CN106909799A - A kind of Application of Data Mining theoretical based on new random fractal - Google Patents

Abstract

The invention discloses a kind of Application of Data Mining theoretical based on new random fractal, by addition polymerization time series being amplifying observation yardstick changes point shape slope index parameter and wave amplitude index parameters of NLARI, identification Long Memory Properties, self-similarity, have concurrently Long Memory Properties and self-similarity difference point shape level minimized aggregation degree time series generating process and dynamic characteristic.The present invention can simultaneously recognition time sequence varying level fractal generation mechanism and dynamic characteristic.The self similarity sequence of present invention identification minimized aggregation yardstick provides scientific and standard for dynamic data sampling, compression, feature extraction；Identification data generting machanism of the invention, annotate translate point formed because, adjust memory span, using or avoid the fractal structure from producing various uses；Although the approach that the present invention sets up new fractal theory is extremely complex, the fractal method that the theory is provided is abnormal simple.

Description

A kind of Application of Data Mining theoretical based on new random fractal

Technical field

It is dynamic in big data the invention belongs to nonlinear kinetics, fractal behavior and time series modeling and analysis theories State data mining applied technical field, more particularly to a kind of Application of Data Mining theoretical based on new random fractal.

Background technology

The fractal behavior of recognition time sequence is most one of problem of challenge in Dynamic Data Mining.It is typical random Fractal behavior includes statistical self-similarity, power law and Long Memory Properties (i.e. time-length interrelation), and these behaviors occur certainly extensively So, the complication system such as medical science, ecology, water conservancy, engineering, network, economy and finance.It was found that self similarity sequence, growth or shortening length The methods such as degree of correlation bring various uses.For example, self similarity is in many fields such as network traffics, stock market's dynamic, physiological signals There is important application.Stock yield Long Memory Properties mean that volatility has a kind of persistence or long-rang dependence, to assets The effect of pricing model has potential material impact, thus growth dividend yield Long Memory Properties have major economic value.

Fractal date is excavated according to the meaning of digging utilization data set fractal dimension to data set, is existed in fractal dimension at present Characteristic attribute selection, cluster, correlation rule, classification and prediction etc. be on direction, network data excavation, finance data analysis, There is certain application in the fields such as reason information excavating.Fractal date faces lot of challenges according to digging technology, such as how to judge data Collection with fractal characteristic, how quickly to calculate data set fractal dimension, how on computers simulated implementation, how to explain number Practical significance according to collection fractal dimension etc..These problems are mainly due to fractal dimension itself, including 1) fractal dimension as general Suitable complexity scaling law is introduced into, but it is not a qualified demarcation rule, and not can determine that a Fractal Pattern.Point Shape dimension has many definition modes, such as Hausdorff dimension, information dimension, correlation dimension, similar dimension, capacity dimension, multiple Divide shape spectrum, filling dimension, Divider dimension, Lyapunov exponent, group's dimension, quality dimension, differential dimension, Brig dimension Number, fuzzy dimension, Generalized Dimension etc..The fractal dimension estimate of same target can because computational methods are different different, phase Same fractal dimension can correspond to different Fractal Patterns.2) estimation that is difficult to of fractal dimension leads to not quickly calculate data set Fractal dimension.Obtained by statistics or approximate method mostly, for example, calculate the most frequently used Hausdorff dimension, typically led to Box-counting dimension is crossed to estimate its upper bound and estimate its lower bound by local dimension.3) classical point shape process Such as discrete fractal Brown motion, it can not iterative make it difficult to realize simulation on computers.4) fractal dimension with point Between shape behavior, either parse relation or intuitive relationship is all unclear, hinder fractal method and participate in Accurate Model, as right The fine description of Fractal Phenomenon as petroleum reservoir crack is also still the worldwide difficulty that petroleum geology circle fails to be fully solved Topic.The time series models that fractal dimension is incorporated into classics attempt to realize Accurate Model, but bring new problem again, for example, pass through The ARFIMA of allusion quotation points of shape process model building needs to calculate very big sample inverse matrix.5) fractal dimension is no clear and definite as scaling law Physical significance, so the origin cause of formation on fractal behavior and its correlated phenomena cannot be provided.Why emerging cannot for example explain Market generally existing Long Memory Properties, and phenomenon of the international meat market in the absence of significant Long Memory Properties as the U.S..

The generting machanism of recognition time sequence is the highest objective of Dynamic Data Mining.It is expected to take off using data genaration mechanism Show the formation of behavioral characteristics and controlling mechanism and following data are inferred and predicted.But existing dynamic data The generating process of data set is not provided with fractal date according to method for digging.Many models such as Time Series AR MA and ARCH models, skill Art such as obscurity model building, neutral net, genetic algorithm, mathematical optimization and self-organizing method, be used to extract useful letter in dynamic data Breath, generally obtains a result, and is unable to explanation results, less provides the generating process of data set.On the other hand, behavioral characteristics and point Shape behavior is closely related with observation yardstick, and too small observation yardstick can influence intactly to reflect data genaration mechanism, excessive sight Examining yardstick can be because the time span of sample be excessive so that cannot be collected into reflection systematic sample number enough, or cause money Source wastes and because timeliness loses data value.Therefore the identification behavioral characteristics of reflection complication system and fractal behavior enough The generating process of minimum observation yardstick will produce substantial worth.Such as Hydrologic scaling is just put into 21 century hydrology basis The advanced subject of research.From the point of view of current academic research or patent, there is no and started with derived mould from system based on physics principle Type is used for the methods and techniques of non-linear kinetic characteristic and random fractal behavior.In recent years, existed by newton second law of motion One class is restrained oneself recover the application of regulating system and then by discretization at random, is derived a quasi-nonlinear autoregression and is integrated (NLARI) Process.This kind of system for recovering regulation with self-discipline is also referred to as Stochastic Elasticity system universally present in nature, ecology, medical science, work In many real systems such as journey, economy and society.NLARI processes can be by specific as follows：

Allow Y_t=X_t-μ_t, equation (1) can be rewritten as

There

Whereinω represents the expected value of external disturbance, and σ is represented The standard deviation of external disturbance, ε_tIt is the Gaussian white noise of standard variance σ, α is resistance coefficient, and β is to recover force coefficient, κ₁It is in resistance Time lag in power, κ₂It is the time lag in restoring force.There is ε when σ=0 or to all time t_t=0, equation (2) is one Individual deterministic system, with respect to the stability and bifurcation that restoring force coefficient gamma controls the system：As κ₂=1, it be one gradually Zero fixed point of nearly stabilization is in 0 ＜ γ ＜ 1, an asymptotically stable two cycles ring One unstable Two cycles ring Notice that stability here is locally rather than Existence of Global Stable.When γ=0, NLARI mistakes Journey deteriorates to a linear autoregression and integrates ARI (2,1) process.The present invention will be based on NLARI models dynamic characteristic and Statistical property develops a kind of new fractal theory, so as to derive difference point shape level and its control and the life of recognition time sequence Into the method for mechanism.

