A Resampling Prediction Method for Seasonal Time Series with Non-negative Integer Values

Abstract

This invention discloses a resampling prediction method for non-negative integer value seasonal time series, comprising the following steps: acquiring historical non-negative integer value time series data and determining the seasonal cycle length corresponding to the time granularity of the data; constructing an integer value time series model and estimating the parameters of the model using the data to obtain a fitted model and a newsletter sequence; performing non-negative correction on newslets with negative values ​​in the newsletter sequence to obtain a corrected newsletter sequence containing only non-negative values; establishing multiple seasonal groups according to the seasonal cycle length, and assigning each newsletter value in the corrected newsletter sequence to the corresponding seasonal group according to its season, forming a perturbation data set with seasonal labels, etc. This invention achieves high-precision and highly practical prediction of non-negative integer counting sequences by constructing a dedicated integer model system, non-negative newsletter correction, seasonal group resampling, and robust median output.

Description

Technical Field

[0001] This invention relates to the field of time series data analysis technology, and in particular to a resampling prediction method for seasonal time series with non-negative integer values. Background Technology

[0002] With the widespread application of data acquisition and sensing technologies, various count-type monitoring indicators have achieved routine collection and storage, forming historical time-series data with non-negative integer observations as the core. This type of data exhibits typical integer counting characteristics, along with obvious monthly / quarterly periodicity, time-series autocorrelation, and excessive dispersion with variance much greater than the mean. It serves as an important basis for trend analysis, resource allocation, decision analysis, and planning management.

[0003] In practical applications, managers need to accurately predict count indicators over a certain period to rationally allocate resources, formulate planning schemes, optimize scheduling strategies, and provide data support for overall trend analysis. However, current mainstream time series forecasting technologies are ill-suited to the inherent characteristics of such data and cannot meet the engineering requirements for high-precision and high-reliability forecasting. Traditional forecasting methods mainly suffer from two types of defects: The first type is continuous time series models represented by ARIMA, VAR, and GARCH. These models are designed for continuous real numbers and, when directly applied to integer count data, are prone to producing invalid results such as negative numbers and decimals that do not conform to business realities. They also cannot handle overly discrete problems and have insufficient fitting ability for seasonal fluctuations. The second type is conventional integer time series models. Although they can adapt to count data, they suffer from problems such as negative innovation estimation, large cumulative bias in multi-step forecast recursion, and lack of dynamic optimization based on seasonal patterns. Their forecasting stability and practicality are weak, making it difficult to support routine decision-making and refined management. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a resampling forecasting method for seasonal time series with non-negative integer values. By constructing a dedicated integer model system, applying non-negative innovation correction, seasonal grouping resampling, and robust median output, it achieves high-precision and highly practical forecasting of non-negative integer count series.

[0005] According to one aspect of the present invention, a method for resampling and forecasting seasonal time series with non-negative integer values ​​is provided, comprising the following steps: Obtain historical non-negative integer time series data and determine the seasonal cycle length corresponding to the time granularity of the data; Construct an integer-valued time series model, and use the data to estimate the parameters of the model to obtain the fitted model and the innovation sequence; The negative values ​​in the aforementioned innovation sequence are corrected to non-negative values ​​to obtain a corrected innovation sequence containing only non-negative values. Multiple seasonal groups are established according to the length of the seasonal cycle. Each innovation value in the modified innovation sequence is assigned to the corresponding seasonal group according to its season, forming a perturbation data set with seasonal labels. Set the number of repetitions to B, and generate B prediction paths through model-guided random sampling: For the h-th future step, determine the seasonal label to which the step belongs, randomly read a modified innovation value from the seasonal group corresponding to the seasonal label as a perturbation term, and recursively calculate using the fitted model and the previously generated prediction value to obtain the candidate prediction value for the h-th step; traverse all future time steps to form a prediction path; repeat the random reading and recursive calculation process to obtain a total of B independent prediction paths; For each future time step, from the B candidate predicted values ​​generated by the B predicted paths in this step, the numerical value used to characterize the final prediction result of this step is determined through numerical sorting and centering operations, and the final output is ensured to be a non-negative integer.

[0006] The aforementioned technical solution aims to address three core issues faced by multi-step forecasting of seasonal time series with non-negative integer values: first, the output of traditional continuous models does not conform to the constraints of count data; second, existing integer models suffer from severe error accumulation in multi-step recursion and lack seasonality utilization mechanisms; and third, random perturbations in a single forecast path lead to insufficient stability of the results. To address these issues, the solution constructs a technical process that combines innovation correction, reuse of seasonal grouping perturbations, and robust integration of multiple paths, enabling the forecasting process to stably produce legitimate and usable non-negative integer results.

