Hydrological time sequence length dependency type identification method based on correlation
By constructing a unified hydrological time series analysis framework, and using models such as AR, MA, and ARMA and correlation coefficients to assess the short-term dependence of hydrological time series, the problem of existing technologies being unable to accurately distinguish and fit the dependence characteristics of hydrological time series is solved, thus achieving accurate prediction and assessment of hydrological processes.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- INST OF GEOGRAPHICAL SCI & NATURAL RESOURCE RES CAS
- Filing Date
- 2026-02-04
- Publication Date
- 2026-05-15
AI Technical Summary
Existing technologies cannot accurately distinguish and reasonably fit the short-term and long-term dependence characteristics in hydrological time series, leading to misjudgments of the evolution patterns of hydrological time series, reduced reliability of long-term predictions, and inaccurate uncertainty assessments.
By identifying deterministic components in hydrological time series, short-dependent components are fitted using AR, MA, and ARMA models, and long-dependent components are fitted using FAR, FMA, FARMA, and SMA models. The type of dependence is evaluated by combining correlation coefficients and significance levels, thus constructing a unified framework for hydrological time series analysis.
It enables accurate identification and quantitative assessment of the dependence type of hydrological time series, selects the optimal model for fitting, and solves the problems of inconsistent discrimination indicators, vague standards and strong subjectivity in traditional methods, thereby improving the understanding of the intrinsic evolution mechanism of hydrological processes and the accuracy of prediction.
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Figure CN122046307A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of hydrological and climatic science and technology, specifically referring to a method for identifying the type of long-short dependence of hydrological time series based on correlation. Background Technology
[0002] Accurately interpreting the rich characteristic information contained in hydrological time series is fundamental to scientifically understanding hydrological dynamics and their evolutionary patterns. Dependence is an important type of characteristic change in hydrological time series, referring to the correlation between the value of a hydrological variable at a certain moment and its previous values; for example, drought or flood events often tend to occur in clusters. The detection and identification of dependency is crucial and is a necessary prerequisite for hydrological analysis and design, simulation and forecasting, and water resource management. Dependence can be divided into two types: long-term dependency and short-term dependency, which are fundamentally different. However, in practice, short-term dependency receives widespread attention, while long-term dependency receives less attention and is often ignored. Short-term dependency, also known as short-memory dependency, exhibits an exponential decay in its autocorrelation coefficient with increasing lag order; long-term dependency, also known as long-memory dependency, exhibits a slow decay in its autocorrelation coefficient with increasing lag order. However, the rapid or slow decay of the autocorrelation coefficient cannot be objectively quantified, thus making it difficult to accurately and reasonably distinguish between short-term and long-term dependency characteristics.
[0003] Currently, many methods have been proposed to detect and characterize the dependence features in time series. In both theoretical research and applied analysis, it is generally accepted that short dependence is described using the first-order autocorrelation coefficient, while long dependence is characterized by the Hearst coefficient. However, the essence of these methods is that they require prior assumptions about the dependence type (short / long) before assessing its statistical significance. In other words, if the prior assumptions are invalid or incorrect, the corresponding dependence type and the significance assessment results will be severely biased. Therefore, using the above two indicators and related analytical methods cannot fundamentally distinguish between the two basic types of short and long dependence.
[0004] Autoregressive (AR), moving average (MA), and autoregressive moving average (ARMA) models provide concise and mathematically tractable modeling frameworks for characterizing short-term dependencies in time series. For describing long-term dependencies, fractional-difference autoregressive moving average (FARIMA) and fractional-Gaussian noise (FGN) models have become two important and widely used stochastic modeling approaches. However, accurately identifying the type of dependency in hydrological time series—whether it is short-term or long-term—and selecting a matching stochastic model for accurate fitting remains a key technical challenge. Furthermore, due to the fundamental differences in theory and characteristics between the two types of dependency, systematically comparing, identifying, and evaluating long-term and short-term dependencies within the same framework is particularly difficult. Currently, no research has systematically integrated models of different dependency types into a unified hydrological time series analysis framework, failing to improve the overall ability to identify the patterns of hydro-climate variable changes. In summary, rationally identifying the type of dependency and selecting an appropriate model for fitting is an important foundation for deepening the understanding of the intrinsic evolution mechanism of hydrological processes and achieving accurate prediction and assessment. Summary of the Invention
[0005] To address the shortcomings of the existing technologies, the present invention aims to provide a correlation-based method for identifying the short-term and long-term dependencies in hydrological time series. This method solves the problems in the existing technologies where the inability to reasonably distinguish and accurately fit the short-term and long-term dependencies in hydrological time series leads to misjudgments of the evolution patterns of hydrological time series, reduced reliability of long-term predictions, and inaccurate uncertainty assessments.
