CN112131529B - E-G two-step method-based pairing transaction coordination relation acceleration verification method - Google Patents
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Abstract
The application discloses a pairing transaction coordination relation acceleration verification method based on an E-G two-step method, which comprises the following steps of: acquiring two time sequences of a to-be-verified synergistic relationship; -performing an augmented dir fowler test on its residual and the difference of said residual, wherein: solving a regression analysis result corresponding to the maximum hysteresis order by using an LDLT decomposition method; obtaining regression analysis results corresponding to all hysteresis orders according to the regression analysis results corresponding to the maximum hysteresis order, and obtaining corresponding error square sums; calculating the red pool information quantity criterion function value corresponding to all hysteresis orders by using an optimized red pool information quantity criterion formula; selecting the hysteresis order corresponding to the minimum information quantity criterion function value of the red pool as the optimal hysteresis order; and obtaining a regression coefficient corresponding to the optimal hysteresis order. The method reduces the algorithm strength and approximately calculates the algorithm by applying the common least square algorithm for multiple times in the traditional algorithm, and improves the verification speed of the coordination relation of the two time sequences.
Description
Technical Field
The application relates to the field of paired transaction coordination relation verification, in particular to a paired transaction coordination relation acceleration verification method based on an E-G two-step method.
Background
Pairing trading is a statistical arbitrage strategy widely used in the financial market, based on two highly correlated stocks or other securities whose trends remain close for a long period of time, once a departure occurs, which is considered to be transient, and their trend can be predicted to return in the future, thereby making a profit by judging their future trend.
An important link in the pairing transaction is how to find out the two stocks with long-term retention, and the more classical method is the E-G two-step method proposed by Engle and Granger, and the two stocks with long-term retention are determined through synergistic relationship verification.
However, because the stock market data size is large and stock prices are frequently changed, and the E-G two-step method has the characteristics of high computational complexity and circulation, when the price sequence length is long or the number of the to-be-selected stocks is large, the direct running on the CPU or the GPU can generate very large system delay; the parallel computation consumes relatively large resources, generates large power consumption, and is very difficult to deploy on an FPGA or ASIC platform due to the existence of operations which are very unfriendly to hardware such as matrix inversion, logarithmic operation and the like in the algorithm. Too long a calculation time may result in a decrease in pairing efficiency, so that missing a profit opportunity may even result in a loss due to the end of the pairing relationship.
Disclosure of Invention
The application provides a pairing transaction coordination relation acceleration verification method based on an E-G two-step method, which is based on the traditional E-G two-step method to carry out algorithm intensity reduction and approximate calculation on a core calculation module and simultaneously skillfully designs hardware unfriendly calculation such as matrix inversion and logarithmic operation.
A pairing transaction coordination relation acceleration verification method based on an E-G two-step method comprises the following steps:
acquiring two time sequences of a to-be-verified synergistic relationship;
performing common least square regression analysis on the two time sequences of the to-be-verified synergistic relationship to obtain a residual error of the regression analysis and a difference of the residual error;
-performing an augmented dir fowler test on the residual and the difference of the residual, wherein:
presetting a maximum hysteresis order, and carrying out common least square regression analysis on a residual error corresponding to the maximum hysteresis order and a difference of the residual error;
solving a regression analysis result corresponding to the maximum hysteresis order by using an LDLT decomposition method;
obtaining a regression analysis result corresponding to each hysteresis order according to the regression analysis result corresponding to the maximum hysteresis order;
obtaining the error square sum corresponding to each hysteresis order according to the regression analysis result corresponding to each hysteresis order;
calculating the red pool information quantity criterion function value corresponding to each hysteresis order by using an optimized red pool information quantity criterion formula according to the error square sum corresponding to each hysteresis order;
selecting the hysteresis order corresponding to the minimum information quantity criterion function value of the red pool as the optimal hysteresis order;
performing common least square regression analysis on the residual error corresponding to the optimal hysteresis order and the difference of the residual error to obtain a regression coefficient corresponding to the optimal hysteresis order;
according to the regression coefficient corresponding to the optimal hysteresis order, checking the stability of the residual error corresponding to the optimal hysteresis order;
and judging whether a synergistic relationship exists between the two time sequences of the synergistic relationship to be verified according to the stability of the residual error corresponding to the optimal hysteresis order.
