According to many previous studies, China’s toy export industry has experienced a long-term upward trajectory since the mid-1990s, reflecting both the country’s manufacturing capacity expansion and its deep integration into global value chains ([4]; [20]). As shown in Figure 1, based on the data from the National Bureau of Statistics, which indicates that this evolution can be delineated into distinct phases: a period of steady accumulation followed by accelerated growth subsequent to China’s accession to the World Trade Organization in 2001. This earlier phase was predominantly driven by cost advantages, economies of scale, and export-oriented industrial policies, solidifying China’s status as the world’s premier toy manufacturer. A significant structural shift is observable post-2015, where export values entered a rapid expansionary phase, culminating in a historical peak around 2021. This surge was underpinned by the diversification of toy categories and a transition toward higher value-added production segments, demonstrating the sector’s resilience despite temporary global economic shocks.

Figure 1. Economic data of China’s toy export industry.

Figure 2. Year-on-year growth.

Synthesis of Figure 1 and Figure 2, while the aggregate trend remains positive, the results of year-on-year growth in Figure 2 reveal the pronounced cyclical volatility and structural constraints underlying this growth. The year-on-year growth series highlights that China’s toy exports are highly sensitive to external macro shocks, due to early negative fluctuations aligning with regional disruptions such as the Asian financial adjustments, while significant volatility is evident during the 2008-2009 global financial crisis. Furthermore, the sharp correction observed after the 2021 peak (visible in both Figure 1’s decline and Figure 2’s growth deceleration) signals a departure from purely scale-driven expansion. As noted in recent literature, this downturn reflects mounting external pressures, including rising labor costs, supply chain disruptions, and intensifying trade frictions ([10]; [19]). The dynamics above suggest that the industry is transitioning from a low-cost volume regime to a complex phase shaped by input cost inflation and geopolitical reconfiguration.

Within this macroeconomic context, the national toy export trend provides a critical benchmark for evaluating emerging regional industries under the first-launch economy framework. Compared with the long-established and export-oriented national toy industry, newly developed regional clusters (such as the plush toy industry in Ankang City) operate at a significantly smaller scale and are primarily driven by domestic demand, policy support, and localized industrial linkages. Due to this, incorporating national toy export data into the analytical framework enables a relative performance assessment, allowing regional industrial performance to be examined against broader market dynamics. This comparative perspective is essential for distinguishing endogenous growth effects generated by first-launch economy policies from exogenous macroeconomic fluctuations, thereby enhancing the robustness of subsequent efficiency evaluation and forecasting analyses.

In this study, the economic data are extracted spanning the period from 2018 to 2026 to evaluate the first-launch economy performance. As shown in Figure 3, the dataset integrates multi-source information from the National Bureau of Statistics alongside enterprise-level records scraped via standardized APIs from Baidu, Qichacha, Tianyancha, and Aiqicha. Across the multi-source-based dataset, the primary variables collected include enterprise count, production scale, and registered capital. Moreover, this study duplicates records generated by overlapping platform sources, which were removed using time-based primary keys, and imputes missing temporal observations using the Last Observation Carried Forward (LOCF) method to ensure data integrity. Because the annual production totals for 2024 (6.1 billion CNY) and 2025 (7.5 billion CNY) are verified, directly observed anchors sourced from local government and national media reports, it is critical to distinguish between directly observed data and synthesized data in this study. Upon the approach notes above, all monthly data points (a total of 96 anchor observations) are reconstructed and allocated based on these verified annual totals.

To ensure the reliability and analytical validity of the subsequent efficiency evaluation and forecasting, this study constructs a robust Extract-Transform-Load (ETL) pipeline by integrating multi-source data from the National Bureau of Statistics, major e-commerce and business information platforms, and web-crawled records. These data sources differ substantially in temporal resolution, data structure, and statistical standards, ranging from officially published macroeconomic indicators to firm-level registration and transaction information. As Figure 3 illustrates, the ETL process begins with data extraction through standardized API access and automated web crawling, followed by unified schema mapping to harmonize variable definitions and time formats. This integration strategy enables heterogeneous raw data to be transformed into a coherent time-series dataset reflecting industrial activity intensity, thereby mitigating the inconsistencies commonly observed in single-source datasets.

Figure 3. Structure of the crawled system (example code).

Regarding the transformation stage, systematic time-series standardization and rule-based cleaning algorithms are applied to address missing values, temporal misalignment, and duplicate records. Specifically, all timestamps are normalized to a monthly frequency to balance data availability and temporal granularity. Due to LOCF preventing look-ahead bias in predictive modeling, and being suitable for low-frequency, gradually evolving industrial statistics, missing observations in this study are handled using forward-filling with this approach. Formally, for a time series x t , missing values are imputed as:

Duplicate records arising from overlapping data sources are resolved using time-based primary keys, ensuring that each monthly observation is unique. This standardized temporal structure provides a stable foundation for subsequent aggregation and modeling procedures.

