Comparative Study of Sarima and Lstm Model to Forecast the Insurance Comprehensive Income (Loss) in Indonesia

Technical Summary: Comparative Study of SARIMA and LSTM Models for Forecasting Indonesian Insurance Comprehensive Income

Problem Statement
The study addresses the challenge of forecasting the Total Comprehensive Income (Loss) of insurance companies in Indonesia, a metric that encompasses net profit/loss and other comprehensive income. While traditional financial analysis relies on historical earnings for strategic planning, investors and creditors face inherent uncertainties in projecting future cash flows. Existing literature often focuses on isolated metrics like premiums or claims, or relies solely on linear statistical models (e.g., ARIMA) without comparing them against deep learning alternatives. Furthermore, there is a gap in applying these forecasting techniques specifically to Indonesian insurance data, which exhibits pronounced seasonality and high volatility driven by premiums, claims, investment returns, and operating expenses. The core problem is determining whether statistical models (SARIMA) or deep learning architectures (LSTM) are better suited to capture the complex, non-linear, and seasonal dynamics of this specific financial time series.

Methodology
The research employs a quantitative time series forecasting approach using secondary data from Indonesian life insurance companies covering the period January 2017 to May 2025 (101 monthly observations). The dataset was split into training (80%) and testing (20%) sets.

1. Data Preprocessing:

   • Stationarity: The Augmented Dickey-Fuller (ADF) test confirmed stationarity (p-value = 0.0197). Seasonal differencing was applied to address annual cycles.
   • Decomposition: Time series decomposition was performed to isolate observed, trend, seasonal, and residual components, revealing significant annual seasonality.

2. Model 1: SARIMA (Seasonal Autoregressive Integrated Moving Average):

   • Followed the Box–Jenkins framework (identification, estimation, diagnostics).
   • Parameters were identified using ACF/PACF plots and the auto-ARIMA algorithm, optimizing for AIC, BIC, and HQIC.
   • The selected model was SARIMA (1,0,0)(0,1,1)[12].
   • Diagnostics included the Ljung-Box test to ensure residuals were white noise.

3. Model 2: LSTM (Long Short-Term Memory):

   • A deep learning architecture consisting of one LSTM layer connected to a dense output layer.
   • Hyperparameter Tuning: A manual grid search was conducted over 144 variations, testing combinations of:
     • Neurons: 4, 8, 12, 16
     • Epochs: 10, 25, 40, 60
     • Learning Rates: 0.001, 0.0001, 0.00001
     • Optimizers: Adam, RMSProp, SGD
   • The best configuration identified was 16 neurons, 60 epochs, learning rate 0.001, and the Adam optimizer.
   • Data was normalized and converted into sequential windows (input-target) for training.

4. Evaluation Metrics:

   • Both models were evaluated on the test set using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE).

Key Results

• SARIMA Performance:

  • The SARIMA model successfully captured the general seasonal trends and overall direction of the data.
  • Metrics: RMSE = 3,858,420.47; MAPE = 85.00%.
  • Observation: The model produced smoother predictions and struggled to capture sharp, sudden fluctuations (spikes) in the test data, leading to a high relative error.

• LSTM Performance:

  • The LSTM model followed the general level of the series but exhibited significant underfitting. It failed to capture large spikes and extreme variations, producing overly smoothed predictions.
  • Metrics: RMSE = 3,067,615 × 10⁶ (indicating massive absolute deviation); MAPE = 165.29%.
  • Observation: The LSTM's inability to model the specific volatility and amplitude of the Indonesian insurance data resulted in significantly lower accuracy compared to SARIMA.

• Comparison:

  • SARIMA outperformed LSTM in this specific context, particularly in modeling the annual seasonal patterns inherent in the data.
  • However, the authors note that the predictive accuracy of both models remains limited, as indicated by the high MAPE values for both.

Significance and Claims
The paper claims that while SARIMA demonstrates a stronger ability to reflect seasonal trends in Indonesian insurance comprehensive income compared to LSTM, neither model achieved optimal accuracy. The study highlights that:

1. Contextual Gap: It contributes to the sparse academic coverage of forecasting Indonesian insurance financial data, specifically using Total Comprehensive Income (Loss) rather than just premiums or claims.
2. Model Limitations: The results suggest that while statistical methods like SARIMA are effective for seasonal data, and deep learning (LSTM) is theoretically capable of handling non-linear dynamics, the current implementations failed to generalize well to the specific volatility of this dataset.
3. Future Direction: The authors modestly conclude that future research should move beyond single-model approaches. They propose investigating hybrid modeling strategies (e.g., combining SARIMA with LSTM or GRU) to leverage the seasonal strengths of statistical models and the non-linear learning capabilities of deep learning. Additionally, they suggest refining hyperparameter selection and incorporating external variables to improve generalizability and accuracy.

The study does not claim to have solved the forecasting problem definitively but rather provides a comparative baseline indicating that hybrid approaches are necessary for better outcomes in this domain.