CN107067096A - The financial time series short-term forecast being combined based on point shape with chaology - Google Patents
The financial time series short-term forecast being combined based on point shape with chaology Download PDFInfo
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Abstract
Apply to the short term prediction methods of financial field price series the invention discloses a kind of be combined fractal theory and chaology, including step：The Hurst indexes and statistic of time series are calculated using R/S analytic approach, determine the cycle of time series；Embedded dimensions and the time delay of time series are obtained, phase space reconfiguration is carried out to time series, sample data is generated；Sample data is normalized；Difference point is determined according to the sequencing of sampling time point；Vertical scaling fac tor is determined using Hurst indexes；The iterated function series of every group of sample are determined, final iterated function series are determined according to weight；Extrapolate a time point, corresponding initial value is set to zero, set a step-length to convert respective value, re-start iteration；The mean error of curve, calculating difference result and historical data is drawn, the minimum corresponding extrapolated value of error is exactly predicted value.Present invention is generally directed to the short-term forecast of self similarity in financial field and periodically unconspicuous time series, the Billy that predicts the outcome is more accurate with traditional fractal method.
Description
Technical field
It the present invention relates to the use of the method that point shape and chaology be combined and short-term forecast carried out to financial time series
Method, belongs to finance data mining field.
Background technology
As financial globalization and liberalization develop, more and more fierce, the traditional financial analysis side of the competition of financial industry
Method can not meet the dependence and sensitivity analysis for mass data to a certain extent.In recent years, for finance data
Nonlinear theory is introduced financial market by dynamic, complicated, nonlinear feature, people, to more accurately from these data
The operation law in middle announcement financial market.
Chaos and point shape are the main theories of nonlinear science, with nonlinear theory can preferably analyze DYNAMIC COMPLEX,
Nonlinear big data.At present, verified financial market has obvious multi-fractal and mixed for correlative study achievement and document
Ignorant dynamic characteristic.But most research is that qualitative analysis is carried out to financial market, or individually with point shape or
The theory of chaos is predicted.
The present invention proposes a kind of new method, by point shape difference in the phase space reconfiguration and fractal theory in chaology
Forecast model combines, and short-term forecast analysis is carried out to financial time series.Sample is carried out first with phase space reconfiguration principle
This selection；Then collage theorem and difference iterative algorithm in conjunction with fractal theory is predicted modeling to time series,
In difference iterative algorithm, fractal dimension Hurst indexes and vertical scaling fac tor are combined, make result more accurate；Last profit
Outer with fractal theory opens up principle, and short-term forecast is carried out to time series.The present invention solves similitude and periodically indefinite
Time series short-term forecast problem, improve predictablity rate.
The content of the invention
In view of this, it is a kind of for self-similarity and periodically unconspicuous finance it is a primary object of the present invention to provide
The short term prediction method of time series.
In order to achieve the above object, technical scheme proposed by the present invention is：
A kind of financial time series short term prediction method being combined based on point shape and chaology, the appraisal procedure is included such as
Lower step：
Step 1, Hurst indexes and statistic using R/S analytic approach calculating time series, the cycle of time series is determined,
The selection cycle, unconspicuous time series was used as original time series；
Step 2, using chaology phase space reconfiguration is carried out to original time series, it is empty that One-dimension Time Series are converted into higher-dimension
Between multidimensional vector, in higher dimensional space using similitude choose data sample, according to the sequencing of sampling time point determine
Simultaneously sample data group is normalized for difference point；
Step 3, the vertical scaling fac tor for determining using Hurst indexes every group of sample data, determined according to vertical scaling fac tor
The conversion coefficient of affine transformation（、、、）, so that it is determined that iterated function series, final iteration function is determined according to weight
System；
Step 4, one time point of extrapolation, corresponding initial value are set to zero, set a step-length to convert respective value, re-start repeatedly
In generation, the mean error of curve, calculating difference result and historical data is drawn, the minimum corresponding extrapolated value of error is exactly predicted value.
