JPH0635895A - Time-series data predicting method - Google Patents

Abstract

PURPOSE:To identify and predict highly nonlinear time-series data with high accuracy. CONSTITUTION:In the nonlinear transformation process of a step 2, one of prey-predator relation, competitive relation and symbiosis relation prepared beforehand is set by the judgement of an operator. In the successive estimating process of the step 4, the estimated values of the time series data are successively obtained by solving a recurrence formula and a differential equation using a preset parameter, the initial value and nonlinear relation of variables and teacher data. In the parameter adjusting process of the step 5, the estimated values of the time series data obtained as mentioned above and the time-series data (actual value) prepared as the teacher data are compared and the parameter is varied so that error is to be minimum. In the successive predicting process of the step 6, the predicted values of the time-series data are successively obtained by solving the recurrence formula or the differential equation using the obtained value of the parameter and test data.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a time-series data predicting method which is particularly useful for predicting time-series data having a strong non-linearity, particularly time-series data in the distribution field such as demand for consumer goods.

[0002]

2. Description of the Related Art Conventionally, in order to predict time series data, Time Series Analysis (1976) (GEBox
and GMJenkins, Time Series Analysis: Forcasting
and Control, Holden-Day, 1976). The order of this model is IEE, Transaction on Automatic Control AC 19, 1974.
Year, 716th to 723rd pages (IEEE, Tran
s. on Automatic Control, AC-19, 1974, pp.716-723)
AIC (Akaike Inform
ation Criterion).

[0003]

When it is attempted to identify strongly nonlinear time-series data, for example, the demand amount of consumer goods by the above-mentioned conventional technique, it is difficult to determine the order,
There was a problem that the degree of fit was not good.

An object of the present invention is to identify and predict time series data having strong non-linearity.

[0005]

On the other hand, in the present invention, a plurality of time-series data are picked up, and a non-linear relationship representing predation-prey relation, competition relation, and symbiotic relation in the ecosystem between them is taken. The predicted value of the time series data is sequentially obtained by constructing and adjusting the parameters so as to minimize the error between the estimated value and the realized value of the time series data, by using the solution solving mechanism of the recurrence formula or the differential equation.

[0006]

[Operation] In the nonlinear transformation mechanism, the interaction between multiple time series data is constructed as a nonlinear relation representing predation-prey relation, competition relation, and symbiotic relation in the ecosystem. The parameters are adjusted so as to minimize the error by comparing, and in the iterative estimation mechanism and the sequential prediction mechanism, the prediction value is sequentially obtained by the solution mechanism of the recurrence formula or the differential equation.

[0007]

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 is a flow chart showing the outline of the present invention.

When the time-series data is read in step 1, in the non-linear conversion process of step 2, any one of a prey-prey relation, a competition relation, and a symbiosis relation prepared in advance is established between the time-series data. Operation
Set by the judgment of the data. Here, the predation-prey relationship is the relationship that the value of the other variable decreases when the value of one variable increases, and the competitive relationship is the value of the other variable when the value of one variable decreases. Also, the symbiotic relationship is a relationship in which when the value of one variable increases, the value of the other variable also increases.

In the step of setting parameters and initial values in step 3, parameters and initial values for the model of the time series data are set. In the successive estimation process of step 4, the estimated values of the time series data are sequentially obtained by solving the recurrence equation and the differential equation using the parameters, the initial values of the variables and the nonlinear relationship, and the teacher data which have already been set. In the parameter adjustment process of step 5, the estimated value of the time-series data obtained as described above is compared with the time-series data (realized value) prepared as teacher data, and the parameter is adjusted to minimize the error. The amount of variation is calculated and the parameters are varied.

When the parameter value is determined by such learning, the predicted value of the time-series data is recurrenced by using the parameter value obtained as described above and the test data in the sequential prediction process of step 6 or Sequentially obtain by solving the differential equation.

FIG. 2 is a block diagram showing the outline of the present invention. Turn on the switch to read the time series data. Then, the non-linear conversion mechanism sets a non-linear relationship with respect to this time series data. The non-linear relationship here means predation-prey relationship, competition relationship,
Either symbiotic relationship or relationship. Next, in the parameter initial value setting mechanism, initial values of parameters and variables for the model of the time series data are set. Using these parameters, initial values of variables, nonlinear relations, and teacher data, the estimated value of time-series data is successively obtained by solving recurrence equations or differential equations in the iterative estimation mechanism. Further, the parameter adjustment mechanism changes the parameter so that the error is minimized by comparing the estimated value of the time series data with the realized value. Once the parameters are determined, the test data is used to obtain the predicted value of the time series data in the sequential prediction mechanism.

FIG. 3 shows the hardware configuration of the present invention. That is, the data of the consumer goods demand amount is sent via the communication control device 1. The calculation device 2 and the database 3 receive the sent data of the demand amount of the consumer goods and process the data. Each step shown in FIG. 1 is implemented in a computer.

Here, a case where the consumer goods demand amount is taken as time series data will be described. That is, two consumer goods X and Y are taken, and the demand amount at time t is x.
(T), y (t). First, according to the mechanism of the present invention, the demand amount of consumer goods {x (t)}, {y (t)}, (t = 1,
, N) and N is the number of data. The operator
It is assumed that there is a predator-prey relationship between the two consumer goods X and Y, and a model representing such a relation is selected.
Here, the predator-prey relationship means that when the consumer good X is a predator and the consumer good Y is a prey, the consumer good X increases as the consumer good Y increases, and the consumer good Y increases the consumer good X. Then, there is a relationship that it decreases. At this time, in the non-linear conversion process, a non-linear relationship such as Equations 1 and 2 is set between the consumer product demand amounts x and y which are variables. In addition, in the process of setting the parameter initial value, six parameters {s,
r, γ, K, k, D} initial values and variable initial values are set.

