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Statistics-computation-and-Application

This repository showcases a collection of problem sets that I've tackled in the domain of time series analysis. Through these exercises, I've gained invaluable insights into the intricacies of modeling time-dependent data and refined my skills in various statistical methodologies and techniques.

Skills and Insights Gained:

1. Data Cleaning and Preprocessing

  • Managed and cleaned raw data, ensuring removal of missing entries.
  • Transformed data to prepare for time series modeling.

2. Regression Modeling

  • Applied linear regression to model trends over time.
  • Explored higher-order polynomial fits (quadratic and quartic) to better capture data nuances.
  • Evaluated model performance using metrics such as Mean Squared Error (MSE).

3. Time Series Decomposition

  • Identified and accounted for seasonality in time series data.
  • Implemented adjustments to the model to accommodate seasonal variations.

4. ARIMA and AR Models

  • Utilized Autoregressive (AR) models to forecast future data points based on its own past values.
  • Explored the Autoregressive Integrated Moving Average (ARIMA) model to capture different components of the time series.

5. Model Optimization

  • Optimized ARIMA parameters and seasonal parameters for improved forecasting with the SARIMAX model.
  • Applied regular model evaluations to prevent overfitting and enhance model robustness.

6. Advanced Time Series Techniques

  • Implemented SARIMAX, an extension of ARIMA, to incorporate external regressors.
  • Evaluated how different aggregation methods for regressors (e.g., monthly averages versus monthly first values) influence model outcomes.

7. Moving Average (MA) Models

  • Delved into MA models where forecasts are based on a linear combination of past white noise error terms.
  • Evaluated the auto-covariance of an MA(1) model.

8. Understanding and Application of Statistical Concepts

  • Engaged deeply with concepts like auto-covariance, stationary conditions, and the equivalence between AR and MA models.

9. Tools and Programming

  • Employed Python as the primary tool for data processing, visualization, and modeling.
  • Leveraged Python libraries like SARIMAX for sophisticated model fitting and forecasting.

Conclusion:

The journey through these problem sets has provided a robust foundation in time series analysis. Each problem tackled not only honed my technical skills but also refined my approach towards data-driven decision-making, ensuring that insights derived are both statistically sound and contextually relevant.