Method and apparatus for executing short-term prediction of timeseries data

• US 5,748,851 A
• Filed: 02/28/1995
• Issued: 05/05/1998
• Est. Priority Date: 02/28/1994
• Status: Expired due to Term

• Current Assignee: Kabushiki Kaisha Meidensha
• Original Assignee: Kabushiki Kaisha Meidensha
• Inventors: Iokibe, Tadashi, Fujimoto, Yasunari, Tanimura, Takayoshi
• Primary Examiner(s): Hafiz, Tariq R.
• Application Number:
  US08/395,980
• Time in Patent Office: 1,162 Days
• Field of Search: 395/3, 395/10, 395/50-51, 395/60-61, 395/54, 395/900
• US Class Current: 706/58
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04

Abstract

An apparatus for executing a short-term prediction of chaotic timeseries data includes a parameter determining section that changes each of parameter values according to the dynamics of observed chaotic timeseries data, and a predicting section that predicts a near future value of objective by reconstructing an attractor of timeseries data of the objective data in a multi-dimensional state space and by using vector neighboring to the data vector including the objective data. Therefore, it becomes possible to quickly and accurately execute a short-term prediction of chaotic timeseries data and to be responsive to the changes of the dynamics of the timeseries data.

Claims

1. An apparatus for executing a short-term prediction of chaotic timeseries data, said apparatus comprising:

a data storage means for storing, as sample data, detected values of the timeseries data;

a parameter determining means for selecting a value of each of a plurality of parameters to be a component of a data vector;

a predicting means for generating the data vector from the detected values of the timeseries data according to the value of each parameter determined by said parameter determining means, and for obtaining a predicted value by reconstructing an attractor into a predetermined dimensional state space by means of embedding;

a prediction result storage means for storing the obtained predicted value; and

a prediction result evaluating means for detecting a predicted value corresponding to the detected values of the timeseries data from said prediction result storage means, and for evaluating a prediction accuracy by comparing the detected value and the predicted value,

wherein said parameter determining means selects a subset of the sample data at a predetermined time and a predetermined number of past data with respect to the sample data stored in said data storage means, said parameter determining means receiving a predicted value of the subset of the sample data on the basis of each combination of the parameters from said predicting means, said parameter determining means comparing the predicted value of the subset of the sample data from said prediction means with an actual value of the subset of the sample data, said parameter determining means again executing to select an undated value of each of the parameters so that a prediction accuracy of the sample data takes a maximum value, and outputting the updated selected values of the parameters to said predicting means,

wherein said parameter determining means determines the maximum value from all possible combinations of values of the parameters, so as to obtain one combination of values of each of the parameters of the data vector corresponding to the maximum value, the maximum value being outputted as the updated selected values of the parameters to said predicting means, and

wherein said predicting means reconstructs the attractor by embedding, using the updated selected values and a most-recently-stored sample of said sample data.

2. A prediction apparatus as claimed in claim 1, wherein said predicting means comprises a local fuzzy reconstructing means that comprises:

a neighboring vector detecting means for detecting a plurality of vectors neighboring to the data vector by using the reconstructed attractor;

an axis component detecting means for detecting a difference between an axis component value of the detected each neighboring vector and an axis component value of the data vector;

a fuzzy inference means for determining the axis component value of the data vector at a predetermined time period ahead upon detecting the axis component value of each of the neighboring vectors at the predetermined time period ahead, so as to decrease a difference between the detected axis component value of each neighboring vector at the predetermined time period ahead and the component value of the neighboring vector that generated the minimum difference in said axis component detecting means; and

a prediction data generating means for generating prediction data by transforming the result in said fuzzy inference means into timeseries data,

wherein a state-space structure of the predetermined dimensional state space is undated based on the updated selected values of the parameters, and

wherein the attractor is reconstructed based on the updated state-space structure.