Further, the common least squares regression analysis performed on the two time sequences of the to-be-verified synergistic relationship is as follows:
Y＝αI+ρX+ε
wherein, X and Y are two time sequences of the to-be-verified synergistic relationship, N is the length of the time sequences, alpha is a constant term, and I= (1, …, 1) T I is an n×1 vector, ρ is a coefficient, ε= (e) 1 ，e 2 ，…，e N ) T As n×1 residual vector, Δε= (e) 2 -e 1 ，e 3 -e 2 ，…，e N -e N-1 ) T ＝(Δe 1 ，Δe 2 ，…，Δe N-1 ) T Is the (N-1) x 1 difference vector of the residual epsilon.
Further, the maximum hysteresis order is preset as:
wherein maxlag is the maximum hysteresis order.
Further, the performing an augmented discipline test on the residual and the difference of the residual includes: performing common least square regression analysis on the residual error corresponding to each hysteresis order and the difference of the residual errors,
wherein lag is hysteresis order, lag is more than or equal to 0 and less than or equal to maxlag, k j，lag J=0, …, lag, which is the regression coefficient corresponding to the lag order lag, β lag ＝(k 0，lag ，k 1，lag ，…，k lag，lag ) T For the regression coefficient vector corresponding to the lag order lag, epsilon lag ＝(e maxlag+2 ，e maxlag+3 ，…，e N ) T and ε′lag ＝(e maxlag+1 ，e maxlag+2 ，…，e N-1 ) T For the residual vector corresponding to the lag order lag, delta epsilon i，lag ＝(Δe maxlag-i+1 ，Δe maxlag-i+2 ，…，Δe N-i-1 ) T I=1, …, lag, which is the differential vector of the residual error corresponding to the lag order lag, μ lag ＝(u 1，lag ，u 2，1ag ，…，u N-maxlag-1，1ag ) T For the error vector corresponding to the lag order lag, E lag ＝(ε′ lag ，Δε 1，lag ，…，Δε lag，lag )。
Further, the regression analysis result corresponding to the maximum hysteresis order is solved by using the LDLT decomposition method, specifically:
performing a common least square regression analysis according to the residual error corresponding to each hysteresis order and the difference of the residual error, so that lag=maxlag, and calculating a regression coefficient corresponding to the maximum hysteresis order maxlag as follows:
wherein the matrix to be inverted isLDLT decomposition is carried out to obtain:
further, the obtaining a regression analysis result corresponding to each hysteresis order according to the regression analysis result corresponding to the maximum hysteresis order specifically includes:
wherein the orientation quantity matrixThe vector matrix composed of the first lag+1 elements is +.>
Taking a matrixThe matrix of elements of the first lag+1 columns is approximately
Further, according to the sum of squares of errors corresponding to each hysteresis order, calculating a criterion function value of the information quantity of the red pool corresponding to each hysteresis order by using an optimized criterion formula of the information quantity of the red pool, specifically:
the optimized red-pool information quantity criterion formula is as follows:
iAIC＝SSR×e 2k/N
wherein ,and k=lag+1 is the number of parameters to be estimated in regression analysis corresponding to the lag order lag.
The application provides a pairing transaction coordination relation acceleration verification method based on an E-G two-step method for pairing transaction, which can quickly find out stocks with two price trends kept close for a long time. The scheme is based on the traditional E-G two-step method for targeted algorithm strength reduction and approximate calculation, and meanwhile, ingenious design is carried out on hardware unfriendly calculation such as matrix inversion and logarithmic operation. We integrate the design with TSMC 28-nm technology, reducing the latency to 1290 and 190 times, respectively, relative to CPU/GPU.
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In order to more clearly illustrate the technical solution of the present application, the drawings that are needed in the embodiments will be briefly described below, and it will be obvious to those skilled in the art that other drawings can be obtained from these drawings without inventive effort.