In sum, also include novel data Mining stream, fractal date according to digging in addition to traditional technology in the prior art Pick, on-line analysis mining, empirical mode decomposition, contact discovery, trend analysis, variance analysis etc., are calculated by statistics and mathematics The method such as method such as obscurity model building, neutral net, genetic algorithm, optimization, self-organizing method, in attribute reduction, classification, cluster, association Rule, sequence pattern, predict, the point analysis that peels off, spatial data analysis etc. have certain application on direction.Many aspects are also stopped Stay in the improvement to traditional static method, face problems.Dynamic Data Mining technology only provides result, it is impossible to explain knot Really, the generating process of data set is not provided.Fractal date is faced danger or disaster in estimation fractal dimension, modeling point shape process, in meter according to excavation surface Simulation is realized on calculation machine, it is impossible to disclose the difficulty point formed because of, controlling mechanism and practical significance.And between most fractal dimensions Relation, the relation of fractal dimension and fractal behavior, the relation of fractal dimension and dynamic mode it is all indefinite.These problems influence Fractal date is according to excavation.In order to thoroughly solve fractal date according to Mining Problems, the present invention will be new based on one of the foundation of NLARI models Random fractal it is theoretical；Prove the interior raw structural property of non-linear kinetic characteristic and fractal behavior respectively as same complication system The response property disturbed with system external portion；Point shape row of the self-similarity power law of identification data collection simultaneously and Long Memory Properties is provided It is, stabilization fixed point stabilization and the method for the non-linear kinetic characteristic and their control parameter of unstable periodic ring；There is provided The method that the behavioral characteristics of reflection complication system and the minimum of fractal behavior observe yardstick and generating process enough.

The content of the invention

It is an object of the invention to provide a kind of Application of Data Mining theoretical based on new random fractal, it is intended to solve Certainly too small and excessive observation yardstick not only influences completely to reflect data genaration mechanism that can also bring sample number few, resource is unrestrained Take, data lose value because of timeliness；In conventional time series model extraction dynamic data, it is impossible to explanation results, it is impossible to which number is provided According to the problem of generating process.

The present invention is achieved in that a kind of Application of Data Mining theoretical based on new random fractal, the base In the theoretical Application of Data Mining of new random fractal being amplifying observation yardstick by addition polymerization time series changes NLARI Point shape slope index parameter and wave amplitude index parameters, identification Long Memory Properties, self-similarity, have Long Memory Properties and self-similarity concurrently Difference point shape level minimized aggregation degree time series generating process and dynamic characteristic.

Further, the time sequence of different point shape levels and dynamic characteristic is recognized by the concentration class of control time sequence Column-generation process；Specifically include：

Step one, data absolute value downsizing treatment, is designated as X=(X_t：T=1 ..., T)；

Step 2, least square method regression straight line is calculated using XUseAnd

ΔY_t=Y_t-Y_t-1, it is rightMake Least Square Method and obtain parameter ValuationNote Y=(Y '₁₀..., Y '_1t..., Y '_1T-1) ',s¹¹And s²²Represent respectively MatrixThe first row first row element and the element of the second row secondary series；

Step 3, calculates θ₁Confidential intervalWhereinIt is that t is distributed in confidence levelIt is critical It is worth and returns the statistic without hypothesis γ=0If θ₁Confidential interval be comprised in interval In (- 1,1) and if returning and being rejected without hypothesis γ=0, receives opposition hypothesis γ ＞ 0, then evidence supports data from NLARI Process, performs step 4, otherwise to j=j+1 (initial value j=1), calculates j reunion collection time serieses X_j, it is designated as X=X_j, perform step Rapid two；If to that can not continue to be aggregated, output result X is that a non-NLARI process or one have γ to circulation time sequence =0 degeneration ARI (2,1) process, exits analysis；

Step 4, remembers j₁=j, allowsFractal Identification is performed, j is obtained₂Meet again and collect sequenceDivide shape It is (δ to spend_{1, k}, δ_{2, k}), it is designated asOr without a point shape

Step 5 is rightWithStep 2 is performed respectively obtains θ₁Confidential intervalθ₂Confidence It is intervalAnd the confidential interval of γWherein If θ₁, θ₂, the confidential interval of γ is comprised in interval (- 1,1), (0,4), (0,1), then to support that X carrys out self-stabilization motionless for evidence NLARI processes on point domain；If θ₁, θ₂, the confidential interval of γ is comprised in intervalIt is interior, then demonstrate,prove According to supporting X from the NLARI processes in stable period annulus；If θ₁, θ₂, the confidential interval of γ is comprised in intervalInterior, then evidence supports X from the NLARI processes in unstable cycle annulus；Otherwise X comes from and faces NLARI processes on dividing value；Fractal sequences of the output with these behavioral characteristicsWith without fractal sequences Including model parameter as conclusion.

Further, the minimized aggregation degree Time Series Method of different long memory levels is recognized, including：

1) one is selected on the occasion of descending series δ_{1, k}If, initial value k=j=1 and X₁=X；

2) calculate jth and meet again and collect time series X_j；

3) X is calculated_jSample autocorrelation coefficient ρ_nAs n=1 ..., N and LM (X_j)；If LM (X_j) ＜ δ_{1, k}, then perform Step 4), step 2 otherwise is performed to j=j+1), when being recycled to time series and can not continue to be aggregated, output result is minimum poly- The Long Memory Properties time series X of intensity_j-1(δ_{1, k-1}) and model parameter X there_j(δ_1,0) mean former time seriesWithout length Memorability；

If 4) k ＜ K, j=1 and k=k+1 is made, performs step 2), otherwise export the long memory of conclusion minimized aggregation degree Property time series X_j(δ_{1, K}) and model parameter.

Further, the minimized aggregation degree Time Series Method of different self similarity levels is recognized, including：

A, selected one on the occasion of descending series δ_{2, k}If, initial value k=j=1 and X₁=X；

B, calculating jth are met again and collect time series X_j；

C, calculating X_jSample likelihood ratio r_{H (i, im)}And SS_hm(X_j) as m=1 ..., M, h=1 ..., H and i=1 ..., n； If SS_hm(X_j) ＜ δ_{2, k}Set up as given m=1 ..., M and h=1 ..., H then performs step D, otherwise to j=j+1 Step B is performed, when being recycled to time series and can not continue to be aggregated, the self-similarity time sequence of output result minimized aggregation degree Row X_j-1(δ_{2, k-1}) and model parameter X there_j(δ_2,0) mean former time seriesThere is no self-similarity；

If D, k ＜ K, j=1 and k=k+1 is made, perform step B, otherwise export the self similarity of conclusion minimized aggregation degree Property time series X_j(δ_{2, K}) and model parameter.

