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Math for Quantitative Finance

# Statistics

Statistics is used to gather information from samples of data to make inferences about the overall population. However, as our computational abilities increase, we can process and analyze more and more data--potentially the entire data sets of all trading activity.

Why, then, is statistics still relevant to modern quantitative finance?

A. Sampling algorithms run faster than looking at the entire data set.

B. Statistics can help determine the significance of results/models.

C. Statistics can help avoid overfitting.

One of the uses of statistics in quantitative finance, as mentioned in the previous question, is to determine the significance of certain results. A classic benchmark for statistical significance is a p-value of 5%.

True or False?

Achieving a $$p$$-value of 5% means that there is a 5% chance that the original hypothesis is true.

You believe that a certain stock goes up with probability 50% and goes down with probability 50% on any given day, independent of any other days. If you observe 8 up days and 2 down days over a two week period, does this suggest your belief is flawed at the 5% significance level?

Which of the following is the biggest drawback of using linear regression to model the relationship between different financial assets?

In a typical statistical model of stock prices, which measure of central tendency is usually the greatest?

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