Advanced Statistics

Module 1 – “Business Statistics”

List of Topics

1. Random variables. 
   • What is a random variable and what are its various types? 
   • What is a probability density function? 
   • How to model rare events and waiting time between events? 
2. Jointly distributed random variables. 
   • How to determine relationships between variables?  
   • How to distinguish between conditional and unconditional expectation and  variances? 
3. Elements of hypothesis testing. 
   • What is a hypothesis? How do you test the same? 
   • What is a test statistic?
   • What are confidence intervals?

The key learning outcomes from this program will be – 

• Acquire a solid foundation in probability and statistics
• Apply tools and techniques to understanding econometrics and advanced econometrics

Module 2 – “Econometrics for Business”

This course will build on the “Business Statistics course” and will address the following topics 

1. Two variable regression 
   • What is a dependent and an explanatory variable? 
   • How to distinguish between an estimator and an estimate? 
   • What is the best linear unbiased estimator?  
2. Multiple Regression Model 
   • How to model relationships when dependent variable depends on more than 1  explanatory variable? 
   • How to remedy the failure of classical assumptions such as multicollinearity,  autocorrelation, heteroskedasticity and selection bias? 
3. Logit and Probit models 
   • How to model situations when the dependent variable is binary or qualitative?  • How to apply these models to business situations? 

The key learning outcomes from this program will be – 

• Learn to formulate a model, estimate the same, and test hypotheses based on economic  theories. 
• Fit an econometric model to real-world data, remedy the problems faced therein
• Handle binary dependent variables in a logistic regression framework
• Use the statistical environment “R” to estimate econometric models and analyse a variety of complex real-world problems. 

Module 3 – “Advanced Econometrics”

This course will build on the “Econometrics for Business” and will address the following topics 

1. Endogeneity: Omitted variable bias, Measurement error, Simultaneity
   • How to remedy the above problems in the case of a multiple linear regressions as  well as structural equation modelling? 
2. Instrumental variables: 2SLS
   • What is an instrument and how does it help when the explanatory variable is  correlated with the error term?
   • How to carry out estimation using instrumental variables? 
3. Applied Time Series Forecasting with AR, MA, ARIMA models
   • How to forecast macroeconomic variables using simple time series models
4. Volatility modelling with ARCH/GARCH models.
   • How is volatility modelled and forecasted in financial markets? 

The key learning outcomes from this program will be –

• Impart necessary skills to model and forecast time series and cross-sectional data
• Emphasise on empirical implementation strategies using extensive business applications