# Online Course on Modeling and Time Series Analysis

## Module 1: Basic Statistics

### Learning Objectives
* Download and install Python/R.
* Familiarise with Online Colab tools.
* Visualize various statistics graphically.
* Create scatter plots and draw inferences from a simple linear regression model in Python/R.

## Module 2: Practical Time Series Analysis

### Learning Objectives
* Analyze time series data through software.
* Describe a time series via time plot.
* Estimate and recognize some simple Autocorrelation Functions (ACF).
* Produce random walk and form simple moving averages for datasets.

## Module 3: Stationarity, Moving Average, and Autoregressive processes

### Learning Objectives
* Explain stationarity in a time series.
* Simulate (construct) moving average MA processes and autoregressive AR processes.
* Interpret the common notation used for MA processes, use invertibility condition and learn duality.
* Calculate and evaluate the ACF to distinguish between various lower order models.
* Develop Yule-Walker equations to calculate the ACF of AR processes.

## Module 4: AR(p) processes, Yule-Walker equations, PACF

* Simulate and analyze autoregressive time series processes of order p, AR.
* Build AR stochastic process models from real-world time series.
* Write Yule-Walker equations in matrix notation, and estimate model parameters in AR processes.
* Examine partial autocorrelation function and use it to estimate the order of AR processes.

## Module 5: Akaike Information Criterion (AIC), Mixed Models, Integrated Models

* Judge the quality of the fitted model by using Akaike Information Criterion (AIC).
* Fit a lower order ARMA or ARIMA model to a time series by assessing a reasonable (p,q) order using ACF and PACF.
* Construct ARMA models as AR infinity and MA infinity processes.
* Detrend time series data via differencing to produce a stationary process.
* Find and interpret the Ljung-Box Q-statistic in a modeling process.

## Module 6: Seasonality, SARIMA, Forecasting

* Write SARIMA models using difference and backshift operator.
* Fit SARIMA models to some time series using sarima() and sarimax() routines.
* Develop forecasts using exponential smoothing techniques.
* VARMA, VARMAX, SES, HWES, etc.