Practical Hypothesis Tests for Financial Data
Summary
This note points readers to a finance and statistics reference whose hypothesis testing chapter works through several tests in market settings. Examples include testing a Poisson default rate for a risky bond portfolio, an exponential model for time between defaults, and stock index return means or variances under specified distributional assumptions. It also mentions comparing the mean returns of two stocks, testing equality of distributions with a Kolmogorov–Smirnov test, and likelihood ratio testing.
The examples connect test choice to the parameter of interest, the null and alternative hypotheses, and whether a test is one or two tailed. The note describes the reference as providing detailed worked examples, but does not show their calculations, discuss assumptions or test performance, or explain how to apply the procedures to real data. The listed tests therefore serve as a guide to topics for further study rather than a complete testing method.
Key ideas
- Financial hypothesis tests can examine default counts and times between defaults under Poisson and exponential models.
- Tests of stock index returns can target a mean or variance under stated distributional assumptions.
- The alternative hypothesis determines whether a test is one tailed or two tailed.
- Two-stock mean comparisons, distribution comparisons, and likelihood ratio tests are also identified as finance applications.
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Full text
# Hypothesis testing book # Hypothesis testing book I am looking for a book that is focused on hypothesis testing. I read "Hypothesis Testing: An Intuitive Guide for Making Data Driven" by Jim Frost and I'm looking for similar book which is focused on practical applications of diferent tests (and exaplains how they works and when to use it) ## Answer by Dimitri Vulis (score 1) https://quant.stackexchange.com/a/66484 I dug up this book: Svetlozar Rachev, Markus Höchstötter, Frank Fabozzi, Sergio Focardi. Probability and Statistics for Finance. Wiley (2011). Chapter 19 is "Hypothesis Testing". It does not go as deep into the theory as Lehman. Starting on page 496, it lists several concrete and practical examples pertinent to finance and markets, worked out in lots of detail. 1 (simple test for parameter $\lambda$ of Poisson distribution) Consider a portfolio of risky bonds, where the number of defaulting bonds within one year is modeled as a Poisson random variable with parameter $\lambda$. The null hypothesis $H_0$ is that $\lambda=\lambda_0$, while the alternative hypothesis $H_1$ is that $\lambda=\lambda_1$, for some values $\lambda_0$ and $\lambda_1$. 2 (1-tailed test for parameter $\lambda$ of exponential distribution) Same risky bond portfolio, and the time between two successive defaults is given by an exponential random variable with parameter $\lambda$. The null hypothesis $H_0$ is that $\lambda \ge 1$, e.g. 1, while the alternative hypothesis $H_1$ is that $0 < \lambda <1$. 3 (1-tailed test for the mean $\mu$ of a normal distribution where the variance is known.) $\mu$ is the mean of the daily returns of a stock index. The null hypothesis $H_0$ is that $\mu \le y$, while the alternative hypothesis $H_1$ is that $\mu > y$ for some value $y$. 4 (1-tailed test for the variance of a normal distribution where the mean is known.) Same stock index, the null hypothesis $H_0$ is that $\sigma^2 >v$, while the alternative hypothesis $H_1$ is that $0 < \sigma^2 <v$ for some value $v$. 5 (2-tailed test for the mean $\mu$ of a normal distribution where the variance is known.) Same stock index, the null hypothesis $H_0$ is that $\mu = y$, while the alternative hypothesis $H_1$ is that $\mu \ne y$ for some value $y$. 6 (Equal tails test for the variance of a normal distribution where the mean is known.) Same stock index, the null hypothesis $H_0$ is that $\sigma^2 = v$, while the alternative hypothesis $H_1$ is that $\sigma^2 \ne v$ for some value $v$. 7 Test for equality of means: given two stocks, are their mean returns the same... 8 2-tailed Kolmogorov-Smirnov test for equality of distribution... 9 Likelihood ratio test...
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