3. A prediction apparatus for executing a short-term prediction of non-linear timeseries data, said prediction apparatus comprising:

a storage means for storing observed timeseries data;

a data vector generating means for generating a data vector having a component that is constituted by the observed timeseries data from said storage means;

an attractor reconstructing means for generating an attractor of the observed timeseries data in an n-dimensional state space by an embedding operation of the data vector;

a neighboring vector detecting means for detecting a plurality of vectors neighboring to the data vector generated in said data vector generating means;

an axis component detecting means for detecting a difference between an axis component value of each of the detected neighboring vector and an axis component value of the data vector;

a fuzzy inference means for determining the axis component value of the data vector at a predetermined time period ahead upon detecting the axis component value of each of the neighboring vectors at the predetermined time period ahead, so as to decrease a difference between the detected axis component value of each neighboring vector at the predetermined time period ahead and the axis component value of the neighboring vector that generated the minimum difference in said axis component detecting means; and

a prediction data generating means for generating the prediction timeseries data of the observed timeseries data by transforming the processing result in said fuzzy inference means into timeseries data,

wherein a state-space structure of the n-dimensional state space is updated based on the processing result of the fuzzy inference means.

4. A prediction apparatus as claimed in claim 3, wherein said fuzzy inference means generates a membership function that takes a peak at each axis component value of the neighboring vectors, and determines a component value after predetermined steps of the axis component value of the data vector by means of a fuzzy inference that applies the membership function.

5. A method for executing a short-term prediction of timeseries data under chaotic condition, comprising the steps of:

(a) storing, as sample data, measured values of timeseries data;

(b) selecting a value of each parameter to be a component of a data vector;

(c) generating the data vector from the detected values of the timeseries data according to the value of each parameter determined by said step (b) and obtaining a predicted value by reconstructing an attractor into a predetermined dimensional state space by embedding;

(d) storing the obtained predicted value;

(e) evaluating a prediction accuracy by comparing the detected value and the predicted value upon detecting the predicted value corresponding to the detected values of the timeseries data from said step (d);

(f) selecting a subset of the sample data at a predetermined time and a predetermined number of past data with respect to the sample data stored in said step (a);

(g) receiving a predicted value of the subset of the sample data on the basis of each combination of the parameters from said step (c); and

(h) comparing the predicted value of the subset of the sample data from said step (c) with an actual value of the subset of the sample data, said step (b) again executing to select an updated value of each of the parameters so that a prediction accuracy of the sample data takes a maximum value, and outputting the undated selected values of each of the parameters to said step (c),

wherein the updated selected values are used to update a state-space structure of the predetermined dimensional state space used in said step (c).

6. A method as claimed in claim 5, wherein the step (c) comprises the steps of:

(i) detecting a plurality of vectors neighboring to the data vector by using the reconstructed attractor;

(j) detecting a respective difference between an axis component value of each of the detected neighboring vectors and an axis component value of the data vector;

(k) determining the axis component value of the data vector at a predetermined time period ahead upon detecting the axis component value of each of the neighboring vectors at the predetermined time period ahead, so as to decrease a difference between the detected axis component value of each neighboring vector at the predetermined time period ahead and the axis component value of the neighboring vector that generated the minimum difference in said step (j); and

(l) generating the predicted value by transforming the processing result in said step (h) into timeseries data.

7. A method for executing short-term prediction of timeseries data under chaotic behavior, said prediction method comprising the steps of:

(a) storing timeseries data to be observed;

(b) generating a data vector having a component that is constituted by the timeseries data;

(c) generating an attractor of the timeseries data in an n-dimension state space by an embedding operation of the data vector;

(d) detecting a plurality of vectors neighboring to the data vector;

(e) detecting a respective difference between an axis component value of each of the detected neighboring vectors and an axis component value of the data vector;

(f) determining the axis component of the data vector at a predetermined time period ahead upon detecting the axis component value of each of the neighboring vectors at the predetermined time period ahead, so as to decrease a difference between the detected axis component value of each neighboring vector at the predetermined time period ahead, and the axis component value of the neighboring vector that generated the minimum difference in the step (e); and

(g) generating the predicted value by transforming the processing result in said step (f) into timeseries data,

wherein the minimum difference is used to update a state space structure of the n-dimension state space used in the embedding operation.

8. A method as claimed in claim 7, wherein the step (f) further comprises the steps of:

(h) generating a membership function that takes a peak value at each axis component value of the neighboring vectors; and

(i) determining a component value at a predetermined time period ahead of the axis component of the data vector by use of a fuzzy inference that applies the membership function.