Further, the different points of minimized aggregation degree Time Series Methods of shape level are recognized, including：

A, selected two on the occasion of descending series δ_{1, k}And δ_{2, k}If, initial value k=j=1 and X₁=X；

B, calculating jth are met again and collect time series X_j；

C, calculating X_jSample autocorrelation coefficient ρ_nAs n=1 ..., N and LM (X_j).If LM (X_j) ＜ δ_{1, k}, then perform Step d, otherwise to j=j+1 perform step b, when time series can not continue to be aggregated, output result minimized aggregation degree point Shape time series X_j-1(δ_{1, k-1}, δ_{2, k-1}) and model parameter, (δ_1,0, δ_2,0) it is former sequenceWithout fractal structure；

D, calculating X_jSample likelihood ratio r_{H (i, im)}As i=1 ..., n and SS_hm(X_j) as m=1 ..., M and h= 1 ..., H；If SS_hm(X_j) ＜ δ_{2, k}As h=1 ..., H and m=1 ..., M set up, then step e is performed, otherwise to j=j+1 Perform step b；

If e, k ＜ K, j=1 and k=k+1 is made, perform step b, otherwise export when dividing shape of conclusion minimized aggregation degree Between sequence X_j(δ_{1, K}, δ_{2, K}) and model parameter；By limiting δ_{1, k}And δ_{2, k}The value different long memories of identification and self similarity level when Between sequence generation process.

Further, new random fractal is theoretical, including：

(1) as the slope index η of fractal parameter₁=ω/α and wave amplitude index η₂=σ/β describes random bullet based on a class The NLARI processes of sexual system：

Whereinε_tFor white Noise, g (x) is the recovery force function for meeting condition g (- x)=- g (x) and xg (x) ＜ 0, and ω is the expected value of external disturbance, σ It is the standard deviation of external disturbance, α is resistance coefficient, and β is to recover force coefficient, κ₁It is the time lag on resistance, κ₂It is to recover Time lag in power；

(2) j meets again and collects time seriesWhereinFully add Big concentration class j will also result in one it is relatively large | η₁| and a relatively small η₂So as to produce long memory and self similarity behavior；

(3) auto-covariance r_hLikelihood ratio r_{H (i, im)}=r_h(X_i)/r_h(X_im), if time series is self similarity, It can tend to a horizontal linear as given h=1 ..., H, m=1 ..., M with the increase of i；

(4) the horizontal index of long memoryWith the horizontal index of self similarity

Further, in step 4, fractal method is recognized, including：

One) calculate j and meet again and collect time series X_j, its auto-correlation coefficient ρ_nAs n=1 ..., N and likelihood ratio r_{H (i, im)}Make It is h=1 ..., H, m=1 ..., M and i=1 ..., n；

Two) concentration class j is increased until meeting long memory level conditions LM (X_j) ＜ δ_{1, k}With self similarity level conditions SS_hm (X_j) ＜ δ_{2, k}For all h=1 ..., H and m=1 ..., wherein M, δ_{1, k}And δ_{2, k}It it is two on the occasion of decreasing sequence of numbers；

Three) by changing δ_{1, k}And δ_{2, k}Value control long memory level and self similarity level.

Further, identification dynamic characteristic method includes：

θ based on t distributions₁, θ₂, the confidential interval calibrating of γ and return the statistic without hypothesis γ=0 opposition hypothesis γ ＞ 0Calibrating, if

Evidence supports that data have the stable fixed point structure of NLARI, if

Evidence supports that data have ring stable period of NLARIStructure, if

Evidence supports that data have the unstable periodic ring of NLARIStructure.

Further, calibration method, including：Use X=X_jCalculate least square method regression straight linePass throughTo Δ Y_t=θ₁ΔY_t-1+θ₂g(Y_t-1)+ε_tMake Least Square Method Δ Y there_t=Y_t-Y_t-1, obtain Parameter estimation

NLAR1 points of shape process disclosed by the invention can show very similar length with ARFIMA points of shape process of classics Memorability (Data Comparison refers to the Fig. 1 in specific embodiment).But ARFIMA points of shape process can not disclose fractal dimension With the physical significance and the origin cause of formation and governing factor of display Long Memory Properties of Long Memory Properties.In contrast to this, The present invention gives The controlling mechanism of the fractal behavior of NLARI processes and clear and definite physical significance：The equal line slope index η of fluctuation₁=ω/α controls The long-range degree of correlation of system, long range dependent be system be subjected to external disturbance horizontally relative to internal drag coefficient intensity compared with A kind of response characteristic of system when big；Wave amplitude index η₂=σ/β determines whether system has self-similarity, and self-similarity is to be System is subjected to a kind of response characteristic of system when external disturbance changes smaller relative to inside recovery force coefficient；The equal line slope of fluctuation Its exterior is depended on to internal relative strength of effect with wave amplitude, but increasing observation yardstick can make the absolute value of Slope metric Be incremented by makes wave amplitude index successively decrease simultaneously, so as to cause Long Memory Properties and self-similarity respectively.In other words, as long as system is present Self-discipline recovers adjusting force, fractal behavior necessarily occurs on sufficiently large observation yardstick.Based on these properties, the present invention is provided simultaneously Recognize the fractal behavior and generting machanism and dynamic characteristic of varying level；The minimum observation yardstick of identification be assemble yardstick from phase Like sequence, so that for dynamic data sampling, compression, feature extraction provide scientific and standard；Identification data of the invention generates machine Make, annotate translate point formed because, adjust memory span, using or avoid the fractal structure from producing various uses；Although the present invention sets up The approach of new fractal theory is extremely complex, but the fractal method that the theory is provided is abnormal simple.

Brief description of the drawings

Fig. 1 is that display NLARI processes provided in an embodiment of the present invention can show and be very similar to classical ARFIMA point One instance graph of shape process Long Memory Properties.

Fig. 2 is the fractal parameter i.e. slope index η of NLARI processes provided in an embodiment of the present invention₁With wave amplitude index η₂With length Memory sexual intercourse.

Fig. 3 is the wave amplitude index η of NLARI processes provided in an embodiment of the present invention₂With self-similarity relation.