[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:
[0007] The present invention provides a method for identifying the length dependence type of hydrological time series based on correlation, comprising the following steps:
[0008] 1) Identify the original hydrological time series The deterministic components in the data are removed to obtain the remaining time series. ;
[0009] 2) Set the remaining time series The data contains short-dependent components. By fitting and describing these components, we obtain the short-dependent component sequence and the remaining time series. The correlation coefficient between them;
[0010] 3) Set the remaining time series The data contains long-term dependent components. By fitting and describing these components, we obtain the long-term dependent component sequence and the remaining time series. The correlation coefficient between them;
[0011] 4) Compare the correlation coefficients obtained in steps 2) and 3), and record the maximum value as . The corresponding model describes the original hydrological time series. The optimal model for the dependent components, the model type representing the original hydrological time series. The type of length-short dependence;
[0012] 5) Set the maximum correlation coefficient. The correlation coefficient threshold r corresponding to the selected significance level α T Compare and assess the significance of dependent components.
[0013] Furthermore, the deterministic components in step 1) include: jump mutation components, trend components, and periodic components.
[0014] Further, step 1) specifically includes:
[0015] 11) The sliding t-test and ordered clustering method were used to identify the original hydrological time series. skipping mutation components Remove skipping mutation components The remaining sequence after that is denoted as ;
[0016] 12) The MK test and Spearman's rank correlation test are used to identify sequences. Trend components The remaining sequence after removing skipping mutations and trend components is denoted as ;
[0017] 13) Identify sequences using maximum entropy spectral analysis. Periodic components The remaining sequence after removing skipping mutations, trends, and periodic components is denoted as... ,as follows:
[0018] .
[0019] Furthermore, the short-dependent components in step 2) are described by fitting the AR model, MA model, and ARMA model, respectively; the short-dependent component sequences obtained after fitting the three models are compared with the remaining time series. The correlation coefficients between them are denoted as follows: , , .
[0020] Further, step 2) specifically includes:
[0021] 21) Fit the remaining time series using an AR model. For the short-dependent components in the model, the optimal order p of the AR model is determined using the CCIC criterion, and the model parameters are estimated using the least squares method. The short-dependent component sequences fitted by the AR model and the remaining time series are calculated. Correlation coefficient between ,as follows:
[0022] ;
[0023] in, , , …, These are the autoregressive coefficients of the AR model; , , …, For the remaining time series The autocorrelation coefficient; p is the optimal order of the AR model;
[0024] 22) Fit the remaining time series using the MA model. For the short-dependent components in the model, the optimal order q of the MA model is determined using the CCIC criterion, and the model parameters are estimated using the least squares method. The short-dependent component sequences and the remaining time series fitted by the MA model are calculated. Correlation coefficient between ,as follows:
[0025] ;
[0026] in, , ,…, q represents the moving average coefficients of the MA model; q is the optimal order of the MA model.
[0027] 23) Fit the remaining time series using the ARMA model. For the short-dependent components in the model, the CCIC criterion is used to determine the optimal order of the ARMA model, and the least squares method is used to estimate its model parameters. The short-dependent component sequences and the remaining time series fitted by the ARMA model are calculated. Correlation coefficient between ,as follows:
[0028] ;
[0029] in, , ,…, These are the autoregressive coefficients of the ARMA model; , ,…, q' represents the moving average coefficient of the ARMA model; p' represents the optimal autoregressive order of the ARMA model; and q' represents the optimal moving average order of the ARMA model.
[0030] Furthermore, the long-term dependent components in step 3) are described by fitting the FAR model, FMA model, FARMA model, and SMA model, respectively. The long-term dependent component sequences obtained after fitting the four models are compared with the remaining time series. The correlation coefficients between them are denoted as follows: , , , .
