Statistics

1. Time Series Analysis
   1. Introduction to Time Series
      1. Definition and Scope
      2. Importance and Applications
      3. Time Series vs. Cross-Sectional Data
   2. Components of Time Series
      1. Trend Component
         1. Long-term Movements
         2. Identifying Trends
         3. Trend Line Methods
      2. Seasonal Component
         1. Seasonal Patterns
         2. Measuring Seasonality
         3. Seasonal Indexes
      3. Cyclical Component
         1. Business Cycles
         2. Distinguishing from Seasonal Components
      4. Irregular Component
         1. Random Fluctuations
         2. Noise in Data
   3. Identifying Patterns in Time Series
      1. Decomposition Methods
         1. Additive Decomposition
         2. Multiplicative Decomposition
      2. Smoothing Techniques
         1. Simple Moving Averages
         2. Weighted Moving Averages
   4. Time Series Models
      1. Autoregressive Models (AR)
         1. Concept and Order of AR Models
         2. Parameter Estimation and Tuning
      2. Moving Average Models (MA)
         1. Definition and Characteristics
         2. Estimating MA Parameters
      3. Autoregressive Integrated Moving Average (ARIMA) Models
         1. Understanding ARIMA: AR, I, and MA Components
         2. Steps for Building ARIMA Models
            1. Identification
            2. Estimation
            3. Diagnostic Checking
         3. Seasonal ARIMA Models
      4. Seasonal Decomposition of Time Series (STL)
         1. Advantages of STL
         2. Implementation of STL
   5. Advanced Time Series Models
      1. Vector Autoregressive Model (VAR)
         1. Overview and Applications
         2. Assumptions and Limitations
      2. Exponential Smoothing Methods
         1. Single Exponential Smoothing
         2. Double Exponential Smoothing (Holt’s Method)
         3. Triple Exponential Smoothing (Holt-Winters Method)
      3. State Space Models
         1. Kalman Filtering
         2. Dynamic Linear Models
   6. Stationarity in Time Series
      1. Concept of Stationarity
      2. Testing for Stationarity
         1. Augmented Dickey-Fuller Test
         2. Phillips-Perron Test
      3. Methods to Achieve Stationarity
         1. Differencing
         2. Log Transformation
   7. Forecasting with Time Series
      1. Forecasting Models and Accuracy
      2. Evaluating Forecast Models
         1. Mean Absolute Error (MAE)
         2. Mean Squared Error (MSE)
         3. Root Mean Squared Error (RMSE)
         4. Akaike Information Criterion (AIC)
      3. Short-term vs. Long-term Forecasting
   8. Time Series in Practice
      1. Data Collection and Preparation
      2. Handling Missing Data
      3. Software and Tools for Time Series Analysis
         1. R Packages for Time Series
         2. Python Libraries for Time Series
   9. Challenges in Time Series Analysis
      1. Overfitting and Underfitting
      2. Handling Large Scale Time Series
      3. Ethical Considerations and Data Privacy