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Introducing the Lee-Mykland Test New Rejection Region method Results for XOM, COP, and CVX

Introducing the Lee-Mykland Test New Rejection Region method Results for XOM, COP, and CVX Problems with the test Possible Corrections to the test Extensions.

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Introducing the Lee-Mykland Test New Rejection Region method Results for XOM, COP, and CVX

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  1. Introducing the Lee-Mykland Test • New Rejection Region method • Results for XOM, COP, and CVX • Problems with the test • Possible Corrections to the test • Extensions

  2. -Creates a statistic L(i), for each price, comparing the change in price on the interval [ ti-1, ti] to an instantaneous volatility measure using the previous 270 returns

  3. -The distribution of L(i) is normal under the null hypothesis that no jumps occur over a given set An {1,2,….n} -The asymptotic distribution of the absolute value of the maximum L(i)in a given day is exponential -Where Cn and Sn, given n= and c=sqrt(2/pi):

  4. -To actually test whether a return represents a significant jump, (|L(i)|-Cn)/Sn > B, where B=4.6001 at 1% level of significance -The size of the BNS test is .1%, where each day has a .001 probability of being a jump day -Then, using a 1% level of significance for each observation for the Lee-Mykland statistic will yield a much higher size than .1%

  5. -The window size they suggest for 5-minute data is K=270 observations -Thus, they calculate the instantaneous volatility going back 2.5 days -While this accounts for changes in local volatility on a larger scale, it does not adequately correct for intra- and inter-day changes in volatility -Specifically, inter-day volatility follows a U-shape, with higher volatility in the morning and lower volatility in the afternoon

  6. -Average BVj=(1/K) ∑ |Rt,j-1|^(1/2)*|Rt,j|*|Rt,j+1|^(1/2)

  7. -The average returns appear to be constant around zero throughout the trading day…(reassuring)

  8. -Let t=day and j=observation number in a given day -So, R4,5 refers to the return of the 9:55 observation of the 4th day -If we scale the return Rt,j by the average BVj at time interval j, the resulting return should account for the daily trend in volatility -Thus, we could try R*= Rt,j/ sqrt(BVj) -Then, we can re-calculate the instantaneous volatility using the adjusted returns -Average BVj=(1/K) ∑ |Rt,j-1|^(1/2)*|Rt,j|*|Rt,j+1|^(1/2)

  9. Correcting the Lee-Mykland test • Factor analysis looking at LM jump statistic across a range of oil and market stocks • Volatility correlation with small lag times • Can we use the implied volatility of same industry companies and oil futures to forecast volatility using the HAR-RV-CJ model? • More familiarity with the practices of the oil industry, especially their trading desk operation to determine how they deal with oil price volatility

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