Second Attempt at Jump-Detection and Analysis

Mike SchwertECON201FS

2/13/08

My Approach This Week• Last time, found too many jump days. Likely explanations include microstructure noise from using minute-by-minute prices and accidental inclusion of overnight returns in intraday calculations.

• This time, rewrote code to sample prices at 5 minute frequency and exclude overnight returns. Recalculated summary statistics and number of jump days.

• Examined effect of sampling frequency on jump detection by calculating z-statistics and counting jump days for 5, 10, 15, and 20 minute sampling frequencies.

• Examined effect of sampling frequency on volatility calculations by creating volatility signature plots for realized variance and bipower variation.

Note: Closed at 39.28 on 9/10/01, opened at 35.50 on 9/17/01, bottomed out at 28.70 on 9/21/01

GE Stock Prices (5 minute frequency)

Statistics Calculated

Realized Variance:

Bipower Variation:

Relative Jump:

Statistics Calculated

Tri-Power Quarticity:

Quad-Power Quarticity:

Z-Statistic:

Summary Statistics

variable mean std. dev min max

Realized

Variance2.6053 x 10-4 3.8553 x 10-4 1.1104 x 10-5 0.0111

Bipower

Variation2.4719 x 10-4 3.7134 x 10-4 8.3864 x 10-6 0.0092

Relative Jump

0.0601 0.1152 -0.2542 0.6221

Tri-power

Quarticity3.9150 x 10-7 7.7188 x 10-6 7.8711 x 10-11 3.8164 x 10-4

Quad-power

Quarticity3.2979 x 10-7 5.8122 x 10-6 0 2.8166 x 10-4

ZQP-max

Statistic0.6545 1.2069 -2.7547 6.9951

ZQP-max Statistics – 5 minute sampling frequency

Number of jumps at 1% level of significance: 234 out of 2670 days (8.76%)

Number of jumps at 0.1% level of significance: 84 out of 2670 days (3.15%)

Number of jumps at 0.01% level of significance: 29 out of 2670 days (1.09%)

Note: 1% significance when Z > 2.33, 0.1% significance when Z > 3.09, 0.01% significance when Z > 3.71.

Number of jumps at 1% level of significance: 186 out of 2670 days (6.97%)

Number of jumps at 0.1% level of significance: 60 out of 2670 days (2.25%)

Number of jumps at 0.01% level of significance: 17 out of 2670 days (0.64%)

Note: 1% significance when Z > 2.33, 0.1% significance when Z > 3.09, 0.01% significance when Z > 3.71.

ZQP-max Statistics – 10 minute sampling frequency

Number of jumps at 1% level of significance: 148 out of 2670 days (5.54%)

Number of jumps at 0.1% level of significance: 42 out of 2670 days (1.57%)

Number of jumps at 0.01% level of significance: 13 out of 2670 days (0.49%)

Note: 1% significance when Z > 2.33, 0.1% significance when Z > 3.09, 0.01% significance when Z > 3.71.

ZQP-max Statistics – 15 minute sampling frequency

Number of jumps at 1% level of significance: 141 out of 2670 days (5.28%)

Number of jumps at 0.1% level of significance: 40 out of 2670 days (1.50%)

Number of jumps at 0.01% level of significance: 11 out of 2670 days (0.41%)

Note: 1% significance when Z > 2.33, 0.1% significance when Z > 3.09, 0.01% significance when Z > 3.71.

ZQP-max Statistics – 20 minute sampling frequency

Volatility Signature Plots• Used idea introduced by Andersen, Bollerslev, Diebold, and Labys (1999).

• Calculated mean daily realized variance and bipower variation over the sample period under sampling frequencies of 1 minute, 2 minutes, …, 30 minutes.

• Plotted mean realized variance and bipower variation on the y-axis with sampling frequency on the x-axis.

• RV and BV are higher for high-frequency samples because returns are distorted by microstructure noise such as bid-ask bounce.

• RV and BV decrease as interval between samples increases because microstructure noise is cancelled out.

• Must be wary of using too low of a sampling frequency, as sampling variation will affect volatility calculations.

• Balance between sampling variation and microstructure noise appears to be reached around 15 minute sampling frequency.

Volatility Signature Plot – Realized Variance

Volatility Signature Plot – Bipower Variation

Possible Extensions• Perform same calculations on S&P 100 index and stocks highly correlated with GE, or those with similar beta, or from a similar industry, etc.

• Check whether GE jumps on the same days as these other assets.

• Determine how much jumps are systematic vs. idiosyncratic.

• Use volatility signature plots from several stocks to determine ideal sampling frequency for jump detection, if possible.

• Incorporate ARCH, GARCH, or stochastic volatility models somehow?