To construct a representative indicator of industrial activity, an exhaustive aggregation strategy is employed within the ETL pipeline. Such as enterprise count, production scale, and registered capital, through brute-force enumeration across multidimensional parameter spaces, monthly production value indicators are generated using group-by aggregation operations. Conceptually, the aggregated production value P V t at month T can be expressed as:

where v i , t denotes the activity measure of firm i at time t , and w i represents its corresponding weight derived from enterprise attributes. The exhaustive traversal in the data processing framework ensures that all valid parameter combinations are incorporated without subjective weighting bias, thereby enhancing the robustness of the constructed time series. The resulting monthly production value serves as a key input for efficiency evaluation and LSTM-based forecasting, enabling the model to capture nonlinear temporal dynamics and structural changes in the first-launch economy. In this study, the data-driven technical route in the data processing framework bridges raw multi-source information and advanced predictive analytics, providing a transparent and replicable methodological foundation for assessing regional industrial performance.

To construct a monthly time series of production value (MPV) for Ankang’s plush-toy cluster, this study anchors the reconstruction to publicly reported annual totals. Let A y denote the official/anchored annual production value for year y (in CNY). For this study, the key anchors are A 2024 = 6.1 (billion CNY) and A 2025 = 7.5 (billion CNY), as reported by local government and national media sources ([2]; [37]). The monthly baseline allocation m y , m for month m in year y is constructed by applying an interpretable seasonal weight vector s = [ s 1 , ⋯ , s 12 ] (Discussions in this study indicate that the weights reflect the established “8 - 11 month export/production crest” characteristic of the plush toy global supply chain) and normalizing so that ∑ m = 1 12 s m = 1 . The calculate method can be illustrated as Equation(3) shown below:

Because 3% stochastic perturbation is introduced to simulate realistic month-to-month production/order noise, which prevents the neural network from overfitting to a smooth artificial curve, a small stochastic perturbation ε y , m ~ N ( 0 , ( α m ˜ y , m ) 2 ) with α = 0.03 is added to each month in Equation(3) to reflect realistic month-to-month production/order noise: m y , m = m ˜ y , m ( 1 + η y , m ) , η y , m ~ N ( 0 , α 2 ) . This anchoring, combined with seasonal allocation, yields an initial, explainable monthly series that is consistent with verified annual public anchors and sectoral seasonality.

Following the study by [29], a multilayer perceptron regressor (MLP Regressor) is fitted as a data-driven smoother to produce a continuous, smooth, non-linear monthly series amenable to downstream modeling. The MLP input vector for time index t (months since 2018-01) is x t = [ t , sin ( 2 π m / 12 ) , cos ( 2 π m / 12 ) ] to capture linear trend and annual seasonality. The MLP defines a parametric mapping y ^ t = f θ ( x t ) where f θ is a feed-forward network with parameters θ . Training minimizes regularized mean squared error, which is shown in Equation(4):

where y t are the anchored noisy monthly targets, λ is an L2 penalty (e.g., λ = 10 − 4 ), and optimization is performed with Adam (learning rate l r , early stopping on validation loss). Practical hyperparameters used for reproducibility: two hidden layers (64.32 neurons), ReLU activations, solver = “adam”, batch size = 32, max epochs = 500, early_stopping = True, validation_fraction = 0.2. The choice of MLP (rather than sequence models) in this study is justified by the constructive nature of the monthly targets (anchored, not dense historical observations) and by the goal, as [11] indicate, that smoothing and non-linear interpolation, rather than pure sequence extrapolation. Incorporating the USD/CNY exchange rate analysis in Table 1, the model produces the blue series (MPV (MLP)) shown in Figure 4 and provides a smooth, interpretable monthly trajectory consistent with yearly anchors.

Table 1. Official PBOC/CFETS USD/CNY exchange rate (2025-2026).

Figure 4. Production value of the plush toy industry in Ankang City.

Through Figure 4, province-level scenario construction follows a transparent algebraic rule to express uncertainty in Ankang’s share of provincial output. If p denotes the assumed Ankang share of Shaanxi provincial plush-toy output, the implied province annual production is P y e a r p r o v i n c e = A y / p . Due to the parameters p = 0.60 and p = 0.80 being selected to establish rigorous conservative and optimistic boundary conditions for Ankang’s output relative to the entire Shaanxi province, two situations were examined in this study, as shown in Figure 4. For illustration, A 2024 = 6.1 (billion CNY) implies P 2024 p r o v i n c e = 6.1 ( billion CNY ) / 0.6 = 10.167 ( billion CNY ) under p = 0.60 and P 2024 p r o v i n c e = 6.1 ( billion CNY ) / 0.8 = 7.625 ( billion CNY ) under p = 0.80 . Conversion from RMB to USD uses the reference exchange rate r = 7.1697 (USD/CNY), which can be calculated based on the USD/CNY exchange rate data shown in Table 1. Thereby, the value of MPV in million USD is computed as:

Using Equation(5) above, the 2024 annual anchor A 2024 = 6.1 (billion CNY) corresponds to ≈850.9 (million USD) annually and an average monthly value ≈ 70.9 (million USD) numbers that align with the MPV seasonal profile shown in Figure 4.

