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<H2><A NAME="SECTION001762000000000000000">
Comparison of two stochastic processes</A>
</H2>
<P>
Let the two tables <TT>OBSERVA.tbl</TT> and <TT>OBSERVB.tbl</TT> contain two
sets of observations. Each set is stored in
the <TT>DOUBLE PRECISION</TT> columns <TT>:TIME</TT>, <TT>:VALUE</TT> and <TT>:VAR</TT> containing the times of
observation, data value and their variances.
<P>
<PRE><TT>
<TT><TT>CREATE/GRAPHICS ! Create graphics window
<BR><TT>SET/CONTEXT TSA ! Enable TSA package <BR><TT>NORMALIZE/TSA OBSERVA :VALUE V ! Normalize variance in both light
<BR><TT>NORMALIZE/TSA OBSERVB :VALUE V ! curves to the same value of 1
<BR><TT>COVAR/TSA OBSERVA OBSERVA AUTOCOVA 1. 0.1 24 LOG
<BR><TT> Compute autocov. of `A' <BR><TT>PLOT/TAB AUTOCOVA :LAG :COVAR ! Plot autocov. function of `A'
<BR><TT>COVAR/TSA OBSERVB OBSERVB AUTOCOVB ? ? ? LOG
<BR><TT> Compute autocov. of `B' <BR><TT>PLOT/TAB AUTOCOVB :LAG :COVAR ! Plot autocov. function of `B'
<BR><TT>COVAR/TSA OBSERVA OBSERVB CROSSCOV ? ? ? LOG
<BR><TT> Compute crosscov. of `A' and `B' <BR><TT>PLOT/TAB CROSSCOV :LAG :COVAR ! Plot crosscovariance function
<BR><TT> <BR>! Now you have to fit a common analytic formula to both autocor-
<BR>! relation functions, AUTOCOVA and AUTOCOVBB. The MIDAS FIT package <BR>! or any other suitable tool may be used for this purpose. <BR>! Choose one of the predefined function forms or code your own <BR>! function UR</TT></TT></TT></TT></TT></TT></TT></TT></TT></TT></TT></TT></TT></TT></TT><SUB><I>i</I></SUB><TT><TT><TT><TT><TT><TT><TT><TT><TT><TT><TT><TT><TT><TT><TT>, </TT></TT></TT></TT></TT></TT></TT></TT></TT></TT></TT></TT></TT></TT></TT>0 < <I>i</I> < 10<TT><TT><TT><TT><TT><TT><TT><TT><TT><TT><TT><TT><TT><TT><TT>, in FORTRAN. Then, the analysis <BR>! of the delay can proceed: <BR><TT> <BR><TT>DELAY/TSA OBSERVA OBSERVB CHI2LAG 0 5 200 EXP 0,1,-0.25
<BR><TT> ! Do Chi2-time lag analysis
<BR><TT>PLOT/TAB CHI2LAG :LAG :CHI2 ! Plot the results <BR>
</TT></PRE></TT></TT></TT></TT></TT></TT></TT></TT></TT></TT></TT></TT></TT></TT></TT></TT></TT></TT></TT>
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<BR>
<P>
<UL>
<LI><FONT SIZE="+2"><B>References</B></FONT>
<BR>
<BR>
<P>
Abramovitz, M. & Stegun, I.A.: 1972, <EM>Handbook of Mathematical
Functions</EM>, Dover, New York.
<P>
Acton, F.S.: 1970, <EM>Numerical Methods that Work</EM>,
Harper & Row, New York.
<P>
Bloomfield, P.: 1976, <EM>Fourier Analysis of Time Series: An
Introduction</EM>, Wiley, New York.
<P>
Brandt, S.: 1970, <EM>Statistical and computational methods in data
analysis</EM>, North Holland, Amsterdam.
<P>
Chatfield, C.: 1985, <EM>The Analysis of Time Series: An Introduction</EM>,
Chapman & Hall, London.
<P>
Deeming, T.J.: 1975, <EM>Astron. Astrophys. Suppl</EM>. <B>36</B>, 137.
<P>
Dvoretsky, M.M.: 1983, Mon. Not. R. astr. Soc. <B>203</B>, 917.
<P>
Eadie, W.T., Drijard, D., James, F.E., Roos, M. & Sadoulet, B.: 1971,
<EM>Statistical methods in experimental physics</EM>, NorthHolland,
Amsterdam.
<P>
Edelson, R.A. & Krolik J.H.: 1988, <EM>Astrophys. J</EM>. <B>333</B>, 646.
<P>
Gray, D.F. & Desikachary, K.: 1973, <EM>Astrophys. J</EM>. <B>181</B>, 523.
<P>
Lafler, J. & Kinman, T.D.: 1965, <EM>Astrophys. J. Suppl</EM>. <B>11</B>,
216.
<P>
Lomb, N.R.: 1976, <EM>Astrophys. Space Sci</EM>. <B>39</B>, 447.
<P>
MIDAS Users Guide: 1992 November, European Southern Observatory, Garching.
<P>
Press, W.H., Flannery, B.P, Teukolsky, S.A. & Vetterling, W.T.: 1986,
<EM>Numerical Recipes</EM>, Cambridge University Press, Cambridge.
<P>
Press, W.H. & Rybicki, G.B.: 1989, <EM>Astrophys. J</EM>. <B> 338</B>, 277.
<P>
Press, W.H. et al.: 1992, <EM>Astrophys. J</EM>. <B>385</B>, 404.
<P>
Renson, P.: 1978, <EM>Astron. Astroph</EM>. <B>63</B>, 125.
<P>
Roberts, D.H. et al.: 1987, <EM>Astron. J</EM>. <B>93</B>, 968.
<P>
Scargle, J.H.: 1982, <EM>Astrophys. J.</EM> <B>263</B>, 835.
<P>
Schwarzenberg-Czerny, A.: 1989, <EM>Mon. Not. R. astr. Soc</EM>. <B>241</B>, 153.
<P>
Schwarzenberg-Czerny, A.: 1991, <EM> Mon. Not. R. astr. Soc</EM>. <B>253</B>, 198.
<P>
Schwarzenberg-Czerny, A.: 1996, <EM>Astrophys. J</EM>. <B>460</B>, L107.
<P>
Stellingwerf, R.F.: 1978, <EM>Astrophys. J</EM>. <B>224</B>, 953.
<P>
</UL>
<P>
<P>
=31 =1 =1993
<P>
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<ADDRESS>
<I>Petra Nass</I>
<BR><I>1999-06-15</I>
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