[0031] Furthermore, step 3) specifically includes:
[0032] 31) Use the Climacogram method to estimate the remaining time series. Given the Hearst coefficients H, calculate the fractional difference order d as follows:
[0033] d = H - 0.5;
[0034] 32) For the remaining time series Perform fractional-order differences to obtain the difference sequence. ,as follows:
[0035] ;
[0036] ;
[0037] in, For fractional difference operators, Represents the Gamma function. This represents the difference weighting coefficient of the h-th term. Represents the remaining time series The values at h time points before time t;
[0038] 33) The FAR model is used to fit and describe the remaining time series. When dealing with long-term dependent components, the process is transformed into fitting the difference sequence using an AR model. The dependent components in the model are analyzed, and the optimal model order is determined using the CCIC criterion. The model parameters are estimated using the least squares method. The long-dependent component sequences and the remaining time series fitted by the FAR model are calculated. Correlation coefficient between ,as follows:
[0039] ;
[0040] in, This represents the optimal order of the FAR model.
[0041] 34) The FMA model is used to fit and describe the remaining time series. When dealing with long-term dependent components, convert them to differential sequences described using an MA model. The dependent components in the model are analyzed, and the optimal model order is determined using the CCIC criterion. The model parameters are estimated using the least squares method. The long-dependent component sequences and the remaining time series fitted by the FMA model are calculated. Correlation coefficient between ,as follows:
[0042] ;
[0043] in, This represents the optimal order of the FMA model.
[0044] 35) Use the FARMA model to describe the remaining time series. The long-term dependent components in the sequence are transformed into differential sequences described by an ARMA model. The dependent components in the model are analyzed, and the optimal order of the model is determined using the CCIC criterion. The model parameters are estimated using the least squares method. The long dependent component sequence and the remaining time series fitted by the FARMA model are calculated. Correlation coefficient between ,as follows:
[0045] ;
[0046] in, Let be the autoregressive order of the FARMA model; Let be the order of the moving average of the FARMA model;
[0047] 36) Use the SMA model to describe the remaining time series. The long-term dependent components in the model are analyzed, and the optimal model order is determined using the CCIC criterion. The model parameters are estimated using the least squares method. The long-term dependent component sequences and the remaining time series fitted by the SMA model are calculated. Correlation coefficient between .
[0048] Furthermore, step 36) specifically includes:
[0049] 361) Calculate the symmetric moving average coefficients of the SMA model using the following formula:
[0050] ;
[0051] ;
[0052] in, For the remaining time series The variance; , , …, , , , …, , Let be the coefficients of the symmetric moving average; all symmetric moving average coefficients with respect to the central term. symmetry, The order of the symmetric moving average model;
[0053] 362) Calculate the long-dependent component sequence and the remaining time series fitted by the SMA model. Correlation coefficient between The formula is as follows:
[0054] .
[0055] Furthermore, step 5) specifically includes:
[0056] 51) Select a 5% significance level and calculate the corresponding correlation coefficient threshold r. T ,as follows:
[0057] ;
[0058] in, Describing the degrees of freedom as and The critical value of the F-distribution at a significance level of α=5%;
[0059] 52) Comparison and r T The magnitude of the value, if If the identified dependent components are statistically significant, then... If the identified dependent components are not statistically significant, then the dependent components are not statistically significant.
[0060] The beneficial effects of this invention are:
[0061] The method of this invention can not only accurately identify the type of dependency characteristics in hydrological time series and quantitatively evaluate their significance, but also simultaneously select the optimal model for fitting, effectively solving the defects of traditional methods in dependency type identification, such as inconsistent discrimination indicators, vague standards, and strong subjectivity.