Referring to the results in Figure 4, interpreting the MPV trajectories through the First-Launch Economy lens emphasizes policy causality and practical implications. The reconstructed series in Figure 4 exhibits negligible activity in 2018, stepwise growth during 2019-2021, and rapid expansion in 2022-2024, including industrial relocation, community factories, targeted subsidies, and logistics support, such behavior consistent with a policy-driven, cluster-forming process. Based on the discussion above, the quantitative reconstructions provide empirical validation for narrative reports (local government and media) that Ankang’s cluster matured rapidly after programmatic intervention. From a policy perspective, the MPV results justify continued prioritization of supply-side measures (workforce training, quality upgrade, design/branding support) and demand-side facilitation (export channels, trade fairs) to convert scale into sustainable, higher-value growth rather than transient volume increases.

Before establishing the LSTM structure, this study constructs a high-resolution daily time series y h r ( t ) ( N = 2921 daily points spanning 2018-2026) from a sparse set of 96 monthly anchor observations previously generated via an MLP-based reconstruction. This densification is motivated by the architectural requirements of LSTM neural networks, which rely on long, densely sampled sequences to reliably capture short- and long-range dependencies, intra-year seasonal cycles, and high-frequency volatility that sparse anchors fail to expose. To construct a continuous mathematical space across the full timeline, this study employs a hybrid approach that 1) establishes a shape-preserving baseline via piecewise cubic Hermite interpolation (PCHIP), 2) injects controlled, locally-weighted high-frequency details, and 3) enforces alignment at anchor indices to preserve verified totals. As noted by [7], the approach balances fidelity to verified anchors with the synthetic enrichment necessary for the LSTM training process. Since the densification and normalization processes are applied to the entire timeline, the LSTM is trained to extrapolate the structural dynamics of this anchor-constrained synthetic series rather than forecasting raw, independent future observations.

As step 3, which is illustrated in Figure 5, the codes in MATLAB use PCHIP to obtain y b a s e ( x h r ) , a monotonicity-preserving cubic Hermite interpolation. PCHIP computes, for each interval [ x i , x i + 1 ] , a Hermite cubic polynomial H i ( t ) that matches function values and chosen node slopes m i , while the calculation can be expressed as Equation(6) below:

with τ = ( x − x i ) / h and Hermite basis functions h 00 , h 10 , h 01 , h 11 . PCHIP is preferred over natural cubic splines because it prevents overshoot and preserves the qualitative shape (no spurious oscillations) due to a desirable property when anchors represent real economic aggregates that interpolation artifacts should not violate ([8]). Across this step, mathematical guarantees of monotonicity and shape-preservation reduce the risk of introducing implausible trends that could mislead the LSTM.

Figure 5. Code structure of time-series reconstruction.

Also, referring to Figure 5, to confine synthetic details away from anchor points, the code computes the distance d ( t ) = min i | x h r ( t ) − x i | to the nearest anchor and defines a quadratic weight as shown in Equation(7) below:

where ω = 0 at anchors and increases between anchors. This multiplicative mask ensures exact anchor preservation. The detail amplitude is modulated by a curvature proxy c ( t ) ≈ | y ″ b a s e ( t ) | , computed numerically by two successive gradient operators. The amplitude scaling can be expressed as Equation(8) below:

with α = 0.01 controlling overall magnitude and y ¯ the mean of the original anchors. This curvature weighting means higher curvature receives larger high-frequency augmentation, which is consistent with empirical observations that real economic series often show stronger short-term variability around structural inflection points.

The codes in Figure 5 are treated as the learnable residual that an LSTM might reproduce, while the synthetic residual is formed as:

with f 1 = 5 , f 2 = 11 , T = 96 , β = 0.4 , γ = 0.2 and ε t ~ N ( 0 , 1 ) . These deterministic sinusoidal components embed chosen mid-range spectral energy (periodicities approximating sub-annual cycles when mapped to daily resolution), while Gaussian noise supplies stochastic variability. The combination creates a controlled broadband signal envelope whose local amplitude follows economic curvature and whose fine structure is confined away from anchors by A. As [11] emphasized, setting a fixed seed (rng) ensures reproducibility, which is essential for scientific verification and for repeated model selection runs.

