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Sampling Frequency and Jump Detection

This study explores different jump detection methods using various jump tests and examines the robustness of these tests. The data includes minute-by-minute price data for GE, ExxonMobil, AT&T, and S&P 500. Tests examined include Barndorff-Nielsen Shephard, Jiang-Oomen, and Lee-Mykland.

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Sampling Frequency and Jump Detection

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  1. Sampling Frequency and Jump Detection Mike Schwert ECON201FS 3/19/08

  2. This Week’s Approach and Data • Last week, found different jump days for different sampling frequencies using the Barndorff-Nielsen Shephard jump test ZQP-max statistic • This week, trying other jump tests to see if they are sample robust • BN-S test using ZQP-max and ZTP-max statistics • Jiang-Oomen jump test • Lee-Mykland jump test • Price Data: • GE minute-by-minute 1997 – 2007 (2670 days) • ExxonMobil minute-by-minute 1999 – 2008 (2026 days) • AT&T minute-by-minute 1997 – 2008 (2680 days) • S&P 500 every 5 minutes, 1985 – 2007 (5545 days, excluding short days)

  3. Barndorff-Nielsen Shephard Tests

  4. Barndorff-Nielsen Shephard Tests

  5. Contingency Tables – ZQP-max Statistic GE S&P 500 Exxon Mobil AT&T

  6. Contingency Tables – ZTP-max Statistic GE S&P 500 Exxon Mobil AT&T

  7. Jiang-Oomen Swap Variance Tests • Introduced by George Jiang and Roel Oomen in a 2005 paper • Tests for daily jumps, similar to BN-S, but uses “Swap Variance” measure instead of Bipower Variation to form a test statistic • Test is called this because it is “directly related to the profit/loss function of a variance swap replication strategy using a log contract”

  8. Jiang-Oomen Swap Variance Tests Difference Test: Logarithmic Test: Ratio Test:

  9. Contingency Tables – SwapVar Difference Test GE S&P 500 Exxon Mobil AT&T

  10. Contingency Tables – SwapVar Log Test GE S&P 500 Exxon Mobil AT&T

  11. Contingency Tables – SwapVar Ratio Test GE S&P 500 Exxon Mobil AT&T

  12. Lee-Mykland Test • Introduced by Suzanne Lee and Per Mykland in a 2007 paper • Allows identification of jump timing, multiple jumps in a day

  13. Lee-Mykland Test – Summary Statistics • GE price data, sampled at 5 minute frequency • Something wrong with code…critical value for jumps is 4.6001 GE - Daily Contingencies GE – Hourly Contingencies

  14. Possible Extensions • Other ways to formally analyze effects of sampling frequency on jump detection? • Identify problem with current implementation of Lee-Mykland test • Best way to compare Lee-Mykland results between samples? • Look at more samples, i.e. {1, 2, …, 20} instead of {5, 10, 15, 20} • Experiment with randomly generated data to examine effect of dependence on contingency tables • Regress z-statistics on changes in daily volume to see if days with high volume correspond to jump days, common jump days between samples

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