[0007] The essential features and technical effects of this solution are reflected in the following three aspects.

[0008] First, the non-negativity constraint handling of the innovation sequence forms the underlying guarantee for the prediction process. Conventional integer models, after parameter estimation, may produce innovation sequences containing negative values. These negative values ​​are repeatedly substituted into the model during multi-step recursion, causing intermediate calculation results to overflow the valid numerical space, thus deviating the predicted values ​​from the actual values ​​of the count data. This scheme, by implementing non-negativity correction on the innovation sequence, fundamentally cuts off the propagation path of negative values ​​to subsequent calculations, ensuring that the input perturbation term in each recursive step always satisfies the non-negativity constraint, providing the necessary conditions for the numerical stability of the prediction process.

[0009] Second, a perturbation grouping and targeted extraction mechanism based on seasonal labels explicitly embeds seasonal information into the stochastic simulation process. Unlike treating historical perturbations as an indiscriminate set for global sampling, this scheme divides the correction information into corresponding groups according to the seasonal cycle. During prediction, the perturbation term is obtained from the corresponding group based on the seasonal label of the target time step. This process ensures that the perturbation injection is synchronized with the cyclical fluctuations of the sequence itself, avoiding interference from the mixing of cross-seasonal error modes on the prediction path, thereby improving the prediction accuracy of seasonal inflection points and peak periods.

[0010] Third, the strategy of generating and centering multiple prediction paths effectively suppresses the amplification effect of fluctuations in stochastic simulations. The recursive process of multi-step prediction can easily amplify the deviation of a single disturbance step by step, making the final result heavily dependent on the accidental performance of a certain path. This scheme generates multiple independent prediction paths through repeated sampling, and then replaces the simple mean or single path result with the output method of sorting and centering. Without relying on the assumption of disturbance distribution, it reduces the interference of abnormal paths on the final output, and makes the prediction results maintain good robustness in multi-step scenarios.

[0011] In some embodiments, the integer value time series model is at least one of the INAR model, INGARCH model, R-ARIMA model, or R-VAR model.

[0012] In the above technical solution, specific limitations are made on the model selection in the aforementioned prediction method, specifying that the integer value time series model is at least one of the INAR model, INGARCH model, R-ARIMA model, or R-VAR model.

[0013] The essential feature of this technology lies in the construction of a hierarchical and complementary model system, and its technical effect is reflected in the comprehensive adaptation of multi-dimensional features of non-negative integer time series data.

[0014] First, the four types of models complement each other in their integer generation mechanisms. The INAR model, with a binomial sparse operator at its core, directly guarantees non-negative integer outputs within its model structure, satisfying the value constraints of count data without post-processing. The R-ARIMA model, on the other hand, employs a strategy of continuous prediction followed by rounding, providing an alternative implementation path for count sequences with strong trends. These two types of models offer solutions with different mechanisms for the same integer adaptation requirement, expanding the technical coverage for different data scenarios.

[0015] Second, the INGARCH model features a dedicated conditional heteroscedasticity structure, which compensates for the shortcomings of the first two types of models when dealing with overly discrete data. When the series variance is significantly greater than the mean, the fixed innovation variance assumption of INAR and R-ARIMA can lead to inaccurate prediction intervals. By associating the conditional variance with the conditional expectation, INGARCH enables the model to adaptively capture volatility clustering, thereby improving the prediction reliability during periods of high volatility.

[0016] Third, the R-VAR model, by introducing seasonal dummy variables, explicitly encodes seasonal effects at the model structure level, achieving joint modeling of multivariate count indicators and seasonal cycles. Combined with the seasonal grouping resampling mechanism in the aforementioned prediction framework, this model simultaneously embeds seasonal information into both parameter estimation and perturbation injection, making fuller use of seasonal patterns in diverse scenarios.

[0017] The four types of models mentioned above approach the problem from three dimensions: integer generation, over-discrete fitting, and seasonal effect modeling. The selection method supports single-model operation or multi-model parallel integration, enabling the prediction method to maintain a unified process framework while having the ability to respond differently to different data characteristics.

[0018] In some embodiments, constructing the integer value time series model further includes: Verify whether the model order satisfies the stationarity condition; If the condition is not met, the model order will be automatically adjusted within the preset order search range until the stationarity condition is met or the upper limit of the order is reached.

[0019] The above technical solution further defines the construction process of the integer-valued time series model in the prediction method. This feature is located in the model preparation stage of the overall prediction process, and its role is to provide a structurally sound and mathematically reliable model foundation for subsequent parameter estimation, innovation extraction, and resampling prediction.