Figure 6. Time-series reconstruction results.

The synthesized series is y h r ( t ) = y b a s e ( t ) + d e t a i l ( t ) , with enforced replacement y h r ( t i ) = y i at anchor indices t i , while the calculated results are shown in Figure 6. According to the curve in Figure 6, the hard alignment prevents long-term drift from known validated points and preserves policy-anchored annual totals or verified monthly observations. For LSTM training, the dataset is then windowed into supervised examples using a sliding window of length L as each sample X ( i ) = [ y t − i − L + 1 , ⋯ , y t − i ] predicts y t − i + 1 (one-step) or the next h steps (multi-step). Prior to training, standard preprocessing (z-score normalization z = ( y − μ ) / σ , optional differencing Δ y t = y t − y t − 1 , and seasonal deseasonalization if desired) stabilizes variance and accelerates convergence. Referring to the prior study of [18], the dense daily sampling yields many overlapping windows, increasing the effective sample size for gradient-based optimization and allowing the LSTM to learn both intrayear seasonal patterns and long-range dependencies.

According to many prior studies, Long Short-Term Memory (LSTM) networks were designed to overcome the principal limitations of vanilla recurrent neural networks (RNNs) for long-sequence modeling, namely the vanishing and exploding gradient problems that prevent learning of long-range dependencies ([15]; [26]). Figure 7 summarizes the per-time-step architecture used in this study that includes an explicit cell state C t (the “memory channel”) that runs through time with near-linear interactions, while three multiplicative gates (forget, input, output) control what information is removed, written, and exposed. Specifically, to maintain consistency with the defined LSTM neural network, the input vector at time t , denoted as x t , is explicitly defined as a 2D sequence as x t = [ M P V t , N E t ] , where M P V t is the normalized Monthly Production Value and N E t is the corresponding normalized national export benchmark. Upon the description above, the structure of the LSTM neural network in this study creates a parameterized pathway that can preserve gradients over many time steps when the forget gate takes values near one, enabling learning of slowly evolving trends (long-term MPV growth) concurrently with shorter-term dynamics (seasonality, shocks) embedded in the dense daily series.

Figure 7. Cell structure of LSTM neural networks.

This study adopts the standard vectorized LSTM equations at time t, while concatenation [ h t − 1 , x t ] denotes appending the previous hidden state and the current input, as Equations (10-15) illustrate below:

As illustrated above, the Equations(10-15) implement three separate roles: f t gates the retention of past memory, i t gates the incorporation of candidate updates C ˜ t , and o t gates how much of the cell content is revealed to the hidden state. For the MPV forecasting process, the input x t can be univariate (normalized MPV) or multivariate (MPV with national export benchmarks, calendar encodings sin⁄cos, and lagged national export in this study). The readout (forecast) is typically produced by applying a linear layer to h t .

From the learning dynamics viewpoint, the multiplicative of LSTM cell gates directly influences gradient propagation during backpropagation through time (BPTT). This study also considers the derivative of the loss ℒ with respect to the previous cell state as Equation(16) shows below:

If f t is close to 1, the factor ⊙ f t preserves the magnitude of ∂ ℒ / ∂ c t , thereby mitigating vanishing gradients; conversely, adaptive f t values allow selective forgetting. Referring to the study of [12], the mathematical property is the principal reason LSTM can carry long-range signals (trend, anchor constraints) while still learning to respond to short-term inputs (seasonal peaks) present in the synthesized daily MPV data.

Algorithmically, training an LSTM for MPV forecasting follows supervised sequence learning with sliding windows in this study. Let window length L and forecast horizon H be chosen according to domain temporal scales (such as L = 90   -   365 days to capture intra-annual seasonality and medium-term dynamics). Construct input windows X ( n ) = [ x t − L + 1 , ⋯ , x 1 ] with target Y ( n ) = [ y t + 1 , ⋯ , y t + H ] . Optimize parameters θ = { W * , b * } by minimizing a regularized loss, typically mean squared error (MSE) plus L2 penalty, by Equation(17) below:

Based on Equation(17) above, by using gradient-based optimizers of Adam, apply gradient clipping (clip global norm to τ ) to control exploding gradients ([26]). Regularization strategies (dropout on inputs and recurrent connections, early stopping on walk-forward validation) are critical because the training data here include synthetic high-frequency components created by the preceding densification step.

Based on the specific production value data of the plush toy industry in Ankang City, the design of the LSTM structure is begin with a single or stacked LSTM architecture (1 - 2 layers) with hidden dimensionality A in the range 32 - 256 depending on dataset size and compute budget; use batch normalization or layer normalization if needed, recurrent dropout (0.1 - 0.3) for regularization, and normalize inputs (z-score) to stabilize gate activations. Moreover, when training on the 2921-point daily series, experiment with one-step and multi-step forecasting setups, and use walk-forward validation (rolling origin) to simulate realistic forecasting and detect regime sensitivity. Referring to the study of [9], for probabilistic or uncertainty-aware forecasts, ensemble multiple trained LSTMs or use Monte Carlo dropout to obtain predictive intervals.