[0062] This invention constructs the correlation coefficient as an effective indicator, realizing a unified and standardized characterization of short-term and long-term dependencies. It solves the technical bottleneck that makes it difficult to conduct simultaneous research within the same framework due to the essential differences in the structures of the two types of dependencies. Thus, it can provide key technical methodological basis for deeply revealing the intrinsic evolution mechanism of hydrological processes and achieving accurate prediction and assessment. Attached Figure Description
[0063] Figure 1 This is a flowchart of the method of the present invention;
[0064] Figure 2a A schematic diagram of an artificially generated sequence S11 with short dependencies that follow an AR(1) process;
[0065] Figure 2b A schematic diagram of an artificially generated sequence S12 with short dependencies that follow an AR(1) process;
[0066] Figure 2c A schematic diagram of an artificially generated sequence S13 with short dependencies that follow an AR(1) process;
[0067] Figure 3a A schematic diagram of an artificially generated sequence S21 with short dependencies that follow an MA(1) process;
[0068] Figure 3b A schematic diagram of an artificially generated sequence S22 with short dependencies that follow an MA(1) process;
[0069] Figure 3c A schematic diagram of an artificially generated sequence S23 with short dependencies that follow an MA(1) process;
[0070] Figure 4a A schematic diagram of an artificially generated sequence S31 with short dependencies that follow an ARMA(1,1) process;
[0071] Figure 4b A schematic diagram of an artificially generated sequence S32 with short dependencies that follow an ARMA(1,1) process;
[0072] Figure 4c A schematic diagram of an artificially generated sequence S33 with short dependencies that follow an ARMA(1,1) process;
[0073] Figure 5a A schematic diagram of an artificially generated sequence S41 that exhibits long dependency following a FAR(1) process;
[0074] Figure 5b A schematic diagram of an artificially generated sequence S42 that exhibits long dependency following a FAR(1) process;
[0075] Figure 5c A schematic diagram of an artificially generated sequence S43 that exhibits long dependency following a FAR(1) process;
[0076] Figure 6a A schematic diagram of an artificially generated sequence S51 with long dependency following an FMA(1) process;
[0077] Figure 6bA schematic diagram of an artificially generated sequence S52 that exhibits long dependency following an FMA(1) process;
[0078] Figure 6c A schematic diagram of an artificially generated sequence S53 that exhibits long dependency following an FMA(1) process;
[0079] Figure 7a A schematic diagram of an artificially generated sequence S61 that exhibits long dependency following a FARMA(1,1) process;
[0080] Figure 7b A schematic diagram of an artificially generated sequence S62 that exhibits long dependency following a FARMA(1,1) process;
[0081] Figure 7c A schematic diagram of artificially generated sequence S63 with long dependency following the FARMA(1,1) process;
[0082] Figure 8a A schematic diagram of an artificially generated sequence S71 that exhibits long dependency following an SMA(1) process;
[0083] Figure 8b A schematic diagram of an artificially generated sequence S72 that exhibits long dependency following an SMA(1) process;
[0084] Figure 8c This is a schematic diagram of an artificially generated sequence S73 that has long dependence following an SMA(1) process. Detailed Implementation
[0085] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and accompanying drawings. The content mentioned in the embodiments is not intended to limit the present invention.
[0086] Reference Figure 1 As shown, the present invention provides a method for identifying the length dependence type of hydrological time series based on correlation, comprising the following steps:
[0087] 1) Identify the original hydrological time series The deterministic components in the data are removed to obtain the remaining time series. ;
[0088] The deterministic components include: jump mutation components, trend components, and periodic components.
[0089] Step 1) specifically includes:
[0090] 11) The sliding t-test and ordered clustering method were used to identify the original hydrological time series. skipping mutation components Remove skipping mutation components The remaining sequence after that is denoted as ;
[0091] 12) The MK test and Spearman's rank correlation test are used to identify sequences. Trend components The remaining sequence after removing skipping mutations and trend components is denoted as ;
[0092] 13) Identify sequences using maximum entropy spectral analysis. Periodic components The remaining sequence after removing skipping mutations, trends, and periodic components is denoted as... ,as follows:
[0093] .
[0094] 2) Set the remaining time series The data contains short-dependent components. By fitting and describing these components, we obtain the short-dependent component sequence and the remaining time series. The correlation coefficient between them;
[0095] The short-dependent components are described by fitting the AR model, MA model, and ARMA model, respectively; the short-dependent component sequences obtained after fitting the three models are compared with the remaining time series. The correlation coefficients between them are denoted as follows: , , .