[0020] The essential feature of this technology lies in embedding stationarity testing and adaptive order adjustment into the model building process, and its technical effect is reflected on two levels.

[0021] First, in integer-valued time series models, non-stationary conditions such as the sum of coefficients in the INAR model exceeding the unit interval, the sum of coefficients of the autoregressive and ARCH terms (or threshold terms) in the INGARCH model exceeding the limit, and the eigenvalues ​​of the VAR model falling within the unit circle can cause the recursive process of multi-step prediction to diverge or produce systematic shifts. Existing conventional methods often rely on manual trial and error or fixed low-order settings, making it difficult to balance flexibility and reliability. This technical feature automatically iterates and verifies within the order search range, enabling the model construction process to avoid non-stationary structures and ensuring that the recursive skeleton meets the mathematical conditions for stable convergence, providing a reliable structural guarantee for the generation of subsequent prediction paths.

[0022] Second, time series data with non-negative integer values ​​from different sources exhibit significant differences in their autocorrelation structures, making it difficult to universally apply a single preset order. This feature uses a preset search range as a boundary and stationarity as a constraint to drive order adjustment, ensuring that the determination of the model order is guided by the inherent characteristics of the data rather than by human pre-setting. This enhances the reproducibility and engineering deployment efficiency of the method in various application scenarios.

[0023] In some embodiments, the non-negative correction of negative values ​​in the information sequence specifically involves: setting the negative information to 0; or taking the absolute value of the negative information; or performing an exponential transformation on the negative information to convert it into a non-negative value.

[0024] In the above technical solution, three specific implementation methods are given for the non-negative correction operation of the innovation sequence in the prediction method. This feature is located after the innovation sequence is generated and before the seasonal grouping is constructed in the overall prediction process. It is a transitional link connecting model fitting and perturbation data preparation. Its role is to ensure that all historical perturbation terms entering the subsequent resampling process satisfy the non-negativity constraint.

[0025] The essential feature of this technology is that it provides three optional nonnegation processing paths, each with a technical effect corresponding to different application requirements, forming a hierarchical correction strategy.

[0026] First, the negative value zeroing strategy eliminates illegal perturbations in the most direct way, uniformly reducing the negative biases generated by the model in historical fitting to zero. This method is computationally simple, efficient in execution, and applicable to most conventional prediction scenarios. It can block the propagation path of negative values ​​to subsequent recursive calculations with minimal overhead, ensuring the legitimacy of perturbation data in the sampling pool.

[0027] Secondly, the absolute value correction strategy achieves non-negativity while preserving the amplitude of the perturbation. When the historical information is negative, its absolute value reflects the magnitude of the model fitting deviation; simply setting it to zero would lose this amplitude information. By taking the absolute value of the negative value, this method preserves the fluctuation intensity distribution characteristics of the original perturbation sequence while satisfying the non-negativity constraint, making it suitable for scenarios with high sensitivity requirements for the prediction interval.

[0028] Third, the exponential transformation correction strategy transforms all innovation values ​​into the positive range through nonlinear mapping, eliminating negative values ​​while maintaining the original relative order of magnitude among perturbations. Compared to the first two methods, the exponential transformation neither truncates nor reverses the numerical relationships, better preserving the statistical distribution structure of the original innovation sequence, and is suitable for complex counting sequences where the perturbation distribution shape has a significant impact on prediction accuracy.

[0029] These three approaches enable the method to flexibly select the appropriate nonnegation processing path based on the degree of data dispersion, fluctuation characteristics, and prediction sensitivity requirements, thus avoiding the problem that a single correction strategy is not adaptable to different data scenarios.

[0030] In some embodiments, the number of times B is repeated is an odd number.

[0031] In the above technical solution, a specific limit is made on the number of times the prediction path is repeatedly generated in the prediction method, B. The parity of the B value is directly related to the operational determinism and output validity when selecting the final result from multiple candidate prediction values.

[0032] The essential feature of this technology lies in providing determinism for the centering selection operation through odd number constraints, and its technical effect is reflected on two levels.

[0033] First, setting B to an odd number ensures the uniqueness of the center selection result. When sorting and selecting the center from B candidate predicted values ​​generated from B prediction paths, if B is even, the center position will correspond to two candidate values. In this case, additional rules such as mean calculation are needed to determine the final output. Mean calculation not only adds computational steps, but more importantly, it may output the mean of two integer candidate values ​​as a decimal, requiring rounding again later, thus introducing quadratic error. By limiting B to an odd number, the sorted candidate sequence has a unique center position, avoiding the ambiguity of double medians and extra computation caused by even values.