FIG. 1 is a block diagram of a paired transaction cooperative relationship acceleration verification method based on an E-G two-step method;
FIG. 2 is a flow chart of the application for performing an augmented Diyl Fowler test on residuals and differences thereof;
FIG. 3 is a schematic flow chart of the OLS module of FIG. 2 according to the present application;
FIG. 4 is a schematic diagram of systolic array accumulator register data processing of FIG. 2 according to the present application.
Detailed Description
In the embodiment, as shown in an overall structure diagram of a paired transaction coordination relation acceleration verification method based on an E-G two-step method in fig. 1, in paired transaction, a price time sequence X and Y of two stocks of a coordination relation to be verified are obtained;
and carrying out common least square regression analysis on the price time sequences X and Y of the two stocks of the to-be-verified synergistic relationship to obtain a regression equation:
Y＝αI+ρX+ε
wherein X, Y is an N X1 vector of the price time series of the two stocks of the to-be-verified synergistic relationship, N is X, Y time series length, alpha is a constant term, I= (1, …, 1) T I is an Nx1 vector, ρ is a coefficient,
and further obtaining a residual error of the regression analysis and a difference of the residual error,
ε＝Y-αI-ρX
wherein ε= (e) 1 ，e 2 ，…，e N ) T For an N x 1 residual vector,
let Δε= (e) 2 -e 1 ，e 3 -e 2 ，…，e N -e N-1 ) T ＝(Δe 1 ，Δe 2 ，…，Δe N-1 ) T Is the (N-1) x 1 difference vector of the residual epsilon.
Fig. 2 is a flow chart of an augmented diresfowler test for residuals and their differences, as shown in fig. 2,
-performing an Augmented di fowler test (Augmented di ckey-Fuller test) on the residual epsilon and the difference delta epsilon of the residual, wherein:
after the maximum hysteresis order maxlag is preset, the maxlag calculation formula is as follows:
wherein maxlag is the maximum hysteresis order and N is the sequence length of the residual vector epsilon, i.e. the X, Y time sequence length.
The common least square regression analysis is required to be carried out on the residual errors and the differences of the residual errors when each hysteresis order is lag (0-0 maxlag), and the regression equation is as follows:
wherein lag is hysteresis order, lag is more than or equal to 0 and less than or equal to maxlag, k j，lag J=0, …, lag, which is the regression coefficient corresponding to the lag order lag, β lag ＝(k 0，lag ，k 1，lag ，…，k lag，lag ) T For the regression coefficient vector corresponding to the lag order lag, epsilon lag ＝(e maxlag+2 ，e maxlag+3 ，…，e N ) T and ε′lag ＝(e maxlag+1 ，e maxlag+2 ，…，e N-1 ) T For the residual vector corresponding to the lag order lag, delta epsilon i，lag ＝(Δe maxlag-i+1 ，Δe maxlag-i+2 ，…，Δe N-i-1 ) T I=1, …, lag, which is the differential vector of the residual error corresponding to the lag order lag, μ lag ＝(u 1，lag ，u 2，lag ，…，u N-maxlag-1，lag ) T For the error vector corresponding to the lag order lag, E lag ＝(ε′ lag ，Δε 1，lag ，…，Δε lag，lag )。
It can be seen that:
Δε i，lag ＝(Δe maxlag-i+1 ，Δe maxlag-i+2 ，…，Δe N-i-1 ) T i.e. a vector consisting of elements from position maxlag-i+1 to position N-i-1 in Δε, i=1, 2, …, lag;
to be different from the above delta epsilon i，lag Is kept consistent with the sequence vector length of (a) and the residual epsilon is calculated lag and ε′lag The definition is as follows:
ε lag ＝(e maxlag+2 ，e maxlag+3 ，…，e N ) T i.e., a vector composed of the elements from the (maxlag+2) th bit to the (N) th bit in epsilon;
ε′ lag ＝(e maxlag+1 ，e maxlag+2 ，…，e N-1 ) T i.e., a vector composed of the elements from the maxlag+1st to the N-1 st in epsilon;
E lag ＝(ε′ lag ，Δε 1，lag ，…，Δε lag，lag ) (N-maxlag-1) × (lag+1) matrix composed of residual vector and differential vector, μ lag ＝(u 1，lag ，u 2，lag ，…，u N-maxlag-1，lag ) T Is an (N-maxlag-1) x 1 error vector.