In summary, point shape difference prediction in the phase space reconfiguration and fractal theory of the present invention by chaology
Models coupling gets up, and short-term forecast analysis is carried out to financial time series.Sample is carried out first with phase space reconfiguration principle
Choose；Then collage theorem and difference iterative algorithm in conjunction with fractal theory is predicted modeling to time series, in difference
In iterative algorithm, fractal dimension Hurst indexes and vertical scaling fac tor are combined, make result more accurate；Finally utilize and divide
The outer of shape theory opens up principle, and short-term forecast is carried out to time series.The wherein selection of sample data, the selection of vertical scaling fac tor
Improve the accuracy rate of prediction.
Brief description of the drawings
Fig. 1 is total for the financial time series short term prediction method of the present invention being combined based on point shape and chaology
Body schematic flow sheet；
Fig. 2 chooses the schematic flow sheet of data sample for the present invention；
Fig. 3 is present invention determine that the schematic flow sheet of point shape difference iterated function series；
Fig. 4 is the schematic flow sheet of outside forecast in the present invention.
Embodiment
Below in conjunction with the accompanying drawing of the present invention, technical scheme is clearly and completely described, it is clear that institute
Give an actual example for illustrating, and non-limiting embodiments of the present invention, it is of the invention to pass through other different specific realities
The mode of applying is implemented.The every other implementation that those of ordinary skill in the art are obtained under the premise of creative work is not made
Example, belongs to the scope of protection of the invention.
Fig. 1 is total for the financial time series short term prediction method of the present invention being combined based on point shape and chaology
Body schematic flow sheet.As shown in figure 1, financial time series short term prediction method of the present invention, comprises the following steps：
Step 1, Hurst indexes and statistic using R/S analytic approach calculating time series, the cycle of time series is determined,
The selection cycle, unconspicuous time series was used as original time series；
Step 2, using chaology phase space reconfiguration is carried out to original time series, it is empty that One-dimension Time Series are converted into higher-dimension
Between multidimensional vector, in higher dimensional space using similitude choose data sample, according to the sequencing of sampling time point determine
Simultaneously sample data group is normalized for difference point；
Step 3, the vertical scaling fac tor for determining using Hurst indexes every group of sample data, determined according to vertical scaling fac tor
The conversion coefficient of affine transformation（、、、）, so that it is determined that iterated function series, final iteration function is determined according to weight
System；
Step 4, one time point of extrapolation, corresponding initial value are set to zero, set a step-length to convert respective value, re-start repeatedly
In generation, the mean error of curve, calculating difference result and historical data is drawn, the minimum corresponding extrapolated value of error is exactly predicted value.
In a word, the financial time series short term prediction method of the present invention being combined based on point shape and chaology is first
It is that financial time series are analyzed, the Hurst indexes and statistic of time series is calculated using R/S analytic approach, it is determined that
The cycle of time series, mainly for the short-term forecast of self-similarity and periodically unconspicuous financial time series；Then it is sharp
Time series is reconstructed with the phase space reconstruction technique in chaology, the sequence after reconstruct has self similarity well
Property, using the sequence after reconstruct as data sample, put forward forecasting accuracy；It is successively suitable according to the sampling time in sequence after reconstitution
Sequence determines difference point；Vertical scaling fac torSelection iterated function series are had a very big impact, because the sequence after reconstruct has
Good self-similarity, is utilizedAnalysis method calculates the Hurst indexes of time series, is calculated using Hurst indexes
Free variable in iterated function series, then calculate conversion coefficient（、、、）, so that it is determined that iterated function series；According to
Every group of iterated function series determine the iterated function series of system in statistical significance；Finally one future position of extrapolation, determines a step
Long, each step-length brings iterated function series into by future position is counter, determines prediction curve, calculating prediction curve and actual value must put down
Equal error, error minimum is predicted value.
