 2023
Specialize this into all applicable models.
models≔SpecializeExponentialSmoothingModel,ts
models≔< an ETS(A,A,A) model >,< an ETS(A,A,N) model >,< an ETS(A,Ad,A) model >,< an ETS(A,Ad,N) model >,< an ETS(A,N,A) model >,< an ETS(A,N,N) model >,< an ETS(M,A,A) model >,< an ETS(M,A,M) model >,< an ETS(M,A,N) model >,< an ETS(M,Ad,A) model >,< an ETS(M,Ad,M) model >,< an ETS(M,Ad,N) model >,< an ETS(M,M,M) model >,< an ETS(M,M,N) model >,< an ETS(M,Md,M) model >,< an ETS(M,Md,N) model >,< an ETS(M,N,A) model >,< an ETS(M,N,M) model >,< an ETS(M,N,N) model >
Next, initialize each of these models.
initialization_tables≔mapInitialize,models,ts
initialization_tables≔tableβ=110,s=−0.3750000000000000.512500000000000,b0=0.0351190476190477,α=12,γ=1100,l0=2.41071428571428,tableβ=110,b0=0.0773809523809526,α=12,l0=2.28928571428571,tableβ=110,s=−0.3750000000000000.512500000000000,b0=0.0351190476190477,α=12,γ=1100,φ=0.978,l0=2.41071428571428,tableβ=110,b0=0.0773809523809526,α=12,φ=0.978,l0=2.28928571428571,tables=−0.3812500000000000.518750000000000,α=12,γ=1100,l0=2.56875000000000,tableα=12,l0=2.63750000000000,tableβ=110,s=−0.3750000000000000.512500000000000,b0=0.0351190476190477,α=12,γ=1100,l0=2.41071428571428,tableβ=110,s=0.8678777973255601.22504867885882,b0=0.0471683829401126,α=12,γ=1100,l0=2.31025399169193,tableβ=110,b0=0.0773809523809526,α=12,l0=2.28928571428571,tableβ=110,s=−0.3750000000000000.512500000000000,b0=0.0351190476190477,α=12,γ=1100,φ=0.978,l0=2.41071428571428,tableβ=110,s=0.8663373208274781.22045629439217,b0=0.0474547670432530,α=12,γ=1100,φ=0.978,l0=2.31594155793230,tableβ=110,b0=0.0773809523809526,α=12,φ=0.978,l0=2.28928571428571,tableβ=110,s=0.8664119113811891.22047262484913,b0=1.02015799136523,α=12,γ=1100,l0=2.30027768778461,tableβ=110,b0=1.03693927243796,α=12,l0=2.19796110842741,tableβ=110,s=0.8664119113811891.22047262484913,b0=1.02015799136523,α=12,γ=1100,φ=0.978,l0=2.30027768778461,tableβ=110,b0=1.03693927243796,α=12,φ=0.978,l0=2.19796110842741,tables=−0.3809891091774520.519010890822548,α=12,γ=1100,l0=2.55701180603960,tables=0.8694900847111761.21615190130110,α=12,γ=1100,l0=2.51642347897302,tableα=12,l0=2.58767635294028
Because the models have different sets of parameters, the tables have different sets of indices.
mapprint,mapindices,initialization_tables,nolist:
β,s,b0,α,γ,l0
β,b0,α,l0
β,s,b0,α,γ,φ,l0
β,b0,α,φ,l0
s,α,γ,l0
α,l0
Every model contains l0, the initial value for the variable ℓt. The values are different for different models:
mapx↦xl0,initialization_tables
2.41071428571428,2.28928571428571,2.41071428571428,2.28928571428571,2.56875000000000,2.63750000000000,2.41071428571428,2.31025399169193,2.28928571428571,2.41071428571428,2.31594155793230,2.28928571428571,2.30027768778461,2.19796110842741,2.30027768778461,2.19796110842741,2.55701180603960,2.51642347897302,2.58767635294028
On the other hand, α (also present in all models) is always initialized to 12.
mapx↦xα,initialization_tables
12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12
Hyndman, R.J. and Athanasopoulos, G. (2013) Forecasting: principles and practice. http://otexts.org/fpp/. Accessed on 2013-10-09.
Hyndman, R.J., Koehler, A.B., Ord, J.K., and Snyder, R.D. (2008) Forecasting with Exponential Smoothing: The State Space Approach. Springer Series in Statistics. Springer-Verlag Berlin Heidelberg.
The TimeSeriesAnalysis[Initialize] command was introduced in Maple 18.
For more information on Maple 18 changes, see Updates in Maple 18.
See Also
LogLikelihood
Optimize
Specialize
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