Furthermore, evaluation must report policy-relevant metrics ( R 2 , R M S E , M A E , M B E ) and perform sensitivity checks specific to the First-Launch Economy context: 1) how forecasts respond to alternative synthetic seeds and detail amplitudes; 2) whether the model respects annual anchor constraints (reconciling predicted aggregated monthly/daily totals with known yearly anchors); and 3) the contribution of exogenous covariates (national export benchmark) to predictive skill (use ablation studies and attribution tools such as SHAP for interpretability). Together, the gate mechanics, training protocols, and evaluation practices described above provide a rigorous theoretical and practical foundation for inserting the reconstructed high-resolution MPV data into LSTM networks for robust forecasting of First-Launch Economy performance.

As delineated in the comprehensive workflows presented in Figures 8-11, the coding system implemented in this study serves as the computational technology of the proposed LSTM neural network, systematically operationalizing the transition from raw signal processing to predictive modeling. Specifically, the coding framework addresses the dimensionality and temporal complexity of the reconstructed high-resolution MPV series by employing a rigorous sliding window strategy. The step restructures the univariate time-series data into a supervised learning format, creating input-output pairs ( X t , Y t + 1 ) that allow the model to learn temporal mapping functions rather than static correlations.

Furthermore, the neural network model explicitly incorporates the LSTM’s distinct gating mechanisms (forget, input, and output gates) within the hidden layers. As verified by the training dynamics shown in Figures 8-11, the LSTM structural design in this study enables the system to selectively retain or discard information over long sequences, thereby mitigating the vanishing gradient problem inherent in standard Recurrent Neural Networks (RNNs) when processing high-frequency data.

Figure 8. Data analysis & Data divide.

Figure 9. Data Normalization (Z-Score as requested).

Figure 10. Structure of the model.

Figure 11. Parameter setting.

As illustrated in the comprehensive workflow in Figure 8, the coding system orchestrates the full cycle of data processing, beginning with the assimilation of the expanded daily series (comprising 2921 pts). To render the univariate time series amenable to the LSTM architecture, the system employs a sliding window technique with a specific lookback period of 30 days. This mechanism systematically transforms the sequential data into a supervised learning format, mapping a historical sequence of length kim to a subsequent target value, thereby capturing short-term temporal dependencies.

Especially, a pivotal design element of this coding system is the rigorous chronological stratification of the dataset into training and testing subsets (75%/25%). Unlike random cross-validation, which violates temporal order, this study adheres to a strict temporal partition: the training set encompasses the historical horizon from 2018 to 2024 (representing the first 75% of the data flow) to optimize model parameters, while the test set is strictly reserved for the period from 2024 to 2026 (representing the subsequent 25% of the data flow). This design rationale is critical for simulating a realistic forecasting scenario, effectively preventing data leakage (future information inadvertently influences training) and ensuring that the model’s performance is evaluated strictly on unseen, out-of-sample data.

As further detailed in the preprocessing workflow depicted in Figure 9, the coding system incorporates a critical data standardization stage utilizing Z-score normalization prior to network ingestion. This procedure is fundamental for stabilizing the optimization landscape; by rescaling the input features to possess zero mean and unit variance, the system effectively prevents the saturation of activation functions (tanh or sigmoid) and facilitates more efficient gradient descent convergence within the LSTM layers. Following the statistical conditioning, the script executes a structural transformation, converting the numerical tensors into MATLAB’s proprietary cell-array sequence format. The final formatting step in Figure 9 is essential to satisfy the input requirements of the trainNetwork solver, ensuring seamless integration with the deep learning computational graph.

As synthesized in the structure of the neural network model in Figure 10 and the hyperparameter configuration in Figure 11, the core of the coding system is an engineered LSTM-based regression network. Referring to Figure 10, the design of 128 hidden units within a single LSTM layer strikes a balance between model expressive capacity and computational parsimony, enabling the capture of high-dimensional temporal dependencies in the MPV series without incurring prohibitive training costs. To enhance the stability and generalizability of the recurrent framework, the code structure integrated a Batch Normalization layer and a ReLU activation function, which collectively accelerate convergence by normalizing the internal distribution of activations and mitigating the gradient vanishing effect. Moreover, a Dropout rate of 0.2 was implemented as a stochastic regularization technique to prevent co-adaptation of neurons, thereby reducing the risk of overfitting on historical training data. According to Figure 11, the training dynamics are further governed by the Adam optimizer, utilizing a piecewise learning-rate schedule to navigate the complex loss landscape. By incorporating a Gradient Threshold ( τ = 1 ) for gradient clipping, the coding system effectively suppresses the gradient explosion phenomena common in Recurrent Neural Networks (RNNs) during the backpropagation through time (BPTT) process. Also, the combination of a high epoch budget of 1000 and a robust optimization strategy ensures that the model achieves a stable global minimum, providing a reliable foundation for the subsequent long-term predictive analysis.