Thus, equation (1) can obtain the residual epsilon through the common least square regression analysis lag 、ε′ lag Difference delta epsilon of the residuals i，lag The regression coefficients of (2) are:
because the common least square regression analysis algorithm is called for a plurality of times in the augmentation-DietFowler test algorithm, a plurality of common least square regression analysis hardware modules are designed in parallel, so that great resource consumption is brought. The method performs targeted algorithm strength reduction and approximate calculation aiming at a plurality of common least square regression analysis algorithms in the traditional augmented Diyl Fowler test algorithm.
For the hysteresis order lag (0. Ltoreq. Lag. Ltoreq. Maxlag) analyzed in sequence, the corresponding ε 'is input' lag Differential delta epsilon i，lag (i=1, 2, …, lag) is a column added on the basis of the last analysis data, so that all the results of the regression analysis corresponding to different hysteresis orders are obtained by calculating the regression analysis results of the common least squares algorithm when lag=maxlag.
Firstly, carrying out common least square regression analysis on residual errors corresponding to the maximum hysteresis order and differences thereof, and according to (1), enabling lag=maxlag to obtain a regression equation corresponding to the maximum hysteresis order:
ε maxlag ＝E maxlag β maxlag +μ maxlag
thereby calculating the maximum hysteresisRegression coefficient beta corresponding to the post-order maxlag maxlag The following are provided:
and obtaining a regression analysis result corresponding to each hysteresis order according to the regression analysis result corresponding to the maximum hysteresis order, and solving a regression coefficient in regression analysis by using an LDLT (Low Density discharge) decomposition method.
Considering that for each lag order lag (0. Ltoreq. Lag. Ltoreq. Maxlag), the residual ε is required lag 、ε′ lag Differential delta epsilon i，lag (i=1, 2, …, lag) ordinary least squares regression analysis is performed, so that ordinary least squares regression analysis needs to be performed a plurality of times, and the calculation amount is large. Therefore, the matrix operation result in the regression analysis process corresponding to each lag order lag can be obtained according to the matrix operation result in the regression analysis process corresponding to the maximum lag order maxlag.
As shown in FIG. 2, input ε maxlag ，E maxlag By calculating the regression analysis result corresponding to the maximum hysteresis order maxlag and further utilizing the calculation characteristic of pulse array multiplication accumulation, the regression analysis result corresponding to the lag=0, 1,2, … and maxlag can be taken out of the accumulation register in a periodic manner, and the specific analysis is as follows:
as can be seen from the formula (2), the matrix operation required in the regression analysis process corresponding to each lag order lag (0.ltoreq.lag.ltoreq.maxlag) includes: and />
The application firstly carries out matrix operation in the regression analysis process corresponding to the maximum hysteresis order: and />And then obtaining matrix operation results corresponding to other hysteresis orders, thereby obtaining regression coefficients corresponding to the hysteresis orders according to the formula (2).
For the followingThe matrix operation of (2) is as follows:
ε maxlag ＝(e maxlag+2 ，e maxlag+3 ，…，e N ) T
can be obtainedThe operation result of (a) is
Since there is Δε when 1.ltoreq.i.ltoreq.lag i，maxlag ＝Δε i，lag And epsilon maxlag ＝ε lag ，Therefore can be according to +.>The result (3) of the calculation of (2) can be obtained corresponding +.>The result of the operation is->The vector matrix formed by the previous lag+1 elements of the operation result (3) is:
for the followingThe result of the matrix operation is as follows:
since there is Δε when 1.ltoreq.i.ltoreq.lag i，maxlag ＝Δε i，lag And (2) andso can be according to the aboveThe corresponding +.>The operation result of (a) isThe matrix formed by the elements corresponding to the previous lag+1 row and the previous lag+1 column of the operation result is:
for the followingThe operation process is as follows:
solving for maximum hysteresis order using LDLT decomposition methodRegression coefficients corresponding to numbers, i.e. matrix to be invertedLDLT decomposition was performed as follows:
then solving the inverse matrix of the lower triangular matrix L and the inverse matrix of the diagonal matrix D to obtain the matrix to be solvedThe inverse matrix of (2) is:
it can be seen that the LDLT decomposition method solves the problem that matrix inversion is not friendly to hardware by decomposing the matrix to be solved into a lower triangular matrix and a diagonal matrix.