Fig. 2 chooses the schematic flow sheet of data sample for the present invention.As shown in Fig. 2 in step 2, it is described to time series
Carry out phase space reconfiguration and determine that sample data group comprises the following steps：
Step 21, former length of time series are, with auto-relativity function method andWhen algorithm calculates the delay of time series
BetweenAnd Embedded dimensions；According to Phase-space Reconstruction, the attractor of dynamical system is reconstituted in one and does not change opening up for it
That flutters feature has in the new phase space of delay coordinate, according to embedding theorems, by introducing time delay, by time seriesIt is reconstructed intoTie up phase space（Corresponding point set is）, whenWhen determining,WithRelation be
Then obtained by phase space reconfigurationOrganizing length isReproducing sequence；
Step 22, length is obtained by step 21 it isTime series after reconstruct,It is the minimum member that vector set is included after reconstructing
Plain number, therefore willAs the radix of construction sample data length, the sample data length of selection isIntegral multiple, delay
TimeIt is constant；
Step 23, according to the sequencing of sampling time point difference point determined to every group of sample data, every group of sample data is to adopt
Sample time-series is as abscissa, and the size of each sample point data is as ordinate, and these points constitute difference point together；
Step 24, according to formula
Sample data group is normalized, value is reducedIt is the predicted value progress overall situation for convenience to the later stage
Search；WhereinWithThe respectively abscissa and ordinate of difference point,WithRespectively the maximum of abscissa and
Minimum value,WithThe respectively maximum and minimum value of sample data,For sample data length.
Fig. 3 is present invention determine that the schematic flow sheet of point shape difference iterated function series.As shown in figure 3, in step 3, utilizing
Hurst indexes determine the vertical scaling fac tor and iterated function series of every group of sample data, comprise the following steps：
Step 31, every group of sample data all have self-similarity, therefore utilizeAnalytic approach every group of sample data of calculating
Hurst indexes；
Step 32, according to fractal theory, it is assumed that it is eachIt is equal in magnitude, then directly using Hurst indexes according to formula
Determine vertical scaling fac tor, whereinFor Hurst indexes；
Step 33, iteration factor all is obtained using Hurst indexes to every group of sample dataAfterwards, pass throughAffine transformation can be tried to achieveConversion coefficient（、、、）, so that it is determined that the IFS codes of point shape difference；
Step 34, the iterated function series made according to the iterated function series exploitation right reconstruct of every group of sample in statistical significance, wherein because
Sample is chosen Deng the time, the weight of each group sample data is the same, that is, seeks the average value of each conversion coefficient of all iterated function series,
What is obtained is the iterated function series of system, for predicting.
In the present invention, in step 33, the conversion coefficient that affine transformation is determined according to vertical scaling fac tor（、、
、）, so that it is determined that iterated function series, specifically include following steps：
Step S1, the principle of point shape difference are to construct corresponding IFS to one group of given interpolation point, and the attractor for making IFS is logical
Cross the functional arrangement of this group of interpolation point.The IFS codes of shape difference are divided to pass through affine transformationTry to achieve, formula is as follows：
It is spaceCompression mapping,、、、、For conversion coefficient,It is selected difference point set；
Step S2, obtained according to above-mentioned formula
WillRegard free variable as, then according to formula
Each conversion coefficient of iterated function series is determined（、、、、）, counted according to the iterated function series of each group
The iterated function series of system in meaning.
Fig. 4 is the schematic flow sheet of outside forecast of the present invention.As shown in figure 4, in step 4, one time point of the extrapolation,
Corresponding initial value is set to zero, sets a step-length to convert respective value, re-starts iteration, draws curve, calculating difference result
With the mean error of historical data, the minimum corresponding extrapolated value of error is exactly predicted value, is comprised the following steps：
Step 41, the time predicted as needed determine the abscissa of future position, ordinate, by future positionOriginal error value point set is added as new difference point, new difference point set is produced；
Step 42, again according to formula iterated function series are calculated to new difference point set, further according to a point shape difference iteration theorem
Iteration 20 times, obtains the point set that the 20th iteration is produced；
Step 43, from the point concentration of generation abscissa is selected closest to initial data'sIt is individual, meter
Calculate the interpolation result of these points and the mean error of historical data；
Step 44, selection step-length, gradually change the ordinate of future position from 0 to 1, then it is iterated again and asks flat
Equal error, repeat step is found corresponding when making mean error minimum, then restore and obtain final predicted value.