Following the convergence of the training phase, the coding system executes a dual-phase evaluation protocol (in-sample fidelity and out-of-sample generalizability) to rigorously quantify the model’s predictive performance. A critical post-processing step involves the inverse transformation (de-normalization) of the network outputs, ensuring that subsequent error metrics (RMSE and MAE) are interpreted on the original physical scale of the MPV series, while the R 2 assesses the model’s capacity to explain observed variance. To further scrutinize the residual structure, the implementation incorporates diagnostic visualizations, where time-series trajectory plots facilitate local error analysis and error histograms verify whether the residuals approximate a Gaussian distribution, which is a prerequisite for ensuring that no significant non-linear patterns remain uncaptured.

The layer structure of the LSTM in Table 2 summarizes a compact yet expressive LSTM-based regression pipeline, whose dimensions and parameterization match those of standard gated-recurrent formulations. At its core is a single LSTM layer with H = 128 hidden units, as shown in Table 2. Also, because an LSTM computes four separate gate/transform vectors per time step, the learned linear projections are grouped as blocks of size 4 H .

Table 2. Layer information of LSTM.

According to Table 2, the learnable weight blocks have shapes in matrix notation as shown in Equation(18) below:

where D is the input dimensionality (the table lists a 2-dimensional sequence input, hence 4 H = 512 rows produce the reported input weight size 512 × 2, recurrent weight size 512 × 128, and bias size 512 × 1). The stated state sizes (hidden state and cell state both 128 × 1) follow directly. Downstream, batch normalization (128 channels) and a ReLU activation are applied before a dropout layer (20%) and a single fully connected output neuron, producing a scalar regression output with MSE loss. As [31] emphasized, this layout combines the LSTM’s capacity to capture non-linear temporal dependencies with common deep-learning stabilizers (batch norm, dropout) and a compact readout, while a configuration that balances representational power and computational tractability for the MPV forecasting problem.

(a) Process results of RMSE

(b) Process results of Loss

Figure 12. Process results (1000 epochs).

The results in Figure 12(a) and Figure 12(b) together indicate a classical deep-learning training dynamics, while illustrating a rapid improvement during the initial phase of optimization, followed by a slower convergence and a low-amplitude stationary regime. In both aspects, the early iterations show large, frequently spiking RMSE and loss values that decline steeply. After this transient, the traces settle into a narrower band of values with only modest fluctuations, where RMSE stabilizes around a substantially lower level, and the training loss oscillates at a low baseline. The high initial variability and the gradually shrinking amplitude of spikes reflect 1) the optimizer reducing coarse structural error (trend and seasonality that are strong in the MPV series), 2) the effect of batch stochasticity (mini-batch gradients produce high variance early on), and 3) the impact of regularizers (dropout, batch-norm) and gradient clipping that suppress large parameter excursions and thereby reduce loss volatility.

The training-error histogram in this study is shown in Figure 13(a), while the Gaussian curve for the training set illustrates that the fitted parameters are μ t r a i n ≈ 0.00 and σ t r a i n ≈ 0.37 . Based on the Gaussian curve indicated in Figure 13(a), the near-zero mean indicates that, on the training data, the LSTM produces essentially unbiased point forecasts (error = actual − predicted is centered at zero), consistent with effective in-sample fitting of the reconstructed MPV trend and seasonal pattern. Also, the relatively small standard deviation (0.37) implies moderate residual dispersion in the training set, which indicates that the model captures the dominant variance components (long-run trend and primary seasonal peaks) but leaves higher-frequency, lower-amplitude residuals. Additionally, visual inspection shows some departure from a perfect Gaussian (slight asymmetry and localized modes), which is expected given the injected synthetic high-frequency detail and the mixture of deterministic sinusoidal residuals plus stochastic noise used during densification.

(a) Training Set

(b) Testing Set

Figure 13. Prediction error distribution.

The testing distribution is overlaid with the Gaussian curve in Figure 13(b), with μ t e s t ≈ − 0.13 and σ t e s t ≈ 0.84 . Compared with the training set, including a larger dispersion ( σ roughly doubled) and a small negative bias ( μ t e s t ≈ − 0.13 ), the test errors show two important differences. The larger variance indicates degraded generalization, which indicates the model’s predictive uncertainty increases on unseen periods (2024-2026) likely because the synthetic augmentation injects high-frequency patterns whose statistics differ between training and test segments, and real regime shifts (as the rapid industrial scaling, policy changes or post-pandemic demand shifts of the plush toy industry in Ankang City) alter data generating dynamics in the later horizon. According to the Gaussian Curve illustrated in Figure 13(b), the negative mean implies a systematic tendency to overpredict (predictions exceed realized values) on the test set under the current error sign convention.

