Method for Prediction for Nonlinear Seasonal Time Series
First Claim
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1. A method for predicting future values of a time series from past values of the time series, wherein Lt and It are values of an initial local mean level, and a seasonal index at a time t, and α
- and δ
are smoothing parameters for updating the mean level and the seasonal index, respectively, and p is a duration of a seasonal pattern, comprising for each next local mean level Lt the steps of;
determining {circumflex over (X)}t (1)=It-pFt(Lt), wherein {circumflex over (X)}t (1) is a prediction made at time t one time step in the future, and Ft is a nonlinear function for a vector Lt of local level means;
updating the local mean Lt and the seasonal index according to
Lt=α
(Xt/It−
p)+(1−
α
)({circumflex over (X)}t−
1 (1)/It−
p)
It=δ
(Xt/Lt)+(1−
δ
)It−
p; and
estimating a next Ft (L) from past values of L, wherein the determining, updating and estimating steps are performed in a processor.
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Abstract
A method predicts nonlinear seasonal time series data. More particularly, the method predicts short term power demand. The method uses an exponential smoothing technique and dynamic modeling of seasonal time series data with kernels. The kernels are used to predict future values of the time series from past values using nonlinear functions such as a least-squares radial basis function or support vector regression using a Gaussian kernel.
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Citations
5 Claims
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1. A method for predicting future values of a time series from past values of the time series, wherein Lt and It are values of an initial local mean level, and a seasonal index at a time t, and α
- and δ
are smoothing parameters for updating the mean level and the seasonal index, respectively, and p is a duration of a seasonal pattern, comprising for each next local mean level Lt the steps of;determining {circumflex over (X)}t (1)=It-pFt(Lt), wherein {circumflex over (X)}t (1) is a prediction made at time t one time step in the future, and Ft is a nonlinear function for a vector Lt of local level means; updating the local mean Lt and the seasonal index according to
Lt=α
(Xt/It−
p)+(1−
α
)({circumflex over (X)}t−
1 (1)/It−
p)
It=δ
(Xt/Lt)+(1−
δ
)It−
p; andestimating a next Ft (L) from past values of L, wherein the determining, updating and estimating steps are performed in a processor. - View Dependent Claims (2, 3, 4, 5)
- and δ
Specification