* this data set has daily closing prices of the 
* Dow Jones Industrial Average from
* January 1950 through January 2007

* load the data
use djia_daily_data

* open a log file
log using djia_random_walk.log, replace

* get descriptive information about the data
desc

* notice the variable time.  the first day is 
* 1, the second day 2, etc.

* define the data as time series
* the variable time is the index
tsset time


*********************************
*********************************
* check EMH in daily returns
* will take the 1st difference between  two 
* adjacent trading days 
*********************************
*********************************

* take the ln of the daily closing price
gen ln_close=ln(close)

* get the 1st difference
gen ln_close1=ln_close[_n-1]


* test for random walk
* run a regression of change ln(closing price) 
* on one period lag
reg ln_close ln_close1
test ln_close1==1

* run a regression allowing for a time trend 
reg ln_close ln_close1 time
test ln_close1==1

* generate 1st difference in returns
gen dln_close=ln_close-ln_close1

* now get the lag of the 1st difference
gen dln_close1=dln_close[_n-1]

* run a regression of the 1st difference on its lag
reg dln_close dln_close1


* identify some stock anomalies
* generate month and day effects
gen dmonth2=month==2
gen dmonth3=month==3
gen dmonth4=month==4
gen dmonth5=month==5
gen dmonth6=month==6
gen dmonth7=month==7
gen dmonth8=month==8
gen dmonth9=month==9
gen dmonth10=month==10
gen dmonth11=month==11
gen dmonth12=month==12
gen tue=weekday==3
gen wed=weekday==4
gen thur=weekday==5
gen fri=weekday==6
reg dln_close time dmonth* tue wed thur fri
test dmonth2 dmonth3 dmonth4 dmonth5 dmonth6 dmonth7 dmonth8 dmonth9 dmonth10 dmonth11 dmonth12
test tue wed thur fri

* get means of delta daily closing price
sum dln_close



*********************************
*********************************
* check EMH in 2-day returns
* will take the 1st difference between  two 
* lagged days 
*********************************
*********************************

clear
use djia_daily_data

* take the ln of the daily closing price
gen ln_close=ln(close)

* get the 2nd difference
gen ln_close2=ln_close[_n-2]

* generate 1st difference 
* in two day returns
gen dln_close=ln_close-ln_close2

* now get the lag of the 1st difference
gen dln_close2=dln_close[_n-2]


* now delete 1/2 of the obs
gen eventime=int(time/2)==time/2
drop if eventime==0

* test for random walk
* run a regression of change ln(closing price) 
* on 2 period period lag
reg ln_close ln_close2
test ln_close2==1

* run a regression allowing for a time trend 
reg ln_close ln_close2 time
test ln_close2==1


* run a regression of the 2nd difference on its lag
reg dln_close dln_close2



*********************************
*********************************
* check EMH in weekly returns
* will take the returns between the last trading
* days of two adjacent weeks
*********************************
*********************************

clear
use djia_daily_data

gen date1=mdy(month,day,year)
gen date2=date1+3652
gen weekno=int((date2-1)/7)+1


keep day month year time date2 weekno close

sort weekno
egen lastdayofweek=max(date2), by(weekno)
keep if lastdayofweek==date2

tsset time

* take the ln of the daily closing price
gen ln_close=ln(close)

* get the 1st difference
gen ln_close1=ln_close[_n-1]


* test for random walk
* run a regression of change ln(closing price) 
* on one period lag
reg ln_close ln_close1
test ln_close1==1

* run a regression allowing for a time trend 
reg ln_close ln_close1 time
test ln_close1==1

* generate 1st difference in returns
gen dln_close=ln_close-ln_close1

* now get the lag of the 1st difference
gen dln_close1=dln_close[_n-1]

* run a regression of the 1st difference on its lag
reg dln_close dln_close1

*********************************
*********************************
* check EMH in monthly returns
* will take the returns between the last trading
* days of two adjacent weeks
*********************************
*********************************
clear
use djia_daily_data

keep day month year time close

sort year month
egen lastdayofmonth=max(time), by(year month)
keep if lastdayofmonth==time

tsset time

* take the ln of the daily closing price
gen ln_close=ln(close)

* get the 1st difference
gen ln_close1=ln_close[_n-1]


* test for random walk
* run a regression of change ln(closing price) 
* on one period lag
reg ln_close ln_close1
test ln_close1==1

* run a regression allowing for a time trend 
reg ln_close ln_close1 time
test ln_close1==1

* generate 1st difference in returns
gen dln_close=ln_close-ln_close1

* now get the lag of the 1st difference
gen dln_close1=dln_close[_n-1]

* run a regression of the 1st difference on its lag
reg dln_close dln_close1