[0014]

[Equation 1]

[0015]

[Equation 2]

When the relations are set as described above, the values of the parameters {s, r, γ, K, k, D} and the variables x,
When the initial value of y is determined, the estimated value and predicted value of x and y are uniquely determined. In order to improve the prediction accuracy, since the initial values of the variables x and y are almost fixed, it is important how to set the parameter values. Conventionally, it was not clear how to set the parameters even if a non-linear relationship was set between the time series data, and the operator set the parameters by trial and error. In the present invention, the parameters are determined by the criterion of the minimum error as follows.

That is, according to the present invention, teacher data {x (t)}, {y (t)}, t = 1, ..., N, (n ≦
N) and n select the number of data. Then, the estimated value of the time series data is obtained, and the parameter is changed so that the error from the actual value is minimized. Such actions are performed in the sequential estimation process and the parameter adjustment process. That is, in the iterative estimation process, the initial values of the parameters {s (1), r
(1), γ (1), K (1), k (1), D (1)}, and the initial value of the variable x (1),
When y (1) is given, the estimated values of x and y are {x (t) *}, {y (t)
*}, T = 1, ..., N are sequentially obtained by the recurrence formula given above. Then, in the parameter adjustment process,
The value of the parameter is changed so as to minimize the error defined as above.

[0018]

[Equation 3]

In the present invention, the value of the parameter is changed by the simulated annealing method in which the above error is regarded as energy. The process of the change is as follows.

(1) Setting of initial value: learning number i = 0,
When taking variables, for example, s = s (0) and temperature T = T (i) = T ₀ / log (1 + i), T = T (0).

(2) Generation of change amount: The change amount Δs is generated by a normal random number having an average of 0 and a variance T.

(3) Calculation of change in estimation error: Change Δ
Let E = E (s + Δs) −E (s).

(4) Comparison and judgment: ξ = exp (-ΔE / T)
And a uniform random number η of (0, 1) are compared. (A) If ξ ≧ η, the next state is s + Δs. (B) If ξ <η, the next state is s.

(5) State update i → i + 1. Step two
What.

Each of these processes is performed in a parameter adjustment process or parameter adjustment mechanism.
By varying the value of the variable stochastically, it is possible to obtain a parameter that reduces the estimation error.

When the predation-prey relationship of two variables as described above is set, the error is calculated as the value of the equilibrium point x *, y * of the model.
Can be defined as the square of the difference between the average x #, y # of the realized values, and the parameter can be varied to reduce this value. At this time, the error is defined as in Expression 4. Also,
The equilibrium point of the above model can be expressed as in Equation 5.

[0027]

[Equation 4]

[0028]

[Equation 5]

After the parameters are obtained, the future values of the time series data are obtained in the sequential prediction process using the teacher data as test data.

FIG. 4 shows the predicted values of the demand quantities x and y of the consumer goods X and Y obtained by setting parameters and initial values of the model. The solid line represents the predicted value and the solid line represents the predicted value. As shown in this figure, according to the present invention, time series data having strong nonlinearity can be predicted with high accuracy.

Further, it is easy to realize each mechanism of the present invention by an LSI.

[0032]

According to the present invention, it is possible to highly accurately predict a time series phenomenon having a strong non-linearity.

[Brief description of drawings]

FIG. 1 is a flowchart showing an outline of processing according to an embodiment of the present invention.

FIG. 2 is a block diagram showing a functional configuration of an embodiment of the present invention.

FIG. 3 is a block diagram of a hardware configuration according to an embodiment of the present invention.

FIG. 4 is a diagram showing predicted values of consumer goods demand amounts and realized values of demand amounts according to the present invention.

[Explanation of symbols]

1: communication control device, 2: computing device, 3: database,
4: Console

Claims (8)

[Claims] 1. When a plurality of time series data are given,
(1) a step of setting a non-linear relationship between the time series data, and (2) a step of setting initial values of model parameters and variables for the time series data,
(3) Steps of sequentially obtaining estimated values of time series data using teacher data, (4) Steps of adjusting model parameters for time series data using teacher data, and (5) Time series data A time-series data prediction method comprising the steps of sequentially obtaining a prediction value using test data. 2. The time-series data prediction method according to claim 1, wherein the step (1) includes some non-linear relations among the time-series data, that is, predation-prey relations in the ecosystem, competitive relations, A time series data prediction method comprising a process of setting a non-linear relationship expressing a symbiotic relationship. 3. The time series data prediction method according to claim 1, wherein the steps (3) and (5) are (1) and (2).
A time-series data prediction method comprising the process of sequentially calculating future values of time-series data by using recurrence formulas or differential equations. 4. The time series data prediction method according to claim 1, wherein said step (4) comprises a process of changing parameters so that an error between an estimated value of the time series data and an actual value is minimized. Data prediction method. 5. The time-series data prediction method according to claim 1, wherein said step (4) is a simulated method in which an error between an estimated value of the time-series data and an actual value is regarded as energy.
A time-series data prediction method comprising a process of varying parameters so that an error is minimized by an annealing method. 6. The time series data prediction method according to claim 1, wherein in the step (4), when the predator-prey relationship of two variables is set to a non-linear relationship, the value of the equilibrium point of this non-linear model and the realized value. A time-series data prediction method comprising a process of changing parameters so that the error of is minimized. 7. The time series data prediction method according to claim 1, wherein the demand amount of consumer goods is taken as the time series data. 8. The time series data prediction method according to claim 1, wherein each step is realized in an LSI.