[0096] Step 2) specifically includes:
[0097] 21) Fit the remaining time series using an AR model. For the short-dependent components in the model, the optimal order p of the AR model is determined using the CCIC criterion, and the model parameters are estimated using the least squares method. The short-dependent component sequences fitted by the AR model and the remaining time series are calculated. Correlation coefficient between ,as follows:
[0098] ;
[0099] in, , , …, These are the autoregressive coefficients of the AR model; , , …, For the remaining time series The autocorrelation coefficient; p is the optimal order of the AR model;
[0100] 22) Fit the remaining time series using the MA model. For the short-dependent components in the model, the optimal order q of the MA model is determined using the CCIC criterion, and the model parameters are estimated using the least squares method. The short-dependent component sequences and the remaining time series fitted by the MA model are calculated. Correlation coefficient between ,as follows:
[0101] ;
[0102] in, , ,…, q represents the moving average coefficients of the MA model; q is the optimal order of the MA model.
[0103] 23) Fit the remaining time series using the ARMA model. For the short-dependent components in the model, the CCIC criterion is used to determine the optimal order of the ARMA model, and the least squares method is used to estimate its model parameters. The short-dependent component sequences and the remaining time series fitted by the ARMA model are calculated. Correlation coefficient between ,as follows:
[0104] ;
[0105] in, , ,…, These are the autoregressive coefficients of the ARMA model; , ,…, q' represents the moving average coefficient of the ARMA model; p' represents the optimal autoregressive order of the ARMA model; and q' represents the optimal moving average order of the ARMA model.
[0106] 3) Set the remaining time series The data contains long-term dependent components. By fitting and describing these components, we obtain the long-term dependent component sequence and the remaining time series. The correlation coefficient between them;
[0107] The length-dependent components are described by fitting the FAR model, FMA model, FARMA model, and SMA model, respectively. The length-dependent component sequences obtained after fitting the four models are compared with the remaining time series. The correlation coefficients between them are denoted as follows: , , , .
[0108] Step 3) specifically includes:
[0109] 31) Use the Climacogram method to estimate the remaining time series. Given the Hearst coefficients H, calculate the fractional difference order d as follows:
[0110] d = H - 0.5;
[0111] 32) For the remaining time series Perform fractional-order differences to obtain the difference sequence. ,as follows:
[0112] ;
[0113] ;
[0114] in, For fractional difference operators, Represents the Gamma function. This represents the difference weighting coefficient of the h-th term. Represents the remaining time series The values at h time points before time t;
[0115] 33) The FAR model is used to fit and describe the remaining time series. When dealing with long-term dependent components, the process is transformed into fitting the difference sequence using an AR model. The dependent components in the model are analyzed, and the optimal model order is determined using the CCIC criterion. The model parameters are estimated using the least squares method. The long-dependent component sequences and the remaining time series fitted by the FAR model are calculated. Correlation coefficient between ,as follows:
[0116] ;
[0117] in, This represents the optimal order of the FAR model.
[0118] 34) The FMA model is used to fit and describe the remaining time series. When dealing with long-term dependent components, convert them to differential sequences described using an MA model. The dependent components in the model are analyzed, and the optimal model order is determined using the CCIC criterion. The model parameters are estimated using the least squares method. The long-dependent component sequences and the remaining time series fitted by the FMA model are calculated. Correlation coefficient between ,as follows:
[0119] ;
[0120] in, This represents the optimal order of the FMA model.
[0121] 35) Use the FARMA model to describe the remaining time series. The long-term dependent components in the sequence are transformed into differential sequences described by an ARMA model. The dependent components in the model are analyzed, and the optimal order of the model is determined using the CCIC criterion. The model parameters are estimated using the least squares method. The long dependent component sequence and the remaining time series fitted by the FARMA model are calculated. Correlation coefficient between ,as follows:
[0122] ;
[0123] in, Let be the autoregressive order of the FARMA model; Let be the order of the moving average of the FARMA model;
[0124] 36) Use the SMA model to describe the remaining time series. The long-term dependent components in the model are analyzed, and the optimal model order is determined using the CCIC criterion. The model parameters are estimated using the least squares method. The long-term dependent component sequences and the remaining time series fitted by the SMA model are calculated. Correlation coefficient between .