According to the matrix inversion operation result of (5), performing matrix inversion operation on the matrix corresponding to the lag order lagBy approximation, i.e. taking (LT) in (5) 1 D- 1 L- 1 The matrix of elements of the preceding lag+1 row of the matrix, the preceding lag+1 column is approximately taken as +.>Is a result of the operation of (a).
From the above analysis, it is clear that the present application corresponds to the case of lag=0, 1,2, …, maxlag-1And (3) withThe matrix may be derived from the time of lag = maxlag/>And->And taking out the corresponding position of the matrix. The common least square algorithm results of all input data with different sizes can be obtained by only calculating a common least square algorithm when the lag=maxlag according to an algorithm strength reduction and approximate calculation method.
For a pair ofAnd->Matrix multiplication using systolic array computation willMarked as matrix R, will->Marked as matrix B, there are
FIG. 4 is a schematic diagram of the systolic array accumulator register data processing of FIG. 2 according to the present application, as shown in FIG. 4:
according to the calculation characteristics of pulse array multiplication accumulation, the lag=0, 1,2, … and maxlag can be taken out from the accumulation register in cyclesAnd->As a result of the matrix multiplication,
the method comprises the following steps:
β lag ＝(r 11 b 1 +…+r 1lag+1 b lag+1 ，…，r lag+11 b 1 +…+r lag+1lag+1 b lag+1 ) (6)
finally, according to the regression coefficient corresponding to each lag order lag obtained in the formula (6), calculating the error mu corresponding to each lag order lag by the formula (1) lag ＝(u 1，lag ，u 2，lag ，…，u N-maxlag-1，lag ) T Error square sum of (2)
According to the sum of squares of errors corresponding to the hysteresis order lagAnd calculating the number k=lag+1 of parameters to be estimated in regression analysis corresponding to the lag order lag and the sequence length N of the residual vector epsilon by utilizing an optimized red pool information quantity criterion formula, wherein the red pool information quantity criterion function value corresponds to each lag order.
The known red-cell information quantity criterion formula is:
AIC＝2k+nln(SSR/N) (7)
because the logarithmic operation also increases the calculation difficulty, a great amount of resources are consumed in the hardware design, and the AIC algorithm is used for inputting different SSRs and k and judging the magnitude relation of AIC function values on the premise of fixed input sequence length N, the application provides an optimized red pool information quantity criterion formula:
iAIC＝(SSR)×e 2k/N (8)
as can be seen from equation (8), for any two sets of input data (k 1 ，N 1 ，SSR 1) and (k2 ，N 2 ，SSR 2 )，(k 1 ，N 1 ，SSR 1 ) The corresponding function values are AIC1 and IAIC1, (k) 2 ，N 2 ，SSR 2 ) The corresponding function values are AIC2 and IAIC2, which satisfy the condition AIC1<In the case of AIC2, IAIC1 is present<IAIC2, therefore, it can be known that the formulas (7) and (8) are equivalent, and the calculation difficulty of the logarithmic operation is reduced in (8), so that the formula (8) can be applied to calculate the red pool information amount criterion function value corresponding to each hysteresis order.
