Initial Data Analysis Kunal Jain February 17, 2010 Economics 201FS.

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)


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


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


Time (Years)

Z V

alue

s

MSFT- Jump Detection (Ratio Adjusted)


Time (Years)

Z V

alue

s

Results- MSFT

Tri-power

Ratio Adjusted



1687 989 667

Percentage 57.8% 33.6% 22.8%

Quad-power

Ratio Adjusted


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


Time (Years)

Z V

alue

s

JNJ- Jump DetectionQuad-power Quarticity

Time (Years)

Z V

alue

s

JNJ- Jump Detection (Ratio Adjusted)


Time (Years)

Z V

alue

s

Results- JNJ

Tri-power

Ratio Adjusted



1972 1557 1096

Percentage 67.5% 53.3% 37.5%

Quad-power

Ratio Adjusted


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

Initial Data Analysis Kunal Jain February 17, 2010 Economics 201FS.

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