markov.stat.rice.edu% matlab 

                            < M A T L A B (R) >
                (c) Copyright 1984-98 The MathWorks, Inc.
                            All Rights Reserved
                            Version 5.2.1.1420
                                Apr 30 1998

 
  To get started, type one of these: helpwin, helpdesk, or demo.
  For product information, type tour or visit www.mathworks.com.
 
>> %this is a comment: I like lots of help, so ...
>> helpwin
>> helpdesk
>> %OK, here's another Dow-Jones data set -- from a much earlier time
>> dowj=dlmread('dowj.dat')

dowj =

  110.9400
  110.6900
  110.4300
  110.5600
  110.7500
  110.8400
  110.4600
  110.5600
  110.4600
  110.0500
  109.6000
  109.3100
  109.3100
  109.2500
  109.0200
  108.5400
  108.7700
  109.0200
  109.4400
  109.3800
  109.5300
  109.8900
  110.5600
  110.5600
  110.7200
  111.2300
  111.4800
  111.5800
  111.9000
  112.1900
  112.0600
  111.9600
  111.6800
  111.3600
  111.4200
  112.0000
  112.2200
  112.7000
  113.1500
  114.3600
  114.6500
  115.0600
  115.8600
  116.4000
  116.4400
  116.8800
  118.0700
  118.5100
  119.2800
  119.7900
  119.7000
  119.2800
  119.6600
  120.1400
  120.9700
  121.1300
  121.5500
  121.9600
  122.2600
  123.7900
  124.1100
  124.1400
  123.3700
  123.0200
  122.8600
  123.0200
  123.1100
  123.0500
  123.0500
  122.8300
  123.1800
  122.6700
  122.7300
  122.8600
  122.6700
  122.0900
  122.0000
  121.2300

>> %Whoops; forgot to put a ; after the dlmread statement.
>> %Oh, well, now you have the data
>> size(dowj)

ans =

    78     1

>> %It's a column vector.
>> plot(dowj)     
>> %Looks nonstationary -- generally a bull market trend
>> %Now save it as a file
>> print -deps2
>> %Take logs and differences in an effort to get stationarity
>> ldowj=log10(dowj);
>> dldowj=ldowj(2:78)-ldowj(1:77);
>> plot(dldowj)
>> %Looks much more stationary!!!!
>> print -deps2
>> %Look at the matlab equivalent of the qqnorm from Splus
>> normplot(dldowj)
>> %Not bad, except for 3 values on the upper end
>> print -deps2                                           
>> %typed in the function autocov, which you can download
>> %it is saved in the file 'autocov.m' in the working directory
>> %I am adding my current directory to the path so matlab will find it:
>> path(path,'/home/dcox/Instruct/Stat421/Lessons/Ch2c/Matlab')
>> help autocov

  AUTOCOV(TSERIES) sample autocovariance function
  TSERIES must be a column vector
  returns a column vector

>> ac=autocov(dldowj);
>> %Now the autocorrelation function:
>> acf=ac/ac(1);
>> plot(acf)
>> %Adding the  lines for the informal white noise test
>> length(dldowj)

ans =

    77

>> length(acf)

ans =

    19

>> hold on                         
>> plot([1 19],-ones(2)*2/sqrt(77))
>> plot([1 19],+ones(2)*2/sqrt(77)) 
>> print -deps2
>> %Hmm.  Looks like the acf values at lags 1 and 2 are signficant
>> %Hmm.  Looks like the geometric random walk (=> dldowj is a white noise)
>> % is not tenable here.
>> % Now let's do a periodogram.
>> %So I wrote another function pdgrm.m
>> Idldowj=pdgrm(dldowj);
>> size(Idldowj)

ans =

    38     1

>> %No unrequested padding like Splus forced on me; that's good
>> plot(Idldowj)
>> %Clearly a very strong low frequency component here
>> print -deps2
>> plot(10*log10(Idldowj))
>> print -deps2
>> quit