Fig. 4 is provided in an embodiment of the present invention to increase slope index by addition polymerization time series | η₁| and reduction wave amplitude refers to Number η₂Fractal Identification schematic diagram.

Fig. 5 is the generating process of recognition time sequence provided in an embodiment of the present invention and the schematic flow sheet of behavioral characteristics.

Fig. 6 is the minimized aggregation degree time series generating process of the different long memory levels of identification provided in an embodiment of the present invention Schematic flow sheet.

Fig. 7 is the minimized aggregation degree time series generating process of the different self similarity levels of identification provided in an embodiment of the present invention Schematic flow sheet.

Fig. 8 is the minimized aggregation degree time series generating process of the different point shape levels of identification provided in an embodiment of the present invention Schematic flow sheet.

Fig. 9 is a reality of fractal parameter provided in an embodiment of the present invention and point shape horizontal relationship of heart time sequence Example.

Figure 10 is the minimized aggregation degree time series life of the different point shape levels of present invention identification provided in an embodiment of the present invention Into a demonstration example of process.

Figure 11 is that the Application of Data Mining principle theoretical based on new random fractal provided in an embodiment of the present invention is shown It is intended to.

Specific embodiment

In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to embodiments, to the present invention It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to Limit the present invention.

The Application of Data Mining theoretical based on new random fractal provided in an embodiment of the present invention, it is described based on new The theoretical Application of Data Mining of random fractal is amplifying observation yardstick by addition polymerization time series changes point shape of NLARI Slope index parameter and wave amplitude index parameters, recognize Long Memory Properties, self-similarity, have the difference of Long Memory Properties and self-similarity concurrently Divide the time series generating process and dynamic characteristic of the minimized aggregation degree of shape level.

Below in conjunction with the accompanying drawings and embodiment the present invention is described in detail.

New random fractal of the present invention is theoretical, including：

(1) as the slope index η of fractal parameter₁=ω/α and wave amplitude index η₂=σ/β describes random bullet based on a class The NLARI processes of sexual system：

Whereinε_tFor white Noise, g (x) is the recovery force function for meeting condition g (- x)=- g (x) and xg (x) ＜ 0, and ω is the expected value of external disturbance, σ It is the standard deviation of external disturbance, α is resistance coefficient, and β is to recover force coefficient, κ₁It is the time lag on resistance, κ₂It is to recover Time lag in power；

(2) j meets again and collects time seriesWhereinFully add Big concentration class j will also result in one it is relatively large | η₁| and a relatively small η₂So as to produce long memory and self similarity behavior；

(3) auto-covariance r_hLikelihood ratio r_{H (i, im)}=r_h(X_i)/r_h(X_im), if time series is self similarity, It can tend to a horizontal linear as given h=1 ..., H, m=1 ... with the increase of i, M,

(4) the horizontal index of long memoryWith the horizontal index of self similarity

Identification fractal method of the present invention, including：

(1) calculate j and meet again and collect time series X_j, its auto-correlation coefficient ρ_nAs n=1 ..., N and likelihood ratio r_{H (i, im)} As h=1 ..., H, m=1 ..., M and i=1 ..., n；

(2) concentration class j is increased until meeting long memory level conditions LM (X_j) ＜ δ_{1, k}With self similarity level conditions SS_hm (X_j) ＜ δ_{2, k}For all h=1 ..., H and m=1 ..., wherein M, δ_{1, k}And δ_{2, k}It it is two on the occasion of decreasing sequence of numbers；

(3) by changing δ_{1, k}And δ_{2, k}Value control long memory level and self similarity level.

Described identification dynamic characteristic method, including：θ based on t distributions₁, θ₂, the confidential interval calibrating of γ and return nothing The statistic of hypothesis γ=0 opposition hypothesis γ ＞ 0Calibrating, if there

Evidence supports that data have the stable fixed point structure of NLARI, if

Evidence supports that data have ring stable period of NLARIStructure, if

Evidence supports that data have the unstable periodic ring of NLARIStructure.

Described calibration method, it is characterised in that use X=X_iCalculate least square method regression straight lineIt is logical CrossTo Δ Y_t=θ₁ΔY_t-1+θ₂g(Y_t-1)+ε_tMake Least Square Method Δ Y there_t=Y_t-Y_t-1, obtain Parameter estimation

Application principle of the invention is further described below in conjunction with the accompanying drawings.

The present invention is intended to provide a kind of theoretical Application of Data Mining of new random fractal, it be based on such as drag and Property：

One, describes the General N LARI processes of a class Stochastic Elasticity system：As shown in Figure 1；

Equation (3) can be rewritten as

Y there_t=X_t-μ_t=X₀- (ω/α) t and

Wherein ε_tIt is white noise, g (x) meets condition g (- x)=- g (x) and xg (x) ＜ 0 to recover force function, and other are each Item, parameter and physical meaning are identical with equation (1).NLARI processes, the parameter field of equation (4) is

As g (x)=- x exp (- x²) and κ₂=1, the parameter field of the NLARI processes on stabilization fixed point domain is

Stably the parameter field of the NLARI processes in two cycles annulus is

The parameter field of the NLARI processes in unstable two cycles annulus is

Above-mentioned property is used for the generting machanism of identification data and dynamic characteristic.Present inventor is shown by simulated experiment Above-mentioned property is simultaneously not limited to the concrete structure of restoring force function g (x), i.e., the recovery force function of other form also has similar Dynamic characteristic.It is first noted that NLARI processes have a fractal structure, such as it can one classics of simulation very well The Long Memory Properties that show of ARFIMA points of shape process (as shown in figure 1, g (x)=- x/ (1+x there²))。

Two, fractal parameters：

Property 1 imports slope index in NLARI processes (3)With wave amplitude indexAs fractal parameter.

It is able to demonstrate that μ_t=E (X_t|X₀, X_-1)=X₀+ (ω/α) t still set up, so η₁Represent the oblique of fluctuation average line Rate.Sample standard deviation sd and η₁Perfect positive correlation (as shown in the 2c in Fig. 2, correlation coefficient r=1 is used as g (- x)=- x), with ripple Width index η₂Perfect positive correlation (works as η₁=0, as shown in the 2f in Fig. 2, r=1 is used as g (x)=- xexp (- x²)) or strong positive (work as η in pass₁≠ 0, as shown in the 2i in Fig. 2, r=0.945 is used as g (x)=- x (1+x⁴)^-1).Because sd has weighed sample fluctuation Size, so η₂It is referred to as wave amplitude index.

Three, Long Memory Properties：

If the sample autocorrelation coefficient of property 2As n= 1 ..., N slowly decline with lag order n increases with less than exponential decay rate, show X_tThere are Long Memory Properties.