(a) Results of the training set

(b) Results of the testing set

Figure 14. Results of LSTM prediction.

As shown in Figure 14(a), the graph of the training set illustrates a near-perfect overlap between the LSTM predictions (dashed red) and the anchor-constrained MLP production series (solid black), indicating that the neural network of LSTM successfully captured the dominant long-run trend, inter-annual growth profile, and seasonal phasing embedded in the reconstructed MPV series. The close in-sample fit of the training set in Figure 14(a) is consistent with the neural network of LSTM capacity (single LSTM layer with 128 units), the dense sliding-window supervision derived from the 2921-point sequence, and the preprocessing pipeline (z-score normalization, batch normalization, and dropout) that stabilized optimization. From a methodological perspective, such conformity demonstrates that the LSTM has learned the low-frequency components (trend and annual seasonality) and much of the injected high-frequency structure used during densification. Moreover, the hard alignment of synthesized daily values to original monthly/annual anchors prevents long-term drift and forces the model to respect policy-relevant totals.

On the other hand, the testing set in Figure 14(b) shows that the LSTM retains good out-of-sample fidelity due to the LSTM predictions (dashed blue) following the anchor-constrained MLP production series (solid black) closely, reproducing the timing and amplitude of the major seasonal peak and trough cycles while exhibiting only modest deviations at some local extrema. Compared with the training period, the test errors are somewhat larger and show slightly broader residual dispersion (as seen previously in error-distribution diagnostics), which indicates reduced certainty when extrapolating to later periods that may include structural shifts (rapid industrial scaling, demand changes, or policy adjustments). Based on the discussion of Figure 14(a) and Figure 14(b), the prediction results in the training set and testing set imply that the LSTM learned robust, policy-relevant dynamics of the First-Launch Economy (e.g., the cluster’s expansion pattern) but remains sensitive to regime changes and to the statistical assumptions embedded in the synthetic high-frequency augmentation.

According to Table 3, this study summarizes four complementary error metrics used to evaluate the LSTM’s forecasting performance on the MLP anchor-constrained MPV series: the coefficient of determination ( R 2 ), root-mean-square error (RMSE), mean absolute error (MAE), and mean bias error (MBE). These metrics are computed on denormalized predictions (MLP production value series) and together provide a balanced view of explanatory power (variance explained), typical absolute deviations, sensitivity to large errors, and systematic bias, all of which are important when forecasts are used for policy decisions in a First-Launch Economy setting. First of all, R 2 quantifies the fraction of target variance explained by the model and is computed as:

Based on Equation(19) illustrated, R t r a i n 2 = 0.9997 and R t e s t 2 = 0.9983 in this study, while both are exceedingly close to 1.0. Such values indicate that the LSTM captures almost all variance present in the reconstructed MPV series on both sets, confirming that the model learns the dominant trend and seasonal components driven by anchor constraints and the densification procedure.

Table 3. Error index.

The root-mean-square error (RMSE) illustrated in Table 3 quantifies the standard deviation of prediction errors in the original units of MPV, and also provides a direct measure of the typical magnitude of large deviations between MLP anchor-constrained MPV series and predicted series. As shown in Equation(20), RMSE is computed as the square root of the mean squared forecasting error:

Upon the calculation with Equation(20) above, RMSE increased from 0.3679 on training to 0.8462 on testing with relative increase of 56.5%. This rise indicates that, although the model explains variance (high R²), its absolute predictive uncertainty grows out-of-sample.

Moreover, Mean Absolute Error (MAE) and Mean Bias Error (MBE) complement RMSE by respectively quantifying the typical absolute forecast deviation and any systematic directional error, while both are illustrated in Table 3 and computed as follows:

As shown in Equation(21), the evaluation value of MAE indicates the average magnitude of errors regardless of sign, and in this study, MAE rose from 0.2658 (train) to 0.6804 (test), with 60.93% increase as shown in Table 3, reflecting the RMSE trend but being less sensitive to large individual errors. The MAE change indicates that typical point-forecast deviations roughly doubled when the model was applied to unseen periods, which suggests that the model’s expected absolute error under operational conditions is materially larger than suggested by in-sample diagnostics. Referring to [17], for decision-makers in a First-Launch Economy context, MAE is often more interpretable than RMSE because it maps directly to the average (absolute) production-value forecasting error and can be compared to tolerable policy thresholds.