Selecting the hysteresis order corresponding to the minimum information quantity criterion function value of the red pool as the optimal hysteresis order bestlag, and carrying out residual epsilon corresponding to the optimal hysteresis order bestlag bestlag 、ε′ bestlag Differential delta epsilon i，bestlag (i=1, …, bestlag) performing a general least squares regression analysis to calculate a regression coefficient corresponding to the optimal hysteresis order,
here, Δε i，bestlag ＝(Δe bestlag-i+1 ，Δe bestlag-i+2 ，…，Δe N-i-1 ) T I.e. vectors consisting of the elements from position (bestlag-i+1) to position (N-i-1) in delta epsilon, i=1, 2, …, bestlag;
to be different from the above delta epsilon i，bestlag Is kept consistent with the sequence vector length of (a) and the residual epsilon is calculated bestlag and ε′bestlag The definition is as follows:
ε bestlag ＝(e bestlag+2 ，e bestlag+3 ，…，e N ) T i.e., a vector consisting of the bettlag+2th to nth elements in epsilon;
ε′ bestlag ＝(e bestlag+1 ，e bestlag+2 ，…，e N-1 ) T i.e., a vector consisting of the bettlag+1st to N-1 st elements in epsilon;
E bestlag ＝(ε′ bestlag ，Δε 1，bestlag ，…，Δε bestlag，bestlag ) (N-bestlag-1) × (bestlag+1) matrix, μ for residual vector and differential vector bestlag ＝(u 1，bestlag ，u 2，bestlag ，…，u N-bestlag-1，bestlag ) T Is an (N-bestlag-1) x 1 error vector.
As shown in fig. 2 and 3, a common least square algorithm is performed on the regression analysis corresponding to the optimal hysteresis order by using a 0LS module,
the input is: e (E) bestlag ＝(ε′ bestlag ，Δε 1，bestlag ，…，Δε bestlag，bestlag) and εbestlag ；
The output is:namely the regression coefficient beta corresponding to the optimal hysteresis order bestlag ＝(k 0，bestlag ，k 1，bestlag ，…，k bestlag，bestlag ) T 。
The 0LS module also adopts an LDLT decomposition method to simplify a matrix inversion algorithm. Performing common least square regression analysis on the residual error and the difference corresponding to the optimal hysteresis order through a 0LS module to finally obtain a regression coefficient beta corresponding to the optimal hysteresis order bestlag ＝(k 0，bestlag ，k 1，bestlag ，…，k bestlag，bestlag ) T 。
According to the regression coefficient beta corresponding to the optimal hysteresis order bestlag And checking the stability of the residual error corresponding to the optimal hysteresis order by using a Student's t-test:
if the residual error corresponding to the optimal hysteresis order is stable, a synergistic relationship exists between the two time sequences of the to-be-verified synergistic relationship,
if the residual error corresponding to the optimal hysteresis order is not stable, no coordination relation exists between the two time sequences of the to-be-verified coordination relation.
The application provides a pairing transaction coordination relation acceleration verification method based on an E-G two-step method, which carries out software and hardware coordination optimization on an augmentation-Diyl Fowler test algorithm. Providing a substitution algorithm of a red pool information quantity criterion formula function, and calculating the red pool information quantity criterion function value by using an optimized red pool information quantity criterion formula, wherein the algorithm can achieve the same effect as the original algorithm, and meanwhile, the logarithm operation which is not friendly to hardware is avoided in hardware design; in addition, when the residual error and the difference thereof are subjected to multiple common least square regression analysis, the LDLT decomposition method is utilized, regression analysis results of the maximum hysteresis order are utilized to approximately obtain regression analysis results of all hysteresis orders, and the algorithm strength reduction and approximation calculation method are utilized, so that the calculation complexity is obviously reduced under the condition of sacrificing certain precision.