[0034] Second, the preceding resampling process has already generated independent prediction paths. The subsequent centering selection operation performs filtering based on these paths, and the parity of B determines the implementation method of the filtering operation. Setting B to an odd number eliminates the need for additional ambiguity handling logic at the interface between path generation and result filtering, making the overall computational path of the prediction process simpler and clearer. Furthermore, an odd B value maintains consistency in centering selection behavior across repeated experiments, which is beneficial for the method to produce predictable output patterns across different datasets and different batches.

[0035] In some embodiments, when the integer value time series model is an INAR model, the recursive relation upon which the recursive calculation is based is:

[0036] in, To estimate parameters for the model, , For a binary sparse operator, From the season The corrected information value randomly read from the corresponding partition. For the first The predicted values ​​generated by each path.

[0037] In the above technical solution, the feature of this technology is that it clearly defines the form of the recursive relationship and organically integrates the autoregressive mechanism of the INAR model with the injection of seasonal perturbations. Its technical effect is reflected in three levels.

[0038] Firstly, the core of the INAR model lies in replacing continuous multiplication with a binomial sparse operator, ensuring that the autoregressive term always outputs a non-negative integer. This recursive relation directly uses this operator, ensuring that the recursive process is governed by... The autoregressive part obtained by sparse operation of the predicted value in the previous step naturally conforms to the non-negative integer constraint, and no additional rounding is required. Structurally, it eliminates the generation of decimals or negative numbers in recursive transmission, and provides underlying computational guarantee for the final output of a valid non-negative integer.

[0039] Secondly, the disturbance term The source is limited to the corrected innovation value in the group corresponding to season s, explicitly embedding seasonal information into the recursive path. Traditional INAR models typically generate perturbations by directly using the overall distribution of the innovation sequence or parameterized assumptions, without distinguishing seasonal differences. This recursive relation, however, mandates that the perturbation in step h must be extracted from the historical corrected innovation group corresponding to the seasonal label of that step. This ensures that the random injection in each recursion is synchronized with the historical seasonal fluctuation pattern of the sequence, thereby mitigating prediction bias caused by the mixing of cross-seasonal error patterns and improving the fitting accuracy of seasonal peaks and inflection points.

[0040] Third, this recursive relationship expresses the model's estimated parameters in a concise single-equation form. By linking historical information repositories with the current prediction state, the INAR model maintains its autoregressive dynamics framework while providing data-driven flexibility to path generation through random sampling. Compared to fully parameterized prediction generation, this hybrid "model-oriented + historical sampling" approach reduces reliance on information distribution assumptions, more robustly reflects historical fluctuations in multi-step recursion, and suppresses cumulative errors caused by distribution assumptions deviating from actual data characteristics.

[0041] In some embodiments, determining the numerical value used to characterize the final prediction result of this step, and ensuring that the final output is a non-negative integer, includes: The numerical values ​​obtained through numerical sorting and center selection operations are processed to become non-negative integers, including rounding the non-integer part to the nearest non-negative integer, rounding down when the distance is the same, and setting negative values ​​to 0.

[0042] In the above technical solution, this technical feature further defines the method for determining the final prediction result in the prediction method. After obtaining candidate results through numerical sorting and center selection operations, the numerical value is processed to be non-negative integer: the non-integer part is rounded to the nearest non-negative integer, and when the distance is the same, it is rounded down, and negative values ​​are uniformly set to zero. The purpose is to ensure that no matter what form of intermediate result is generated by the preceding calculation path, the final output conforms to the non-negative integer value constraint of the count data.

[0043] The technical effects of this feature are reflected on two levels.

[0044] First, conventional rounding rounds up when distances are equal, which can cause a slight positive bias in rounding errors over long-term predictions. This feature specifies rounding down when distances are equal, ensuring that the rounding direction in boundary cases always leans towards the smaller value, avoiding systematic overestimation caused by the inconsistency between the symmetry assumption of the rounding rule and the lower limit constraint of the actual count data. For applications such as resource scheduling and inventory management that rely on upper limit control based on predicted values, this conservative bias helps reduce the risk of redundant resource allocation due to overestimation.

[0045] Second, although the preceding information correction stage has constrained historical disturbances to be non-negative and the selection of intermediate values ​​tends to screen stable candidate values, some candidate values ​​may still be negative under extreme path combinations or model recursion scenarios. This feature adds a negative value zeroing operation at the end of the process to intercept such occasional anomalies with minimal computational cost, ensuring that the predicted values ​​delivered to the downstream decision-making stage are formally valid non-negative integers.

[0046] In some embodiments, after obtaining the historical non-negative integer time series data, the data further includes preprocessing such as cleaning, filling in missing values, and removing outliers.