[0125] Specifically, step 36) includes:
[0126] 361) Calculate the symmetric moving average coefficients of the SMA model using the following formula:
[0127] ;
[0128] ;
[0129] in, For the remaining time series The variance; , , …, , , , …, , Let be the coefficients of the symmetric moving average; all symmetric moving average coefficients with respect to the central term. symmetry, The order of the symmetric moving average model;
[0130] 362) Calculate the long-dependent component sequence and the remaining time series fitted by the SMA model. Correlation coefficient between The formula is as follows:
[0131] .
[0132] 4) Compare the correlation coefficients obtained in steps 2) and 3), and record the maximum value as . The corresponding model describes the original hydrological time series. The optimal model for the dependent components, the model type representing the original hydrological time series. The type of long-short dependence.
[0133] 5) Set the maximum correlation coefficient. The correlation coefficient threshold r corresponding to the selected significance level α (usually 5%) T Comparisons were made to assess the significance of dependent components; specifically including:
[0134] 51) Select a 5% significance level and calculate the corresponding correlation coefficient threshold r. T ,as follows:
[0135] ;
[0136] in, Describing the degrees of freedom as and The critical value of the F-distribution at a significance level of α=5%;
[0137] 52) Comparison and r T The magnitude of the value, if If the identified dependent components are statistically significant, then... If the identified dependent components are not statistically significant, then the dependent components are not statistically significant.
[0138] In the example: Since the dependency types and other characteristics of artificially generated sequences are known, using artificially generated sequences is beneficial for verifying the effectiveness of the method of the present invention; however, the dependency types and significance of measured hydrological and climate time series are often unknown, making it impossible to accurately determine the accuracy of the method of the present invention in identifying the dependency types of time series. To demonstrate the accuracy of the method of the present invention in identifying the dependency types of time series, seven types of artificial sequences were generated during the design phase to test the accuracy of the method of the present invention in identifying long / short dependency types under different conditions, as well as the effectiveness of the method of the present invention in improving the identification results of time series dependency features.
[0139] The first type of time series is an AR(1) process with the same sequence length, denoted as S11, S12, and S13. Figure 2a , Figure 2b , Figure 2c The second type of time series is an MA(1) process with the same sequence length, denoted as S21, S22, and S23. Figure 3a , Figure 3b , Figure 3c The third type of time series is an ARMA(1,1) process with the same sequence length, denoted as S31, S32, and S33. Figure 4a , Figure 4b , Figure 4c The fourth type of time series is the FAR(1) process, with the same sequence length, denoted as S41, S42, and S43. Figure 5a , Figure 5b , Figure 5c The fifth type of time series is the FMA(1) process, with the same sequence length, denoted as S51, S52, and S53. Figure 6a , Figure 6b , Figure 6c The sixth type of time series is a FARMA(1,1) process with the same sequence length, denoted as S61, S62, and S63. Figure 7a , Figure 7b , Figure 7c The seventh type of time series is an SMA(1) process with the same sequence length, denoted as S71, S72, and S73. Figure 8a , Figure 8b , Figure 8c The dependency types of all the time series generated above were identified and judged using the method of the present invention. The results are shown in Table 1 (dependency discrimination results of artificially generated sequences with different dependency types).
[0140] Table 1
[0141]
[0142] The dependency identification results show that, regardless of whether it is the AR(1), MA(1), and ARMA(1,1) model sequences (S11-S33) with short dependency characteristics, or the FAR(1), FMA(1), FARMA(1,1), and SMA(1) model sequences (S41-S73) with long dependency characteristics, the method of this invention can accurately identify the corresponding optimal dependency model and accurately determine its long or short dependency type. The identification results of all test sequences are completely consistent with the theoretical model, and no misjudgments have occurred. The above results indicate that accurately identifying the dependency type of hydrological time series is an important prerequisite for establishing a highly fit stochastic model and improving the reliability of hydrological prediction. Compared to traditional methods that rely on the shape of autocorrelation plots for subjective judgment, the method of this invention first accurately identifies the best-fit model of the dependence of hydrological time series based on correlation theory, and then quantitatively determines and evaluates the significance of the long / short dependence type of hydrological time series. This can effectively eliminate the serious bias in the analysis results of traditional methods, thereby obtaining more objective and accurate dependence identification results.