Claims (6)
1. a kind of financial time series short term prediction method being combined based on point shape with chaology, for periodically and from phase
Studied like unconspicuous time series, it is characterised in that the short term prediction method comprises the following steps：
Step 1, Hurst indexes and statistic using R/S analytic approach calculating time series, the cycle of time series is determined, is selected
Cycle unconspicuous time series is taken as original time series；
Step 2, using chaology phase space reconfiguration is carried out to original time series, it is empty that One-dimension Time Series are converted into higher-dimension
Between multidimensional vector, in higher dimensional space using similitude choose data sample, according to the sequencing of sampling time point determine
Simultaneously sample data group is normalized for difference point；
Step 3, the vertical scaling fac tor for determining using Hurst indexes every group of sample data, determined according to vertical scaling fac tor imitative
Penetrate conversionConversion coefficient（、、、）, iterated function series are determined, final iteration is determined according to the weight of every group of sample
Function system；
Step 4, one time point of extrapolation, corresponding initial value are set to zero, set a step-length to convert respective value, re-start repeatedly
In generation, the mean error of curve, calculating difference result and historical data is drawn, the minimum corresponding extrapolated value of error is exactly predicted value.
2. the financial time series short term prediction method according to claim 1 being combined based on point shape with chaology,
Characterized in that, in step 1, the Hurst indexes and statistic of time series are calculated using R/S analytic approach, including following step
Suddenly：
Step 11, for time seriesAccording to formula
Obtain Hurst indexes, wherein variance, extreme difference, add up
Deviation,ForThe average of individual interval sample；
Step 12, according to formula
ObtainStatistic, drawsWithCurve map, find catastrophe point correspondingValue be cycle number of days.
3. the financial time series short term prediction method according to claim 1 being combined based on point shape with chaology,
Characterized in that, in step 2, it is described that sample data group, which comprises the following steps, to be determined to time series progress phase space reconfiguration：
Step 21, former length of time series are, with auto-relativity function method andWhen algorithm calculates the delay of time series
BetweenAnd Embedded dimensions；According to Phase-space Reconstruction, the attractor of dynamical system is reconstituted in one and does not change opening up for it
That flutters feature has in the new phase space of delay coordinate, according to embedding theorems, by introducing time delay, by time seriesIt is reconstructed intoTie up phase space（Corresponding point set is）, whenWhen determining,WithRelation
For
Then obtained by phase space reconfigurationOrganizing length isReproducing sequence；
Step 22, length is obtained by step 21 it isTime series after reconstruct,It is the minimum element that vector set is included after reconstructing
Number, therefore willAs the radix of construction sample data length, the sample data length of selection isIntegral multiple, during delay
BetweenIt is constant；
Step 23, according to the sequencing of sampling time point difference point determined to every group of sample data, every group of sample data is to adopt
Sample time-series is as abscissa, and the size of each sample point data is as ordinate, and these points constitute difference point together；
Step 24, according to formula
Sample data group is normalized, value is reducedIt is the predicted value progress overall situation for convenience to the later stage
Search；WhereinWithThe respectively abscissa and ordinate of difference point,WithThe respectively maximum of abscissa and most
Small value,WithThe respectively maximum and minimum value of sample data,For sample data length.
4. the financial time series short term prediction method according to claim 1 being combined based on point shape with chaology,
Characterized in that, in step 3, the vertical scaling fac tor and iterated function series of every group of sample data are determined using Hurst indexes, wrap
Include following steps：
Step 31, every group of sample data all have self-similarity, therefore utilizeAnalytic approach every group of sample data of calculating
Hurst indexes；
Step 32, according to fractal theory, it is assumed that it is eachIt is equal in magnitude, then directly using Hurst indexes according to formula
Determine vertical scaling fac tor, whereinFor Hurst indexes；
Step 33, iteration factor all is obtained using Hurst indexes to every group of sample dataAfterwards, pass throughAffine transformation can be tried to achieve
Conversion coefficient（、、、）, so that it is determined that the iterated function series of point shape difference；
Step 34, the iterated function series made according to the iterated function series exploitation right reconstruct of every group of sample in statistical significance, wherein because
Sample is chosen Deng the time, the weight of each group sample data is the same, that is, seeks the average value of each conversion coefficient of all iterated function series,
What is obtained is the iterated function series of system, for predicting.