The Long Memory Properties of the NLARI processes (3) of property 3 are attributed to an absolute value for relatively large slope index | η₁|, or The relatively large wave amplitude index η of person one₂Work as η₁=0, or one relatively large | η₁| it is relatively small with one | η₂|。

Because overall auto-correlation coefficient is unknown, it is considered to the average value of a large amount of analog sample auto-correlation coefficients for repeating (still use ρ_nTo represent) as approximate, such simulation ρ of overall auto-covariance_nBe used to find the control of Long Memory Properties Mechanism.It is able to verify that (i) is with slope index when relative restoring force coefficient gamma is increased | η₁| increase, ρ_nWith lag order n Increase its decline degree slow down (as shown in the 2a in Fig. 2), | η₁| and ρ₇₀(the last auto-correlation coefficient, its absolute value Reflect degree of correlation) perfect positive correlation (as shown in the 2b in Fig. 2), it means that relatively large | η₁| Long Memory Properties will be caused Occur as η₂≠0；(ii) η is worked as₁When=0, with slope index η₂Increase, ρ_nWith its decline degree of the increase of lag order n Slow down (just as shown in the 2d in Fig. 2), | η₁| and ρ₇₀Perfect positive correlation (as shown in the 2e in Fig. 2), it is meant that relatively large η₂ Long Memory Properties will be caused to occur；(iii) however work as η₁When ≠ 0, with slope index η₂Increase, ρ_nWith the increase of lag order n It declines degree and increases (just as shown in the 2g in Fig. 2), η₂And ρ₇₀Negatively correlated (as shown in the 2h in Fig. 2), it is meant that work as η₁≠ 0, increase η₂Memory span can be reduced.When relative restoring force coefficient gamma is fixed, with | η₁| increase and η₂Reduction, ρ_n Slow down with the increase of lag order n its decline degree (as shown in the 2j in Fig. 2, γ=0.7) there.This explanation is relative Big | η₁| or a relatively large η₂Work as η₁=0, or one relatively large | η₁| with a relatively small η₂Can cause The Long Memory Properties of time series.The discovery explains emerging market has longer memory because its Endogenous system than mature market More weak, i.e. α and β are smaller, and they cause | η₁| and η₂Value it is bigger than mature market.Crossing small sample can block Long Memory Properties (as shown in the 2k in Fig. 2).

Four, self-similarities：

Because the statistical self-similarity on Distribution Significance is with the presence or absence of still absence of proof, so the present invention considers second order from phase Like property, it is related to the concentration class (or observation yardstick) of time series.Such as monthly price index (refers to the flat fare in units of the moon Lattice change) and the concentration class of annual price index (referring to the variation of the average price in units of year) be respectively Month And Year.

Property 4 allows X=(X_h:H=1 ..., T) represent former time series andRepresent j weights Aggregation sequenceIf there is the self tuning side that a constant δ causes lag order h for arbitrary integer m Difference r_hMeet condition r_h(X_m)=m^δr_h(X), then claiming X has second order self-similarity.

Here the component of δ allows for negative, does not also require that X must be stable.Due to overall auto-covariance be it is unknown, (r is still used here by a large amount of the average of analog sample auto-covariance for repeating_hRepresent) as the approximate of overall auto-covariance.Make It is self-similarity sequence X, there is r_h(X)=i^-εr_h(X_i) and r_h(X_m)=i^-δr_h(X_im), then

Set up.Claim r_{H (i, im)}It is the likelihood ratio,It is the average m likelihoods ratio.Obviously there is following property：

If the X of property 5 is self similarity sequence, then for m=2 ..., M and the h=1 ... that give, H, the likelihood ratio r_{H (i, im)}A horizontal linear, and average likelihood ratio r are shown with the growth of concentration class i_hmObey power law m^-δ。

The self-similarity of the NLARI processes (3) of property 6 gives the credit to a relatively small wave amplitude index η₂。

Present invention demonstrates working as η₂Value it is small to a certain extent, NLARI processes (3) will show self-similarity.Such as with η₂Value drop to 0.1, Self-similar Ratio Algorithm from 1.3As the increase of i is gradually become by the oblique line that dips down One horizontal linear (3a in Fig. 3), Self-similar Ratio Algorithm r_{5 (i, 2i)}Increase with i is intended to a level by downward-sloping curve Straight line (3b in Fig. 3)；Work as η₂When=0.025, as m=2 ..., 20, Self-similar Ratio Algorithm r_{5 (i, im)}As the increase of i shows one Bar horizontal linear (3c in Fig. 3)；Average likelihood ratio r_5mObey power law m^-3.022(3d in Fig. 3).

The time series that the abundant addition polymerization NLARI processes (3) of property 7 produce, that is, allow concentration class (or observation yardstick) j abundant Greatly, an absolute value for relatively large slope index can simultaneously be obtained | η₁| and a relatively small wave amplitude index η₂, they will Assemble index sequence is caused to produce Long Memory Properties and self-similarity.

With the increase of lag order j, assemble index sequence X_jSlope index absolute value | η₁(X_j) | linearly Increase wave amplitude index η (as shown in the 4a in Fig. 4)₂(X_j) exponentially reduce (as shown in the 4b in Fig. 4).Both will be respectively Cause the appearance of Long Memory Properties and self-similarity, such as concentration class j is increased to 100, auto-correlation coefficient ρ from 5_nTo delayed rank Number n curve from quickly fall to hardly decline, until turn into a horizontal linear, it is shown that Long Memory Properties very high are (such as Shown in 4c in Fig. 4)；Self-similar Ratio Algorithm sd_{(i, 2i)}Curve to i progressively becomes horizontal linear by decline curve, it is shown that very high Self-similarity (as shown in the 4d in Fig. 4).It can be seen that the fractal behavior (Long Memory Properties and self-similarity) of NLARI can be by addition polymerization Its time series and present.

Property 8 claimsIt is the horizontal index of long memory n there₀It is respectively just delayed all the time with N Exponent number.ClaimIt is the horizontal index of self similarity.

Initial lag exponent number n₀Differ and be set to 1, for example n₀=2.Usual 0≤LM (X_j)≤1 and 0≤SS_hm(X_j)≤1.Divide shape Horizontal index is smaller to mean that point shape level is higher.

Application principle of the invention is further described with reference to specific embodiment.

The theoretical excavation dynamic data method of new random fractal provided in an embodiment of the present invention, with g (x)=- x (1+x² )^-1, κ₁=κ₂=1 and ε_tIt is Gaussian white noise i.i.d.N (0, σ²) as a example by, illustrate statistics Fractal Theory Applications disclosed by the invention It is made up of four parts in Application of Data Mining, is realized by following specific steps respectively：

The generating process and behavioral characteristics of Part I recognition time sequence：

The downsizing of step 1 data absolute value is processed, and is designated as X=(X_t:T=1 ..., T).