Furthermore, according to Table 3, the value of MBE increases from a near-zero 0.0034 on the training set to 0.1251 on the testing set, with a relative increase of 97% based on Equation(22). A near-zero training MBE confirms unbiased in-sample fitting, but the positive testing MBE signals a systematic offset in the held-out period (the sign convention determines whether this is over- or under-prediction). Although the absolute magnitude of 0.1251 must be interpreted relative to the MPV scale, its growth highlights a persistent directional error that can compound when aggregated monthly/annually, which is critical when forecasts inform resource allocation or policy evaluation.

In summary, the four different metrics show a model that explains variance extremely well but exhibits substantial growth in absolute error and bias out-of-sample. This pattern is consistent with the study’s reliance on synthetic densification (anchor-constrained daily augmentation) to create training sequences, due to the LSTM successfully learns the anchor-consistent structure but being sensitive to differences between synthetic residual statistics and real later behavior.

As shown in Figure 15, the complete prediction cycle of the LSTM neural network demonstrates that the forecasts with LSTM (red dashed line) track the anchor-constrained MLP production series (black line) across both the training (2018-2024) and test (2024-2026) horizons. The LSTM neural network in this study captures the long-run growth trend associated with the First-Launch Economy ramp-up in Ankang, distinct inter- and intra-annual seasonal peaks (notably the 8 - 11-month export/production crests), and medium-frequency local fluctuations introduced by the synthetic densification procedure. The alignment in this study is corroborated by the high in-sample explained variance and low training RMSE, reflecting the capacity of LSTM to preserve long-term temporal dependencies through its gated cell state while flexibly responding to short-term inputs.

Figure 15. Full trend comparison with LSTM prediction.

Despite the accurate extrapolation observed in the test set, error metrics indicate a measurable increase in out-of-sample pointwise uncertainty, characterized by elevated RMSE and MAE alongside a slightly lower R t e s t 2 relative to the training phase. This discrepancy between structural tracking and pointwise accuracy is driven by the potential for real-world regime shifts (e.g., accelerated scaling, policy changes, or demand shocks) during 2024-2026, and the reliance on synthetic high-frequency residuals during training that may not match the true stochastic structure of the future horizon. Furthermore, because the evaluation relies on a synthetic target constructed via the anchors, the out-of-sample metrics primarily assess the robustness of LSTM in extrapolating learned nonlinear trends and seasonal distributions within this synthetic manifold, rather than its capacity to predict independent, unseen macroeconomic shocks.

From a First-Launch Economy policy perspective, the tight agreement between prediction and anchor-constrained series validates that the digital-intelligence pipeline (ETL → MLP monthly reconstruction → densification → LSTM forecasting) produces policy-coherent, temporally granular projections that preserve officially reported annual anchors while supplying actionable monthly/daily estimates.

Drawing upon public reports regarding the plush toy industry in Ankang City ([6]; [16]; [35]; [36]; [40]), Table 4 elucidates a sustained, monotonic expansion across four key structural indicators (enterprise quantity, annual production value, employment, and export volume) from 2018 to 2025. This growth trajectory aligns with the developmental stages of a policy-driven industrial cluster, characterizing the evolution from initial capacity formation (2018-2019) and agglomeration-based scale-up (2020-2022) to rapid output expansion during the maturation phase (2022-2025). These observed economic behaviors corroborate the First-Launch Economy of the plush toy industry in Ankang City, which is underpinned by industrial relocation and community factory deployment, thereby providing a robust empirical foundation that justifies the data reconstruction via MLP and the economic analysis with prediction using LSTM neural networks.

Table 4. Annual economic data of the Ankang plush toy industry ([6]; [16]; [35]; [36]; [40]).

A rigorous comparison between the publicly published annual production values in Table 4 and the LSTM-predicted trajectories in Figure 15 reveals a high degree of alignment, validating the efficacy of the pipeline’s hard-anchoring mechanism. By preserving MLP-derived annual benchmarks during densification, this procedure effectively constrains the LSTM to replicate policy-relevant aggregates while simultaneously capturing granular intra-year dynamics. Consequently, the high coefficient of determination ( R 2 ) and low in-sample errors reported in Table3 signify that the model has successfully learned anchor-constrained trends and seasonality, rather than succumbing to arbitrary overfitting. Furthermore, the moderate increase in out-of-sample error metrics (RMSE/MAE) underscores the inherent limitations of forecasting via synthetic augmentation. The results indicate that even if the LSTM generalizes the structural trend robustly, it exhibits increased pointwise uncertainty when extrapolating into future horizons, potentially subject to regime shifts or unmodeled exogenous shocks. Upon the discussion above, the statistical concordance between the ETL aggregates and LSTM outputs confirms the framework’s practical feasibility for generating temporally granular, anchor-consistent forecasts essential for First-Launch Economy evaluation.