After the completion of this course, a student is able to
- judge in broad terms the relevance and importance of statistical analysis of (financial) data.
- apply the standard statistical techniques to solve standard problems.
- explain and reproduce the mathematical/probabilistic details underlying the standard statistical techniques.
- develop a relevant new statistical technique in certain simple situations.
Whether consciously or not, we come across statistics in our everyday life: from an opinion poll to a forecast of stock market behaviour in the future to a comparison of performances of different investment funds. For example, you may see in newspapers -- "52% support for certain proposal with 4% margin of error" or "estimated yield of a certain portfolio for the next year is 6%". How should you interpret these? After all, the observations from the past do not guarantee the performance in the future! Also, what does it mean to say that the performance of an investment fund is statistically significant than another? |
Answers to these questions lie in better understanding the techniques used to draw the aforementioned conclusions. Since we are going to deal with chance-related phenomena, we start with concepts of Probability theory. We shall study the properties of various probability distributions, such as, Binomial, Poisson, Geometric in the discrete spectrum and Uniform, Normal, Exponential in the continuous setup. This will enable you to model many simple random variables encountered in practice by comparing their observed properties to the theoretical ones such as the moment generating function. You would learn to justify, mathematically, many intuitive notions such as the Law of Large Numbers and also the commonly used results such as the Central Limit Theorem, which are at the very heart of Statistics.
Basic statistical techniques can be categorized into three types: point estimation, interval estimation and hypothesis testing. For each of these we shall first develop a general theory -- how to come up with an estimator; what are the good/desired properties of an estimator, how to develop a good (hypothesis testing) procedure, systematically. Since we will be dealing with chance-related phenomena, we can never be foolproof against making errors. For example, there would always be a chance that we decide in favour of one hypothesis whereas the other one is true in reality. You would learn to take these into account while developing a good test procedure.