China Population Forecast Analysis

This project aims to forecast China's population trends using advanced time series analysis methods, including ARIMA, ARIMAX, and other machine learning approaches. It incorporates external variables such as GDP, birth rate, and urbanization rate, providing a comprehensive framework for understanding population dynamics and influencing factors.

1. Data Preparation and Preliminary Analysis

1.1 Data Collection and Cleaning

• Ensure the completeness of time series data for all variables.
• Handle missing values and outliers.

1.2 Descriptive Statistics

• Compute basic statistical metrics for each variable.
• Plot time series graphs to observe trends and seasonality.

1.3 Correlation Analysis

• Calculate the correlation matrix among variables.
• Visualize correlations using a heatmap.

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2. Time Series Characteristics Testing

2.1 Stationarity Testing

• Perform Augmented Dickey-Fuller (ADF) tests on the target variable (Population).
• Apply differencing to achieve stationarity if necessary.

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3. Feature Engineering and Selection

3.1 Lag Features Creation

• Create lagged variables (e.g., lag1, lag2, lag3) for explanatory variables.
• Use Variance Inflation Factor (VIF) to detect multicollinearity and remove variables with high VIF values.

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4. Model Building and Evaluation

4.1 ARIMA Model

• Build an ARIMA model using only the target variable (Population).
• Determine optimal parameters (p, d, q).

4.2 ARIMAX Model

• Incorporate selected exogenous variables into the ARIMAX model.
• Compare the forecasting performance of ARIMA and ARIMAX models.

4.3 Model Diagnostics

• Check residuals for white noise characteristics.
• Conduct assumption tests (e.g., normality, homoscedasticity).
• Compare model errors.

4.4 Feature Optimization

• Use Lasso regression for feature selection and reapply ARIMAX.
• Consider Principal Component Analysis (PCA) for dimensionality reduction while balancing interpretability.

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5. Forecasting and Results Analysis

5.1 Generating Forecasts

• Use the best-performing model to generate short-term and long-term forecasts.

5.2 Results Interpretation

• Analyze the impact of variables on population forecasts.
• Compare expected outcomes with actual results.

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6. Conclusions and Application

6.1 Key Findings

• Summarize major insights and trends discovered.

6.2 Framework Extension

• Discuss how this analysis framework can be applied to other socio-economic indicators.

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7. Challenges and Improvements

Given the small dataset (39 years) with only 5 years for testing, model reliability may be limited. Strategies for improving evaluation include:

7.1 Advanced Validation Techniques

• Rolling Origin Forecasting: Iteratively expand the training set by one year and predict the next year, ensuring robust evaluation over multiple prediction ranges.
• Forward Validation: Use a fixed rolling window (e.g., the last 10 years) for training, improving performance robustness.
• Block Bootstrapping: Resample sequential blocks of data to preserve time dependency and assess model variability.
• Leave-One-Year-Out Validation: Train on all but one year and test on the excluded year, iterating across the dataset.

7.2 Shorter Prediction Intervals

• Focus on predicting fewer than five years to assess short-term model performance.

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8. Additional Innovations and Directions

1. Comparative Analysis: Compare ARIMA's performance with models like exponential smoothing, linear regression, or machine learning methods (e.g., LSTM, XGBoost).
2. Inclusion of Exogenous Variables: Use external factors (e.g., GDP, birth rate, urbanization) in ARIMAX to enhance predictions.
3. Seasonality Handling: Explore SARIMA (Seasonal ARIMA) for annual patterns in population data.
4. Residual Analysis: Perform comprehensive residual diagnostics to ensure model adequacy.
5. Scenario Analysis: Simulate population forecasts under different scenarios (e.g., varying birth rates or migration policies).
6. Advanced Models: Consider models like SVAR (Structural Vector Autoregression) or Bayesian Dynamic Models for enhanced predictions.

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Project Steps

1. Validate stationarity for [Year, Population] using differencing, ADF tests, KPSS tests, or correlograms.
2. Transform the data by creating lag features or adding exogenous variables. Optimize feature selection using collinearity detection and model outputs.
3. Build ARIMA, ARIMAX, and Lasso models. Ensure model parameters meet significance levels and diagnose residuals for homoscedasticity, normality, and autocorrelation.
4. Leverage variable correlations for hypothesis testing or explore methods like Markov chains to enrich insights.
5. Experiment with advanced time series models like SVAR or Bayesian updates for dynamic modeling.

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Repository Structure

• data/: Raw and cleaned datasets.
• Eviews Project File/.
• models/: Scripts for ARIMA, ARIMAX, and machine learning models.
• results/: Forecasts, evaluation metrics, and visualizations.

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Start exploring China's population trends and forecasting future scenarios with this robust analytical framework!