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Initial Data Analysis
Kunal JainFebruary 17, 2010Economics 201FS
Raw Data
Amazon (AMZN): August 1, 1997 – January 7, 2009 2,846 Days
Johnson & Johnson (JNJ): April 9, 1997 – January 7, 2009 2,923 Days
Microsoft Corporation (MSFT): April 16, 1997 – January 7, 2009 2,921 Days 2:1 Share splits
February 23, 1998, March 29, 1999, Feb 18, 2003,
Price data available every minute from 9:35 AM to 3:59 PM for each trading day
AMZN- Share Price Levels
1997 2000 2002 2005 2007 20100
20
40
60
80
100
120
Time (Years)
Sh
are
Pric
e (
$)
AMZN- Adjusted Log Returns
Time (Years)
Ad
just
ed
1-M
inu
te R
etu
rns
•1-minute returns
AMZN- Realized Variation
Time (Years)
Re
aliz
ed
Va
rian
ce
AMZN- Bi-Power VariationR
ea
lize
d V
aria
nce
Time (Years)
AMZN- RV & BVR
ea
lize
d V
aria
nce
Time (Years)
AMZN- Volatility Signature Plot
0 5 10 15 20 25 301.3
1.35
1.4
1.45
1.5
1.55
1.6
1.65
1.7x 10
-3
Sampling Frequency
Ave
rag
e A
nn
ua
lize
d R
ea
lize
d V
ola
tility
(%
)
AMZN- Jump Detection
Tri-power Quarticity
Time (Years)
Z V
alue
s
AMZN- Jump Detection
Quad-power Quarticity
Time (Years)
Z V
alue
s
AMZN- Jump Detection (Ratio Adjusted)
Tri-power Quarticity
Time (Years)
Z V
alue
s
AMZN- Jump Detection (Ratio Adjusted)
Quad-power Quarticity
Time (Years)
Z V
alue
s
Results- AMZN
Tri-power
Ratio Adjusted
.95 significance .99 significance .999 significance
Number of days with jumps
1972 1557 1096
Percentage 69.3% 54.7% 38.5%
Quad-power
Ratio Adjusted
Number of days with jumps
2044 1656 1264
Percentage 71.8% 58.2% 44.4%
MSFT- Share Price Levels
Time (Years)
Sh
are
Pric
e (
$)
1996 1998 2000 2002 2004 2006 2008 201010
15
20
25
30
35
40
45
50
55
60
MSFT- Adjusted Log Returns
Time (Years)
Ad
just
ed
1-M
inu
te R
etu
rns
•1-minute returns
MSFT- Realized Variation
Time (Years)
Re
aliz
ed
Va
rian
ce
MSFT- Bi-power VariationR
ea
lize
d V
aria
nce
Time (Years)
MSFT- RV & BVR
ea
lize
d V
aria
nce
Time (Years)
MSFT- Volatility Signature Plot
Sampling Frequency
Ave
rag
e A
nn
ua
lize
d R
ea
lize
d V
ola
tility
(%
)
0 5 10 15 20 25 303
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8x 10
-4
MSFT- Jump Detection
Tri-power Quarticity
Time (Years)
Z V
alue
s
MSFT- Jump Detection
Quad-power Quarticity
Time (Years)
Z V
alue
s
MSFT- Jump Detection (Ratio Adjusted)
Tri-power Quarticity
Time (Years)
Z V
alue
s
MSFT- Jump Detection (Ratio Adjusted)
Quad-power Quarticity
Time (Years)
Z V
alue
s
Results- MSFT
Tri-power
Ratio Adjusted
.95 significance .99 significance .999 significance
Number of days with jumps
1687 989 667
Percentage 57.8% 33.6% 22.8%
Quad-power
Ratio Adjusted
Number of days with jumps
1762 1273 825
Percentage 60.3% 43.6% 28.2%
JNJ- Share Price Levels
Time (Years)
Sh
are
Pric
e (
$)
1996 1998 2000 2002 2004 2006 2008 201025
30
35
40
45
50
55
60
65
70
75
JNJ- Adjusted Log Returns
Time (Years)
Ad
just
ed
1-M
inu
te R
etu
rns
•1-minute returns
JNJ- Realized Variation
Time (Years)
Re
aliz
ed
Va
rian
ce
JNJ- Bi-power VariationR
ea
lize
d V
aria
nce
Time (Years)
JNJ- RV & BVR
ea
lize
d V
aria
nce
Time (Years)
JNJ- Volatility Signature Plot
Sampling Frequency
Ave
rag
e A
nn
ua
lize
d R
ea
lize
d V
ola
tility
(%
)
0 5 10 15 20 25 301.6
1.7
1.8
1.9
2
2.1
2.2
2.3x 10
-4
JNJ- Jump Detection
Tri-power Quarticity
Time (Years)
Z V
alue
s
JNJ- Jump DetectionQuad-power Quarticity
Time (Years)
Z V
alue
s
JNJ- Jump Detection (Ratio Adjusted)
Tri-power Quarticity
Time (Years)
Z V
alue
s
JNJ- Jump Detection (Ratio Adjusted)
Quad-power Quarticity
Time (Years)
Z V
alue
s
Results- JNJ
Tri-power
Ratio Adjusted
.95 significance .99 significance .999 significance
Number of days with jumps
1972 1557 1096
Percentage 67.5% 53.3% 37.5%
Quad-power
Ratio Adjusted
Number of days with jumps
2044 1656 1264
Percentage 69.9% 56.7% 43.3%
Results & Plans Experience with MATLAB
Sources of error due to computational skills Intense Introduction
Better understanding of BNS testing AMZN and JNJ jump test results
Run with i.d.d. randomly generated numbers Time interval based on volatility signature plot
Additional Work and Background Reading Refine existing results Use other sampling frequencies to check results Utilize more tests Look at public announcements that relate to z-statistics