Step 2 calculates least square method regression straight line using XUseAnd

ΔY_t=Y_t-Y_t-1, it is rightMake Least Square Method and obtain parameter Valuation Note Y=(Y '₁₀..., Y '_1t..., Y '_1T-1) ', Y_1t=(Δ Y_t,-Y_t(1+Y_t ²)^-1), s¹¹And s²²Difference table Show matrixThe first row first row element and the element (in such as Fig. 5 501) of the second row secondary series.

Step 3 calculates θ₁Confidential intervalWhereinIt is that t is distributed in confidence levelIt is critical It is worth and returns the statistic without hypothesis γ=0If θ₁Confidential interval be comprised in interval In (- 1,1) and if returning and being rejected without hypothesis γ=0, receives opposition hypothesis γ ＞ 0, then evidence supports data from NLARI Process, performs step 4 (in such as Fig. 5 502), otherwise to j=j+1 (initial value j=1), calculates j reunion collection time serieses X_j(such as In Fig. 5 503), be designated as X=X_j, perform step 2.If circulation time sequence is to can not continue to be aggregated, " X is output result One non-NLARI process or degeneration ARI (2, the 1) process with γ=0) " exit analysis (as shown in Fig. 5 504).

Step 4 remembers j₁=j, allowsPart II Fractal Identification is performed, j is obtained₂Meet again and collect sequenceShape degree is divided to be (δ_{1, k}, δ_{2, k}), it is designated asOr without a point shape(as shown in Fig. 5 505).

Step 5 pairWithStep 2 is performed respectively obtains θ₁Confidential intervalθ₂Put Letter is intervalAnd the confidential interval of γWherein If θ₁, θ₂, the confidential interval of γ is comprised in interval（- 1,1), (0,4), in (0,1), then to support that X carrys out self-stabilization motionless for evidence NLARI processes on point domain；If θ₁, θ₂, the confidential interval of γ is comprised in interval (- 1,1),It is interior, then demonstrate,prove According to supporting X from the NLARI processes in stable period annulus；If θ₁, θ₂, the confidential interval of γ is comprised in interval (- 1,1), (0 ,+∞),Interior, then evidence supports X from the NLARI processes in unstable cycle annulus；Otherwise X comes from critical value On NLARI processes (as shown in Fig. 5 506).Fractal sequences of the output with these behavioral characteristicsWith Without fractal sequencesIncluding model parameter as conclusion.

Part II recognizes the minimized aggregation degree time series of different long memory levels

Selected one of step 1 is on the occasion of descending series δ_{1, k}If, initial value k=j=1 and X₁=X the 601 of 6 (in such as Fig. 6).

Step 2 calculates jth and meets again and collects time series X_j(as shown in Fig. 6 602).

Step 3 calculates X_jSample autocorrelation coefficient ρ_nAs n=1 ..., N and LM (X_j).If LM (X_j) ＜ δ_{1, k}, then Step 4 (as shown in Fig. 6 603) is performed, step 2 otherwise is performed to j=j+1, quilt can not be continued when time series is recycled to Output result " the Long Memory Properties time series X of minimized aggregation degree during aggregation_j-1(δ_{1, k-1}) and model parameter X there_j(δ_1,0) meaning Taste former time seriesWithout Long Memory Properties " (such as 604 institutes in Fig. 6 not).

If step 4 k ＜ K, j=1 and k=k+1 is made, perform step 2 (as shown in Fig. 6 605), otherwise exported Conclusion " the Long Memory Properties time series X of minimized aggregation degree_j(δ_{1, K}) and model parameter " (in such as Fig. 6 606).

Part III recognizes the minimized aggregation degree time series of different self similarity levels

Selected one of step 1 is on the occasion of descending series δ_{2, k}If, initial value k=j=1 and X₁=X the 701 of 7 (in such as Fig. 7).

Step 2 calculates jth and meets again and collects time series X_j(as shown in Fig. 7 702).

Step 3 calculates X_jSample likelihood ratio r_{H (i, im)}And SS_hm(X_j) as m=1 ..., M, h=1 ..., H and i= 1 ..., n.If SS_hm(X_j) ＜ δ_{2, k}Set up as m=1 ..., M and the h=1 ... for giving, H (as shown in Fig. 7 703), Step 4 is then performed, step 2 otherwise is performed to j=j+1, when being recycled to time series and can not continue to be aggregated, output result " the self-similarity time series X of minimized aggregation degree_j-1(δ_{2, k-1}) and model parameter X there_j(δ_2,0) mean former time seriesThere is no self-similarity " (as shown in Fig. 7 704).

If step 4 k ＜ K, j=1 and k=k+1 is made, perform step 2 (as shown in Fig. 7 705), otherwise exported Conclusion " the self-similarity time series X of minimized aggregation degree_j(δ_{2, K}) and model parameter " (in such as Fig. 7 707).

Different points of minimized aggregation degree time serieses of shape level of Part IV identification

Selected two of step 1 is on the occasion of descending series δ_{1, k}And δ_{2, k}If, initial value k=j=1 and X₁=X is (in Fig. 8 801)。

Step 2 calculates jth and meets again and collects time series X_j(as shown in Fig. 8 802).

Step 3 calculates X_jSample autocorrelation coefficient ρ_nAs n=1 ..., N and LM (X_j).If LM (X_j) ＜ δ_{1, k}, then Step 4 (as shown in Fig. 8 803) is performed, step 2 otherwise is performed to j=j+1, when time series can not continue to be aggregated, Output result " the fractal varying-time dimension X of minimized aggregation degree_j-1(δ_{1, k-1}, δ_{2, k-1}) and model parameter, there (δ_1,0, δ_2,0) meaning Taste former sequenceWithout fractal structure " (as shown in Fig. 8 804).

Step 4 calculates X_jSample likelihood ratio r_{H (i, im)}As i=1 ..., n and SS_hm(X_j) as m=1 ..., M and h= 1 ..., H.If SS_hm(X_j) ＜ δ_{2, k}As h=1 ..., H and m=1 ..., M set up, then step 5 is performed, otherwise to j=j+1 Perform step 2 (as shown in Fig. 8 805).

If step 5 k ＜ K, j=1 and k=k+1 is made, perform step 2 (in such as Fig. 8 806), otherwise export conclusion " the fractal varying-time dimension X of minimized aggregation degree_j(δ_{1, K}, δ_{2, K}) and model parameter " (in such as Fig. 8 807).