[0047] In the above technical solution, the data preparation stage of the prediction method is further defined, which aims to improve the integrity and consistency of the input data and provide reliable data support for the downstream computing process.

[0048] The technical effect of this feature is reflected in its positive transmission to subsequent computational stages.

[0049] First, data cleaning and outlier removal eliminate input noise in the original records, providing a fundamental guarantee for the accuracy of subsequent parameter estimation.

[0050] Second, missing value imputation maintains the continuity of time series data and the integrity of the seasonal structure. When modeling non-negative integer time series data, it is usually assumed that observations are at equal intervals. The presence of missing points can disrupt the coherence of the autocorrelation structure, especially for seasonal groups. Missing months will result in insufficient sample size in the corresponding season's information pool, affecting the statistical representativeness of the perturbation extraction. Through missing value imputation, this technical feature ensures that each seasonal group can obtain sufficient corrected information samples.

[0051] According to another aspect of the present invention, a resampling prediction device for seasonal time series with non-negative integer values ​​is provided, comprising: At least one processor and a memory communicatively connected to said at least one processor; The memory stores instructions that can be executed by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform the method described above.

[0052] In the above technical solution, to better operate and process the method, the method is stored in memory, and the processor executes the stored method. It should be noted that the principle and effect of each step have been described above and will not be elaborated upon here.

[0053] According to another aspect of the present invention, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the above-described method.

[0054] In the above technical solution, to better operate and use the method, the method is stored in a computer-readable storage medium and implemented using a processor. It should be noted that the principle and effect of each step have been described above and will not be elaborated upon here. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 This is a flowchart illustrating an embodiment of a resampling prediction method for seasonal time series with non-negative integer values ​​according to the present invention. Detailed Implementation

[0057] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be particularly noted that the following embodiments are for illustrative purposes only and do not limit the scope of the invention. Similarly, the following embodiments are only some, not all, embodiments of the present invention, and all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0058] This invention targets non-negative integer time series data, employing a dedicated integer time series model to address the limitations of traditional continuous time series models in adapting to integer counting scenarios and handling excessively discrete data. Furthermore, considering the strong seasonality of the studied series, the model undergoes seasonal adjustments, and a complete prediction methodology is constructed. A resampling prediction method for non-negative integer seasonal time series is proposed, overcoming the limitations of conventional integer time series models in adapting to strongly seasonal data. This achieves more accurate, stable, and practically applicable non-negative integer time series prediction, enhancing the reliability and practicality of count-based time series analysis.

[0059] Example 1 Please see Figure 1 A resampling forecasting method for seasonal time series with non-negative integer values, comprising the following steps: S1. Obtain historical non-negative integer time series data and determine the seasonal cycle length corresponding to the time granularity of the data; For example, historical non-negative integer time series data are obtained, and the data is cleaned, missing values ​​are filled in, and outliers are removed to determine the seasonal cycle length S of the series, thus completing the data preparation before modeling.

[0060] S2. Construct an integer value time series model, and use the data to estimate the parameters of the model to obtain the fitted model and the innovation sequence; In this embodiment, the integer value time series model is an INAR model, an INGARCH model, an R-ARIMA model, or an R-VAR model.

[0061] In this embodiment, constructing the integer value time series model further includes: Verify whether the model order satisfies the stationarity condition; If the condition is not met, the model order will be automatically adjusted within the preset order search range until the stationarity condition is met or the upper limit of the order is reached.

[0062] For example, based on the integer counting characteristics, overdispersion characteristics, and seasonal effects of the data, INAR, INGARCH, R-ARIMA, and R-VAR models are constructed respectively, and the model order is selected. Adaptive estimation methods are used according to the model type to calculate the parameters of the model coefficients, innovation distribution, and seasonal terms. The innovation estimation sequence is calculated from the observed values ​​and the model fitted values. It is important to note that the correspondence between the three data characteristics and the four models in this invention is as follows: For the integer counting characteristics, the INAR model (raw integer generation mechanism) and the R-ARIMA model (rounding after continuous prediction) are provided, and both can be constructed and run in parallel; for the overdispersion characteristics, the INGARCH model is provided, which explicitly models the non-equivalent relationship between variance and mean through a conditional heteroscedasticity structure; for the seasonal effects, the R-VAR model is provided, which captures periodic fluctuations at the model structure level by introducing seasonal dummy variables. These four types of models adapt to the data characteristics of non-negative integer seasonal time series from different perspectives, forming a complementary prediction model system that can be used individually or in combination depending on the actual scenario. In multivariate forecasting scenarios, the R-VARX model (with external explanatory variables) can be used to replace the R-VAR model, introducing external factors such as economic indicators, temperature, and policies to further improve forecast accuracy.