[0143] Comparative analysis of the above time series dependency identification results yields the following important conclusions: (1) Although there are essential differences in statistical significance between the long and short dependency characteristics of hydrological time series, the measured hydrological time series are often short, which makes it very difficult to accurately distinguish and quantitatively describe the long / short dependency characteristics; (2) Traditional methods rely solely on whether the autocorrelation coefficient exhibits "exponential decay" (short dependency) or "slow decay" (long dependency) for qualitative judgment and distinction. This approach is overly dependent on subjective experience, lacks strict statistical testing standards, and is prone to misjudgment; (3) The method of this invention can not only accurately identify the long / short dependency type of the time series, but also further determine its optimal model for fitting, realizing a technological leap from qualitative judgment to quantitative identification. The identification results of this method are more accurate and reliable, and can provide strong methodological support for accurately revealing the evolution characteristics of hydrological and climatic processes, constructing high-precision dependency simulation and prediction models, and scientifically assessing the impact of climate change.
[0144] This invention has many specific applications. The above description is only a preferred embodiment of this invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of this invention, and these improvements should also be considered within the scope of protection of this invention.
Claims
1. A method for identifying the length-dependent type of hydrological time series based on correlation, characterized in that, The steps are as follows: 1) Identify the original hydrological time series The deterministic components in the data are removed to obtain the remaining time series. ; 2) Set the remaining time series The data contains short-dependent components. By fitting and describing these components, we obtain the short-dependent component sequence and the remaining time series. The correlation coefficient between them; 3) Set the remaining time series The data contains long-term dependent components. By fitting and describing these components, we obtain the long-term dependent component sequence and the remaining time series. The correlation coefficient between them; 4) Compare the correlation coefficients obtained in steps 2) and 3), and record the maximum value as . The corresponding model describes the original hydrological time series. The optimal model for the dependent components, the model type representing the original hydrological time series. The type of length-short dependence; 5) Set the maximum correlation coefficient. The correlation coefficient threshold r corresponding to the selected significance level α T Compare and assess the significance of dependent components.
2. The method for identifying the long-short dependence type of hydrological time series based on correlation according to claim 1, characterized in that, The deterministic components in step 1) include: jump mutation components, trend components, and periodic components.
3. The method for identifying the length-short dependence type of hydrological time series based on correlation according to claim 2, characterized in that, Step 1) specifically includes: 11) The sliding t-test and ordered clustering method were used to identify the original hydrological time series. skipping mutation components Remove skipping mutation components The remaining sequence after that is denoted as ; 12) The MK test and Spearman's rank correlation test are used to identify sequences. Trend components The remaining sequence after removing skipping mutations and trend components is denoted as ; 13) Identify sequences using maximum entropy spectral analysis. Periodic components The remaining sequence after removing skipping mutations, trends, and periodic components is denoted as... ,as follows: 。 4. The method for identifying the long-short dependence type of hydrological time series based on correlation according to claim 3, characterized in that, The short-dependent components in step 2) are described by fitting the AR model, MA model, and ARMA model, respectively; the short-dependent component sequences obtained after fitting the three models are compared with the remaining time series. The correlation coefficients between them are denoted as follows: , , .
5. The method for identifying the long-short dependence type of hydrological time series based on correlation according to claim 4, characterized in that, Step 2) specifically includes: 21) Fit the remaining time series using an AR model. For the short-dependent components in the model, the optimal order p of the AR model is determined using the CCIC criterion, and the model parameters are estimated using the least squares method. The short-dependent component sequences fitted by the AR model and the remaining time series are calculated. Correlation coefficient between ,as follows: ； in, , , …, These are the autoregressive coefficients of the AR model; , , …, For the remaining time series The autocorrelation coefficient; p is the optimal order of the AR model; 22) Fit the remaining time series using the MA model. For the short-dependent components in the model, the optimal order q of the MA model is determined using the CCIC criterion, and the model parameters are estimated using the least squares method. The short-dependent component sequences and the remaining time series fitted by the MA model are calculated. Correlation coefficient between ,as follows: ； in, , ,…, q represents the moving average coefficients of the MA model; q is the optimal order of the MA model. 23) Fit the remaining time series using the ARMA model. For the short-dependent components in the model, the CCIC criterion is used to determine the optimal order of the ARMA model, and the least squares method is used to estimate its model parameters. The short-dependent component sequences and the remaining time series fitted by the ARMA model are calculated. Correlation coefficient between ,as follows: ； in, , ,…, These are the autoregressive coefficients of the ARMA model; , ,…, q' represents the moving average coefficient of the ARMA model; p' represents the optimal autoregressive order of the ARMA model; and q' represents the optimal moving average order of the ARMA model.