5. the financial time series short term prediction method according to claim 1 being combined based on point shape with chaology,
Characterized in that, in step 3, the conversion coefficient that affine transformation is determined according to vertical scaling fac tor described in step 33（、、、）, so that it is determined that iterated function series, specifically include following steps：
Step S1, the principle of point shape difference are to construct corresponding IFS to one group of given interpolation point（Iterated function series）, make IFS
Attractor to pass through the functional arrangement of this group of interpolation point；The IFS codes of shape difference are divided to pass through affine transformationTry to achieve, formula is as follows：
It is spaceCompression mapping,、、、、For conversion coefficient,It is selected difference point set；
Step S2, obtained according to above-mentioned formula
WillRegard free variable as, then according to formula
The conversion coefficient of iterated function series is determined（、、、、）, statistical significance is obtained according to the iterated function series of each group
The iterated function series of upper system.
6. the financial time series short term prediction method according to claim 1 being combined based on point shape with chaology,
Characterized in that, in step 4, one time point of the extrapolation, corresponding initial value is set to zero, a step-length is set to become respective value
Change, re-start iteration, draw the mean error of curve, calculating difference result and historical data, the minimum corresponding extrapolation of error
Value is exactly predicted value, is comprised the following steps：
Step 41, the time predicted as needed determine the abscissa of future position, ordinate, by future positionOriginal error value point set is added as new difference point, new difference point set is produced；
Step 42, again according to formula iterated function series are calculated to new difference point set, further according to a point shape difference iteration theorem
Iteration 20 times, obtains the point set that the 20th iteration is produced；
Step 43, from the point concentration of generation abscissa is selected closest to initial data'sIt is individual, calculate
The interpolation result of these points and the mean error of historical data；
Step 44, selection step-length, gradually change the ordinate of future position from 0 to 1, then it is iterated again and asks flat
Equal error, repeat step is found corresponding when making mean error minimum, then restore and obtain final predicted value.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109344995A (en) * | 2018-08-29 | 2019-02-15 | 广东工业大学 | A kind of chaos time sequence multistep forecasting method based on density peaks cluster |
| CN110688365A (en) * | 2019-09-18 | 2020-01-14 | 华泰证券股份有限公司 | Method and device for synthesizing financial time series and storage medium |
| CN110954779A (en) * | 2019-11-29 | 2020-04-03 | 国网上海市电力公司 | Voltage sag source feature identification method based on S transformation and multidimensional fractal |
| CN113837388B (en) * | 2021-09-14 | 2023-12-12 | 广州大学 | Time series complexity measuring method, system, computer device and storage medium |
-
2016
- 2016-12-27 CN CN201611227288.1A patent/CN107067096A/en active Pending
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109344995A (en) * | 2018-08-29 | 2019-02-15 | 广东工业大学 | A kind of chaos time sequence multistep forecasting method based on density peaks cluster |
| CN109344995B (en) * | 2018-08-29 | 2021-06-18 | 广东工业大学 | Multi-step prediction method of chaotic time sequence based on density peak clustering |
| CN110688365A (en) * | 2019-09-18 | 2020-01-14 | 华泰证券股份有限公司 | Method and device for synthesizing financial time series and storage medium |
| CN110954779A (en) * | 2019-11-29 | 2020-04-03 | 国网上海市电力公司 | Voltage sag source feature identification method based on S transformation and multidimensional fractal |
| CN113837388B (en) * | 2021-09-14 | 2023-12-12 | 广州大学 | Time series complexity measuring method, system, computer device and storage medium |
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Application publication date: 20170818 |