By limiting δ_{1, k}And δ_{2, k}Value can recognize the time sequence of different long memories and self similarity level using the above method Column-generation process.

Application principle of the invention is further described with reference to specific embodiment.

Fig. 9 shows that the present invention (is not in the mood for popular name for, 34 years old age, male, 52200 samples for a heart time sequence This value) an example.Because sample falls short of, therefore data are not by addition polymerization, i.e. j₁=1.Original heartbeat data is by logarithm The downsizing treatment of conversion be used to estimate the parameter of NLARI processes, obtain Least Square Method value κ₁=κ₂=1, based on these estimations The θ of value₁, θ₂, the confidential interval of γ is in the theoretical parameter domain (- 1,1) for stablizing fixed point, (0,4), in (0,1).Return as calibrating Statistic without hypothesis γ=0 is γ_n=85, due to P (γ_n＞ 11.9) ＜ 1%, so evidence supports opposition hypothesis γ ＞ 0. These results support the NLARI processes that heart time sequence is come on self-stabilization fixed point domain.The heart time sequence further by 29 time serieses are divided into, each time series has 1800 sample values, each section of Long Memory Properties for showing varying level (as shown in the 9a in Fig. 9), with | η₁| and η₂Increase, sample autocorrelation coefficient ρ_nTo the decline journey of the curve of lag order n Degree is slower, it was confirmed that bigger | η₁| or η₂The memory level (9b in Fig. 9) more grown can be caused.At less m (such as m=2) Place, sd_{(i, mi)}Show the horizontal linear (as shown in the 9c in Fig. 9) of rough approximation, its average sd_mMeet a power function m^1.02(as shown in the 9d in Fig. 9), but r_{H (i, mi)}And η_{2 (i, mi)}And in the sd of larger m_{(i, mi)}Lie in less than level of approximation Straight line, because the heart time sequence has a relatively large η₂Value 0.3140.

Figure 10 shows a demonstration example of present invention identification minimized aggregation degree point shape process.Consider that data result from a stabilization The NLARI processes in fixed point domain, there j₁=1, θ₀=-4.475 × 10^-7, θ₁=0.5027, θ₂=0.0794, σ= 0.0249, η₁=-8.999 × 10^-7, η₂=0.3136, γ=0.0264, T=1.8 × 10⁷, N=70, n=50, m=20.Obtain Obtain in point horizontal index of shapeWithMinimized aggregation degree j₂=100 point shape, Auto-correlation coefficient ρ_nAs the increase of lag order n shows almost one level Straight line, it is shown that height Long Memory Properties (as shown in the 10a in Figure 10), the likelihood ratioLevel is almost to i Straight line, the average likelihood ratio submits to a power law m^-0.97, show X₁₀₀There is the self-similarity (as shown in the 10b in Figure 10) of height.

Presently preferred embodiments of the present invention is the foregoing is only, is not intended to limit the invention, it is all in essence of the invention Any modification, equivalent and improvement made within god and principle etc., is created including based on the spirit and principles in the present invention An application for the smallest dimension time series generating process for meeting varying level point shape and dynamic characteristic requirement is made, all should be wrapped It is contained within protection scope of the present invention.

Claims (9)

1. a kind of Application of Data Mining theoretical based on new random fractal, it is characterised in that described

Based on the theoretical Application of Data Mining of new random fractal by addition polymerization time series being amplifying observation yardstick changes Become point shape slope index parameter and the wave amplitude index parameters of NLARI, recognize the Long Memory Properties of varying level, self-similarity, have concurrently Point shape and the minimized aggregation degree time series generating process of dynamic characteristic of Long Memory Properties and self-similarity.

2. as claimed in claim 1 based on the Application of Data Mining that new random fractal is theoretical, it is characterised in that pass through The concentration class of control time sequence recognizes the time series generating process of different point shape levels and dynamic characteristic；Specific bag Include：

Step one, data absolute value downsizing treatment, is designated as X=(X_t：T=1 ..., T)；

Step 2, least square method regression straight line is calculated using XUseAnd

ΔY_t=Y_t-Y_t-1, it is rightMake Least Square Method and obtain parameter estimationNote Y=(Y '₁₀..., Y '_1t... Y '_1T-1) ',s¹¹And s²²Difference representing matrixThe first row first row element and the element of the second row secondary series；

Step 3, calculates θ₁Confidential intervalWhereinIt is that t is distributed in confidence levelCritical value with And return the statistic without hypothesis γ=0If θ₁Confidential interval be comprised in it is interval (- 1, 1) interior, θ₂Confidential intervalWith the confidential interval of γBe contained in interval (0, ∞), with And if returning and being rejected without hypothesis γ=0, receive opposition hypothesis γ ＞ 0, then evidence supports that data come from NLARI processes, performs Step 4, otherwise to j=j+1 (initial value j=1), calculates j reunion collection time serieses X_j, it is designated as X=X_j, perform step 2；If To that can not continue to be aggregated, output result X is the degeneration that a non-NLARI process or have γ=0 to circulation time sequence ARI (2,1) process, exits analysis；

Step 4, remembers j₁=j, allowsFractal Identification is performed, j is obtained₂Meet again and collect sequencePoint shape degree is (δ_{1, k}, δ_{2, k}), it is designated asOr without a point shape

Step 5 is rightWithStep 2 is performed respectively obtains θ₁Confidential intervalθ₂Confidential intervalAnd the confidential interval of γWherein If θ₁, θ₂, the confidential interval of γ is comprised in interval (- 1,1), (0,4), (0,1), then to support that X carrys out self-stabilization motionless for evidence NLARI processes on point domain；If θ₁, θ₂, the confidential interval of γ is comprised in interval (- 1,1),It is interior, then demonstrate,prove According to supporting X from the NLARI processes in stable period annulus；If θ₁, θ₂, the confidential interval of γ is comprised in interval (- 1,1), (0 ,+∞),Interior, then evidence supports X from the NLARI processes in unstable cycle annulus；Otherwise X comes from critical value On NLARI processes；Fractal sequences of the output with these behavioral characteristicsWith without fractal sequencesIncluding mould Shape parameter is used as conclusion.

3. as claimed in claim 1 based on the Application of Data Mining that new random fractal is theoretical, it is characterised in that identification The minimized aggregation degree Time Series Method of different long memory levels, including：

1) one is selected on the occasion of descending series δ_{1, k}If, initial value k=j=1 and X₁=X；

2) calculate jth and meet again and collect time series X_j；

3) X is calculated_jSample autocorrelation coefficient ρ_nAs n=1 ..., N and LM (X_j)；If LM (X_j) ＜ δ_{1, k}, then step is performed 4) step 2 otherwise, is performed to j=j+1), the output result minimized aggregation degree when being recycled to time series and can not continue to be aggregated Long Memory Properties time series X_j-1(δ_{1, k-1}) and model parameter X there_j(δ_1,0) mean former time seriesWithout long memory Property；

If 4) k ＜ K, j=1 and k=k+1 is made, performs step 2), when otherwise exporting the Long Memory Properties of conclusion minimized aggregation degree Between sequence X_j(δ_{1, k}) and model parameter.