The design of the key calculation step in the augmented discipline test using the present application is generally as follows for the reduction of the algorithm complexity of this step:
wherein ,
Claims (1)
1. the method for accelerating verification of the pairing transaction coordination relation based on the E-G two-step method is characterized by comprising the following steps of:
acquiring two time sequences of a to-be-verified synergistic relationship;
performing common least square regression analysis on the two time sequences of the to-be-verified synergistic relationship to obtain a residual error of the regression analysis and a difference of the residual error;
-performing an augmented dir fowler test on the residual and the difference of the residual, wherein:
presetting a maximum hysteresis order, and carrying out common least square regression analysis on a residual error corresponding to the maximum hysteresis order and a difference of the residual error;
solving a regression analysis result corresponding to the maximum hysteresis order by using an LDLT decomposition method;
obtaining a regression analysis result corresponding to each hysteresis order according to the regression analysis result corresponding to the maximum hysteresis order;
obtaining the error square sum corresponding to each hysteresis order according to the regression analysis result corresponding to each hysteresis order;
calculating the red pool information quantity criterion function value corresponding to each hysteresis order by using an optimized red pool information quantity criterion formula according to the error square sum corresponding to each hysteresis order;
selecting the hysteresis order corresponding to the minimum information quantity criterion function value of the red pool as the optimal hysteresis order;
performing common least square regression analysis on the residual error corresponding to the optimal hysteresis order and the difference of the residual error to obtain a regression coefficient corresponding to the optimal hysteresis order;
according to the regression coefficient corresponding to the optimal hysteresis order, checking the stability of the residual error corresponding to the optimal hysteresis order;
judging whether a synergistic relationship exists between the two time sequences of the synergistic relationship to be verified according to the stability of the residual error corresponding to the optimal hysteresis order;
the common least square regression analysis of the two time sequences of the to-be-verified synergistic relationship is as follows:
Y＝αI+ρX+ε
wherein, X and Y are two time sequences of the to-be-verified synergistic relationship, N is the length of the time sequences, alpha is a constant term, and I= (1, …, 1) T I is an n×1 vector, ρ is a coefficient, ε= (e) 1 ，e 2 ，…，e N ) T As n×1 residual vector, Δε= (e) 2 -e 1 ，e 3 -e 2 ，…，e N -e N-1 ) T ＝(Δe 1 ，Δe 2 ，…，Δe N-1 ) T A (N-1) x 1 differential vector that is the residual ε;
the maximum hysteresis order is preset as follows:
wherein maxlag is the maximum hysteresis order;
the performing an augmented discipline test on the residual and the difference of the residual includes: performing common least square regression analysis on the residual error corresponding to each hysteresis order and the difference of the residual errors,
wherein lag is hysteresis order, lag is more than or equal to 0 and less than or equal to maxlag, k i，lag J=0, …, lag, which is the regression coefficient corresponding to the lag order lag, β lag ＝(k 0，lag ，k 1，lag ，…，k lag，lag ) T For the regression coefficient vector corresponding to the lag order lag, epsilon lag ＝(e maxlag+2 ，e maxlag+3 ，…，e N ) T and ε′lag ＝(e maxlag+1 ，e maxlag+2 ，…，e N-1 ) T For the residual vector corresponding to the lag order lag, delta epsilon i，lag ＝(Δe maxlag-i+1 ，Δe maxlag-i+2 ，…，Δe N-i-1 ) T I=1, …, lag, which is the differential vector of the residual error corresponding to the lag order lag, μ lag ＝(u 1，lag ，u 2，lag ，…，u N-maxlag-1，lag ) T For the error vector corresponding to the lag order lag, E lag ＝(ε′ lag ，Δε 1，lag ，…，Δε lag，lag )；
The regression analysis result corresponding to the maximum hysteresis order is solved by using an LDLT decomposition method, specifically:
performing a common least square regression analysis according to the residual error corresponding to each hysteresis order and the difference of the residual error, so that lag=maxlag, and calculating a regression coefficient corresponding to the maximum hysteresis order maxlag as follows:
wherein the matrix to be inverted isLDLT decomposition is carried out to obtain:
and acquiring a regression analysis result corresponding to each hysteresis order according to the regression analysis result corresponding to the maximum hysteresis order, wherein the regression analysis result corresponding to each hysteresis order is specifically:
wherein the orientation quantity matrixThe vector matrix composed of the first lag+1 elements is +.>
Taking a matrixThe matrix of elements of the first lag+1 columns is approximately
Calculating the red pool information quantity criterion function value corresponding to each hysteresis order by using an optimized red pool information quantity criterion formula according to the error square sum corresponding to each hysteresis order, wherein the method specifically comprises the following steps:
the optimized red-pool information quantity criterion formula is as follows:
iAIC＝SSR×e 2k/N
wherein ,and k=lag+1 is the number of parameters to be estimated in regression analysis corresponding to the lag order lag.
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