1 / 18

Hypothesis Testing

Hypothesis Testing. Correct models?Data similar?Use one series to predict anotherHas something changed in the data?Quality control, portfolio strategiesTesting basic mechanisms for modelling the world. Simulation Methodology. Get statistics from real dataSimulate modelCompare model simulatio

arnon
Download Presentation

Hypothesis Testing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

    1. Hypothesis Testing FIN285a: Lecture 2.2.3 Fall 2010

    2. Hypothesis Testing Correct models? Data similar? Use one series to predict another Has something changed in the data? Quality control, portfolio strategies Testing basic mechanisms for modelling the world

    3. Simulation Methodology Get statistics from real data Simulate model Compare model simulations to real data Question: Could statistics (random variables) be draws from model?

    4. Software pollchange.m dietest.m retdiff.m

    5. Outline Terminology Proportion changes (Political polls) Testing a distribution (die) Portfolio manager regime change

    6. Hypothesis Testing Jorion 3.2.2 Null hypothesis Assumption about how the world works Assume this is true Could data have come from this machine/theory/conjecture??? Do you need more/other data?

    7. Hypothesis Testing Terms Null hypothesis Assumption about the world Test statistic Observed statistic (Random variable) p-value (probability of getting a given test statistic value, with the null hypothesis) Trading profits = 100, given a random walk for prices

    8. Outline Terminology Proportion changes (Political polls) Testing a distribution (die) Portfolio manager regime change

    9. Political Poll Obama/McCain 0/1 Two polls (100 people) First 50/50 Second 55/45 What is the probability that something has changed in the population? Matlab: pollchange.m

    10. Outline Terminology Proportion changes (Political polls) Testing a distribution (die) Portfolio manager regime change

    11. Testing a Die Problem: You’ve observed the following rolls of a die out of 6000 rolls 1: 1014, 2: 958, 3: 986, 4: 995, 5: 1055, 6:992 Could this have come from a fair die with probs of 1/6 for each side?

    12. Dietest.m Method: Think up a test statistic Roll 6000 dies with sample Check how the value of the test statistic from the original data compares with the distribution from the simulations dietest.m

    13. Outline Terminology Proportion changes (Political polls) Testing a distribution (die) Portfolio manager regime change

    14. Testing and “critical values” Reject null hypothesis if stat > C C = critical value Prob(reject | null is true ) = size for test Prob(decide trading rule works | random walk) Also known as type I error Prob(reject | null is false) = power for test Prob(deciding trading rule works | trending prices) Prob(not reject | null is false) = type II error = ( 1 - power)

    15. Mushrooms and Toadstools Test for toadstool (poisonous) Null = mushroom Reject (don't eat) if test stat rejects Eat mushrooms, throw out toadstools Type I error (size): Probability of throwing out good mushrooms Power : probability of throwing out toadstools Type II error: Probability of accepting (eating) a toadstool

    16. Differences in Means Two samples Different means Could they be drawn from the same population? Examples Growth rates Portfolio returns Interest rates Default rates

    17. Peformance Change? Matlab: retdiff Problem: Portfolio manager performance appears to change Is it “significant”? Null hypothesis: Normal distribution for returns with unchanging mean and standard deviation

    18. Outline Terminology Proportion changes (Political polls) Testing a distribution (die) Portfolio manager regime change

More Related