[0063] The process described in step S2 specifically includes: S21. Set the lower and upper limits of the order for INAR, INGARCH, R-ARIMA, and R-VAR respectively to form the initial candidate order range.

[0064] S22. Determine whether the current order satisfies the model stationarity condition. If the stationarity condition is met (INAR coefficients are less than 1, INGARCH coefficients are less than 1, AR eigenvalues ​​of R-ARIMA are outside the unit circle, and VAR eigenvalues ​​are all outside the unit circle), proceed to S24; if the stationarity condition is not met, proceed to S23.

[0065] S23. Automatically adjust the model order within the initial search range and recalculate the stationarity conditions until the stationarity requirements are met or the upper limit of the order is reached.

[0066] S24. Estimate the parameters of the INAR model using the Yule-Walker method and calculate the autoregressive coefficients. With the mean of new information This ensures that the estimation results are strongly consistent.

[0067] S25. The conditional maximum likelihood method is used to estimate the parameters of the INGARCH model. A likelihood function is constructed with the Poisson distribution as the innovation assumption, and the solution is obtained through numerical optimization. , , If the innovation follows a negative binomial distribution, then the conditional quasi-likelihood method is used for estimation.

[0068] S26. Estimate the level parameters of the R-ARIMA model using moment estimation or maximum likelihood estimation. Autoregression coefficient With moving average coefficient .

[0069] S27. Estimate the parameters of the R-VAR model using the multivariate least squares method, and estimate the coefficient matrix. constant vector and seasonal dummy variables .

[0070] S28. Calculate the original innovation estimation sequence recursively based on the model. INAR model according to The remaining models are derived from the residual definition.

[0071] S3. Perform non-negative correction on the negative values ​​in the news sequence to obtain a corrected news sequence containing only non-negative values; In this embodiment, the non-negative correction of negative values ​​in the information sequence specifically involves: setting the negative information to 0; or taking the absolute value of the negative information; or performing an exponential transformation on the negative information to convert it into a non-negative value.

[0072] For example, a forced correction is applied to negative interest rates to ensure that the interest rate is non-negative. Specifically: determine whether the estimated interest rate is non-negative; if... Retain the current value; if Then the negative interest rate is corrected to 0, resulting in a legally corrected interest rate. The revised rule is as follows:

[0073] In addition to adopting the "negative value to 0" strategy, non-negative correction of the new information can also use absolute value correction or exponential transformation correction to retain the information on the fluctuation of the new information, which is suitable for high-sensitivity prediction scenarios.

[0074] S4. Establish multiple seasonal groups according to the length of the seasonal cycle, and classify each innovation value in the modified innovation sequence into the corresponding seasonal group according to its season to form a perturbation data set with seasonal labels; For example, the revised new information is categorized according to the seasonal cycle S, forming a seasonally differentiated new information database for subsequent bootstrap forecasting. The process specifically includes: S41. Set the seasonal cycle length based on the seasonal fluctuation patterns of the acquired historical data. .

[0075] S42. The revised information will be grouped into the corresponding seasonal group according to the season at which the time point belongs. Assigned to season The corresponding set of new information.

[0076] S43. Determine if all new information has been grouped into seasonal groups. If all have been grouped, proceed to S5; otherwise, return to S42 to continue grouping.

[0077] S5. Set the number of repetitions B, and generate B prediction paths through model-guided random sampling: For the h-th future step, determine the seasonal label to which the step belongs, randomly read a modified innovation value from the seasonal group corresponding to the seasonal label as a perturbation term, and recursively calculate using the fitted model and the previously generated prediction value to obtain the candidate prediction value for the h-th step; traverse all future time steps to form a prediction path; repeat the random reading and recursive calculation process to obtain a total of B independent prediction paths; In this embodiment, the number of times B is repeated is an odd number.

[0078] For example, a seasonally adjusted model-guided bootstrap (MB-Bootstrap) is used to perform multi-step forecasting.

[0079] In this embodiment, when the integer value time series model is an INAR model, the recursive relationship upon which the recursive calculation is based is:

[0080] in, To estimate parameters for the model, , For a binary sparse operator, From the season The corrected information value randomly read from the corresponding partition. For the first The predicted values ​​generated by each path.

[0081] For example, a seasonally adjusted model-guided bootstrap (MB-Bootstrap) is used to perform multi-step predictions. It should be noted that, in addition to using seasonally grouped MB-Bootstrap, seasonal processing can use seasonal ARIMA structures or Fourier seasonal terms to replace seasonal dummy variables, which is suitable for complex scenarios with multiple periods such as monthly and weekly. The process described in step S5 specifically includes: S51, Set prediction step size Number of repeated samplings ( Choose an odd number, such as 501, 1001, or 2001.