6. The method for identifying the long-short dependence type of hydrological time series based on correlation according to claim 5, characterized in that, In step 3), the length-dependent components are described by fitting the FAR model, FMA model, FARMA model, and SMA model, respectively. The length-dependent component sequences obtained after fitting the four models are compared with the remaining time series. The correlation coefficients between them are denoted as follows: , , , .
7. The method for identifying the long-short dependence type of hydrological time series based on correlation according to claim 6, characterized in that, Step 3) specifically includes: 31) Use the Climacogram method to estimate the remaining time series. Given the Hearst coefficients H, calculate the fractional difference order d as follows: d = H - 0.5; 32) For the remaining time series Perform fractional-order differences to obtain the difference sequence. ,as follows: ； ； in, For fractional difference operators, Represents the Gamma function. This represents the difference weighting coefficient of the h-th term. Represents the remaining time series The values at h time points before time t; 33) The FAR model is used to fit and describe the remaining time series. When dealing with long-term dependent components, the process is transformed into fitting the difference sequence using an AR model. The dependent components in the model are analyzed, and the optimal model order is determined using the CCIC criterion. The model parameters are estimated using the least squares method. The long-dependent component sequences and the remaining time series fitted by the FAR model are calculated. Correlation coefficient between ,as follows: ； in, This represents the optimal order of the FAR model. 34) The FMA model is used to fit and describe the remaining time series. When dealing with long-term dependent components, convert them to differential sequences described using an MA model. The dependent components in the model are analyzed, and the optimal model order is determined using the CCIC criterion. The model parameters are estimated using the least squares method. The long-dependent component sequences and the remaining time series fitted by the FMA model are calculated. Correlation coefficient between ,as follows: ； in, This represents the optimal order of the FMA model. 35) Use the FARMA model to describe the remaining time series. The long-term dependent components in the sequence are transformed into differential sequences described by an ARMA model. The dependent components in the model are analyzed, and the optimal order of the model is determined using the CCIC criterion. The model parameters are estimated using the least squares method. The long dependent component sequence and the remaining time series fitted by the FARMA model are calculated. Correlation coefficient between ,as follows: ； in, Let be the autoregressive order of the FARMA model; Let be the order of the moving average of the FARMA model; 36) Use the SMA model to describe the remaining time series. The long-term dependent components in the model are analyzed, and the optimal model order is determined using the CCIC criterion. The model parameters are estimated using the least squares method. The long-term dependent component sequences and the remaining time series fitted by the SMA model are calculated. Correlation coefficient between .
8. The method for identifying the long-short dependence type of hydrological time series based on correlation according to claim 7, characterized in that, Step 36) specifically includes: 361) Calculate the symmetric moving average coefficients of the SMA model using the following formula: ； ； in, For the remaining time series The variance; , , …, , , , …, , Let be the coefficients of the symmetric moving average; all symmetric moving average coefficients with respect to the central term. symmetry, The order of the symmetric moving average model; 362) Calculate the long-dependent component sequence and the remaining time series fitted by the SMA model. Correlation coefficient between The formula is as follows: 。 9. The method for identifying the long-short dependence type of hydrological time series based on correlation according to claim 8, characterized in that, Step 5) specifically includes: 51) Select a 5% significance level and calculate the corresponding correlation coefficient threshold r. T ,as follows: ； in, Describing the degrees of freedom as and The critical value of the F-distribution at a significance level of α=5%; 52) Comparison and r T The magnitude of the value, if If the identified dependent components are statistically significant, then... If the identified dependent components are not statistically significant, then the dependent components are not statistically significant.