4. as claimed in claim 1 based on the Application of Data Mining that new random fractal is theoretical, it is characterised in that identification The minimized aggregation degree Time Series Method of different self similarity levels, including：

A, selected one on the occasion of descending series δ_{2, k}If, initial value k=j=1 and X₁=X；

B, calculating jth are met again and collect time series X_j；

C, calculating X_jSample likelihood ratio r_{H (i, im)}And SS_hm(X_j) as m=1 ..., M, h=1 ..., H and i=1 ..., n；If SS_hm(X_j) ＜ δ_{2, k}Set up as given m=1 ..., M and h=1 ..., H then performs step D, otherwise performs step to j=j+1 Rapid B, when being recycled to time series and can not continue to be aggregated, the self-similarity time series X of output result minimized aggregation degree_j-1 (δ_{Z, k-1}) and model parameter X there_j(δ_2,0) mean former time seriesThere is no self-similarity；

If D, k ＜ K, j=1 and k=k+1 is made, step B is performed, when otherwise exporting the self-similarity of conclusion minimized aggregation degree Between sequence X_j(δ_{Z, K}) and model parameter.

5. as claimed in claim 1 based on the Application of Data Mining that new random fractal is theoretical, it is characterised in that identification Have the minimized aggregation degree Time Series Method of the difference point shape level of Long Memory Properties and self-similarity concurrently, including：

A, selected two on the occasion of descending series δ_{1, k}And δ_{2, k}If, initial value k=j=1 and X₁=X；

B, calculating jth are met again and collect time series X_j；

C, calculating X_jSample autocorrelation coefficient ρ_nAs n=1 ..., N and LM (X_i)；If LM (X_j) ＜ δ_{1, k}, then step is performed D, otherwise performs step b to j=j+1, when time series can not continue to be aggregated, when dividing shape of output result minimized aggregation degree Between sequence X_j-1(δ_{1, k-1}, δ_{2, k-1}) and model parameter, (δ_1,0, δ_2,0) it is former sequenceWithout fractal structure；

D, calculating X_jSample likelihood ratio r_{H (i, im)}As i=1 ..., n and SS_hm(X_j) as m=1 ..., M and h=1 ..., H； If SS_hm(X_j) ＜ δ_{2, k}As h=1 ..., H and m=1 ..., M set up, then perform step e, otherwise perform step to j=j+1 b；

If e, k ＜ K, j=1 and k=k+1 is made, perform step b, otherwise export the time fractal sequence of conclusion minimized aggregation degree Row X_j(δ_{1, k}, δ_{2, k}) and model parameter；By limiting δ_{1, k}And δ_{2, k}The time sequence of the different long memories of value identification and self similarity level Column-generation process.

6. as claimed in claim 1 based on the Application of Data Mining that new random fractal is theoretical, it is characterised in that new Random fractal is theoretical, including：

(1) as the slope index η of fractal parameter₁=ω/α and wave amplitude index η₂=σ/β describes Stochastic Elasticity system based on a class The NLARI processes of system：

$X_t={\mathrm{\θ}}_0+(1+{\mathrm{\θ}}_1)X_{t-1}-{\mathrm{\θ}}_1{X}_{t-2}+{\mathrm{\θ}}_{2}g(X_{t-{\mathrm{\κ}}_2}-{\mathrm{\μ}}_{t-{\mathrm{\κ}}_2})+v_t$

Whereinε_tIt is white noise,

G (x) is the recovery force function for meeting condition g (- x)=- g (x) and xg (x) ＜ 0, and ω is the expected value of external disturbance, and σ is The standard deviation of external disturbance, α is resistance coefficient, and β is to recover force coefficient, κ₁It is the time lag on resistance, κ₂It is in restoring force On time lag；

(2) j meets again and collects time seriesWhereinFully

Increase concentration class j will also result in one it is relatively large | η₁| and a relatively small η₂So as to produce long memory and from phase Like behavior；

(3) auto-covariance r_hLikelihood ratio r_{H (i, im)}=r_h(X_i)/r_h(X_im), if time series is self similarity,

It can tend to a horizontal linear as given h=1 ..., H, m=1 ..., M with the increase of i；

(4) the horizontal index of long memoryWith the horizontal index of self similarity ${\mathrm{SS}}_{hm}\left(X_j\right)\≡1-\underset{i=1,\mathrm{...},n}{\min }\left(r_{h(i,im)}\right)/\underset{i=1,\mathrm{...},n}{\max }\left(r_{h(i,im)}\right).$

7. as claimed in claim 2 based on the Application of Data Mining that new random fractal is theoretical, it is characterised in that step In four, fractal method is recognized, including：

One) calculate j and meet again and collect time series X_j, its auto-correlation coefficient ρ_nAs n=1 ..., N and likelihood ratio r_{H (i, im)}As h =1 ..., H, m=1 ..., M and i=1 ..., n；

Two) concentration class j is increased until meeting long memory level conditions LM (X_j) ＜ δ_{1, k}With self similarity level conditions SS_hm(X_j) ＜ δ_{2, k}For all h=1 ..., H and m=1 ..., wherein M, δ_{1, k}And δ_{2, k}It it is two on the occasion of decreasing sequence of numbers；

Three) by changing δ_{1, k}And δ_{2, k}Value control long memory level and self similarity level.

8. as claimed in claim 1 based on the Application of Data Mining that new random fractal is theoretical, it is characterised in that identification Dynamic characteristic method includes：

θ based on t distributions₁, θ₂, the confidential interval calibrating of γ and return the statistic without hypothesis γ=0 opposition hypothesis γ ＞ 0Calibrating, if

Evidence supports that data have the stable fixed point structure of NLARI, if

Evidence supports that data have ring stable period of NLARIStructure, if

Evidence supports that data have the unstable periodic ring of NLARIStructure.

9. as claimed in claim 8 based on the Application of Data Mining that new random fractal is theoretical, it is characterised in that calibrating Method, including：Use X=X_jCalculate least square method regression straight linePass throughTo Δ Y_t=θ₁Δ Y_t-1+θ₂g(Y_t-1)+ε_tMake Least Square Method Δ Y there_t=Y_t-Y_t-1, obtain parameter estimation