[0082] S52, Prediction for each step Disturbance terms are randomly selected from the corresponding seasonal information groups.

[0083] S53, Substitute into the model to recursively generate the first... Predicted paths:

[0084] S54. Determine whether path generation for step B is complete. If complete, proceed to S6; otherwise, return to S52 to continue sampling.

[0085] The specific form of the recursive formula in step S53 depends on the selected integer-valued time series model. When the INAR model is selected, the recursive formula is as follows: It should be understood that the prediction process illustrated above using the INAR model as an example, especially the mechanism of randomly reading the disturbance term from the corresponding seasonal partition and substituting it into the model to recursively generate the prediction path, uses a recursive formula applicable to INAR. Different models use different formulas, which can be modified to match the actual model. When using the INGARCH model, the corrected information is first substituted into the conditional expectation recursive formula, and then candidate predicted values ​​are generated from the corresponding distribution. When using the R-ARIMA or R-VAR model, the corrected information is substituted as a disturbance term into the linear or vector recursive structure of their respective models to generate candidate predicted values. The information used in the recursion of each model is randomly read from the aforementioned seasonal partition cache. After the recursion is completed, the median is uniformly filtered and non-negative integerization is performed as required by S6.

[0086] S6. For each future time step, from the B candidate predicted values ​​generated by the B predicted paths in this step, determine the value used to characterize the final prediction result of this step through numerical sorting and centering operations, and ensure that the final output is a non-negative integer.

[0087] In this embodiment, determining the numerical value used to characterize the final prediction result of this step and ensuring that the final output is a non-negative integer includes: The numerical values ​​obtained through numerical sorting and center selection operations are processed to become non-negative integers, including rounding the non-integer part to the nearest non-negative integer, rounding down when the distance is the same, and setting negative values ​​to 0.

[0088] For example, the median of the results from all predicted paths is taken as the final predicted value. For INAR and INGARCH models, since the model outputs are naturally non-negative integers, the median result is directly usable. For R-ARIMA and R-VAR models, since the recursive output may contain decimals or negative numbers, further non-negative rounding is required. This includes rounding non-integer parts to the nearest non-negative integer, rounding down when the distance is the same, and setting negative values ​​to 0 to ensure that the final output is a valid non-negative integer.

[0089] The method of determining the final predicted value using the median is to... The median of the predicted paths is used to obtain the first path. Step Predicted Value

[0090] Compared with the prior art, what are the advantages of this invention (the advantages can be explained in detail based on specific technical points). advantage: 1. This invention is specifically designed for non-negative integer counting data, ensuring the legality and usability of prediction results from the model's underlying layer. Compared to traditional continuous time series models such as ARIMA, VAR, and GARCH, this invention employs native integer value models such as INAR and INGARCH, along with non-negative rounding and innovation correction mechanisms, fundamentally avoiding prediction results that are inconsistent with practical application scenarios, such as negative numbers or decimals. The output is stable and compliant, and can be directly used for engineering decision-making and quantitative analysis.

[0091] 2. It can effectively handle the over-discreteness of non-negative integer counting sequences, significantly improving prediction accuracy. Traditional models cannot adapt to counting data with deviations much greater than the mean. This invention introduces the INGARCH model, which specifically constructs a conditional heteroscedasticity structure for over-discrete scenarios, greatly improving the fitting and prediction capabilities for scenarios with high fluctuations and sudden changes. 3. Accurately capture and utilize seasonal effects to make the prediction results more consistent with the sequence's own variation patterns. This invention introduces seasonal dummy variables into R-VAR and adopts the MB-Bootstrap strategy with seasonal grouping in the prediction stage, so that future predictions strictly match the seasonal characteristics of the same period in history, solving the prediction bias problem caused by traditional methods ignoring seasonality. 4. The seasonally corrected model-guided bootstrap forecasting method offers enhanced stability in multi-step predictions. Compared to traditional single-point predictions and simple inclusion methods, this invention reduces the impact of random disturbances through multi-path resampling and median output, effectively mitigating the recursive accumulation error problem in multi-step predictions and improving long-term prediction reliability. 5. Constructing a multi-model complementary prediction system with a wider range of applicable scenarios. This invention provides four types of models: INAR (stationary count), INGARCH (overdiscrete), R-ARIMA (trend count), and R-VAR (multivariate mixed variable), which can simultaneously adapt to joint prediction of univariate integer counts and multivariate mixed series, covering the general prediction needs of various non-negative integer time series.

[0092] 6. The overall process is standardized and can be implemented in software, making it more practical for engineering applications. This invention forms a complete and reproducible process for data preprocessing, modeling, parameter estimation, innovation correction, and seasonal bootstrap prediction. It does not require frequent manual adjustments and is easy to encapsulate into software modules and general analysis tools, making it more practical than traditional complex academic models.

[0093] Example 2 A resampling prediction device for non-negative integer value seasonal time series includes: At least one processor and a memory communicatively connected to said at least one processor; The memory stores instructions that can be executed by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform the method described in one of the embodiments.

[0094] In this embodiment, to better run and process the method described in one of the embodiments, the above method is stored in a memory, and the stored method is executed using a processor. It should be noted that the principle and effect of each step have been described above and will not be elaborated further here.

[0095] Example 3 A computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described in one of the embodiments.

[0096] In this embodiment, to better operate and use the method described in one of the embodiments, the above method is stored in a computer-readable storage medium, and the above method is implemented using a processor. It should be noted that the principle and effect of each step have been described above and will not be elaborated further here.

[0097] The above description is only a part of the embodiments of the present invention and does not limit the scope of protection of the present invention. Any equivalent device or equivalent process transformation made based on the content of the present invention specification and drawings, or direct or indirect application in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A resampling forecasting method for seasonal time series with non-negative integer values, characterized in that, Includes the following steps: Obtain historical non-negative integer time series data and determine the seasonal cycle length corresponding to the time granularity of the data; Construct an integer-valued time series model, and use the data to estimate the parameters of the model to obtain the fitted model and the innovation sequence; The negative values ​​in the aforementioned innovation sequence are corrected to non-negative values ​​to obtain a corrected innovation sequence containing only non-negative values. Multiple seasonal groups are established according to the length of the seasonal cycle. Each innovation value in the modified innovation sequence is assigned to the corresponding seasonal group according to its season, forming a perturbation data set with seasonal labels. Set the number of repetitions to B, and generate B prediction paths through model-guided random sampling: For the h-th future step, determine the seasonal label to which the step belongs, randomly read a modified innovation value from the seasonal group corresponding to the seasonal label as a perturbation term, and recursively calculate using the fitted model and the previously generated prediction value to obtain the candidate prediction value for the h-th step; traverse all future time steps to form a prediction path; repeat the random reading and recursive calculation process to obtain a total of B independent prediction paths; For each future time step, from the B candidate predicted values ​​generated by the B predicted paths in this step, the numerical value used to characterize the final prediction result of this step is determined through numerical sorting and centering operations, and the final output is ensured to be a non-negative integer.

2. The resampling prediction method for non-negative integer seasonal time series according to claim 1, characterized in that, The integer value time series model is at least one of the INAR model, INGARCH model, R-ARIMA model, or R-VAR model.

3. The resampling prediction method for non-negative integer seasonal time series according to claim 2, characterized in that, When constructing the integer value time series model, the following is also included: Verify whether the model order satisfies the stationarity condition; If the condition is not met, the model order will be automatically adjusted within the preset order search range until the stationarity condition is met or the upper limit of the order is reached.

4. The resampling prediction method for non-negative integer seasonal time series according to claim 1, characterized in that, The non-negative correction of negative values ​​in the information sequence specifically involves: setting the negative information to 0; or taking the absolute value of the negative information; or performing an exponential transformation on the negative information to convert it into a non-negative value.

5. The resampling prediction method for non-negative integer seasonal time series according to claim 1, characterized in that, The number of times B is repeated is odd.

6. The resampling prediction method for non-negative integer seasonal time series according to claim 2, characterized in that, When the integer value time series model is an INAR model, the recursive relation upon which the recursive calculation is based is: in, To estimate parameters for the model, , For a binary sparse operator, From the season The corrected information value randomly read from the corresponding partition. For the first The predicted values ​​generated by each path.

7. The resampling prediction method for non-negative integer seasonal time series according to claim 1, characterized in that, The process of determining the numerical value used to characterize the final prediction result of this step, and ensuring that the final output is a non-negative integer, includes: The numerical values ​​obtained through numerical sorting and center selection operations are processed to become non-negative integers, including rounding the non-integer part to the nearest non-negative integer, rounding down when the distance is the same, and setting negative values ​​to 0.

8. The resampling prediction method for non-negative integer seasonal time series according to claim 1, characterized in that, After obtaining the historical non-negative integer time series data, the process also includes preprocessing the data by cleaning, filling in missing values, and removing outliers.

9. A resampling prediction device for seasonal time series with non-negative integer values, characterized in that, include: At least one processor and a memory communicatively connected to said at least one processor; The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the method as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 8.

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