Next: PEPSYS general photometry package Up: Examples Previous: Period analysis

## Comparison of two stochastic processes

Let the two tables OBSERVA.tbl and OBSERVB.tbl contain two sets of observations. Each set is stored in the DOUBLE PRECISION columns :TIME, :VALUE and :VAR containing the times of observation, data value and their variances.

```
CREATE/GRAPHICS 		 ! Create graphics window
SET/CONTEXT TSA 		 ! Enable TSA package NORMALIZE/TSA OBSERVA :VALUE V 		 ! Normalize variance in both light
NORMALIZE/TSA OBSERVB :VALUE V 		 ! curves to the same value of 1
COVAR/TSA OBSERVA OBSERVA AUTOCOVA 1. 0.1 24 LOG
Compute autocov. of `A' PLOT/TAB AUTOCOVA :LAG :COVAR 		 ! Plot autocov. function of `A'
COVAR/TSA OBSERVB OBSERVB AUTOCOVB ? ? ? LOG
Compute autocov. of `B' PLOT/TAB AUTOCOVB :LAG :COVAR 		 ! Plot autocov. function of `B'
COVAR/TSA OBSERVA OBSERVB CROSSCOV ? ? ? LOG
Compute crosscov. of `A' and `B' PLOT/TAB CROSSCOV :LAG :COVAR 		 ! Plot crosscovariance function
! Now you have to fit a common analytic formula to both autocor-
! relation functions, AUTOCOVA and AUTOCOVBB. The MIDAS FIT package ! or any other suitable tool may be used for this purpose.  ! Choose one of the predefined function forms or code your own ! function URi, 0 < i < 10, in FORTRAN. Then, the analysis ! of the delay can proceed:           		 DELAY/TSA OBSERVA OBSERVB CHI2LAG 0 5 200 EXP 0,1,-0.25
! Do Chi2-time lag analysis
PLOT/TAB CHI2LAG :LAG :CHI2 		 ! Plot the results
```

• References

Abramovitz, M. & Stegun, I.A.:     1972, Handbook of Mathematical Functions, Dover, New York.

Acton, F.S.:     1970, Numerical Methods that Work, Harper & Row, New York.

Bloomfield, P.:     1976, Fourier Analysis of Time Series: An Introduction, Wiley, New York.

Brandt, S.:     1970, Statistical and computational methods in data analysis, North Holland, Amsterdam.

Chatfield, C.:     1985, The Analysis of Time Series: An Introduction, Chapman & Hall, London.

Deeming, T.J.:     1975, Astron. Astrophys. Suppl. 36, 137.

Dvoretsky, M.M.:     1983, Mon. Not. R. astr. Soc. 203, 917.

Eadie, W.T., Drijard, D., James, F.E., Roos, M. & Sadoulet, B.:     1971, Statistical methods in experimental physics, NorthHolland, Amsterdam.

Edelson, R.A. & Krolik J.H.:     1988, Astrophys. J. 333, 646.

Gray, D.F. & Desikachary, K.:     1973, Astrophys. J. 181, 523.

Lafler, J. & Kinman, T.D.:     1965, Astrophys. J. Suppl. 11, 216.

Lomb, N.R.:     1976, Astrophys. Space Sci. 39, 447.

MIDAS Users Guide:     1992 November, European Southern Observatory, Garching.

Press, W.H., Flannery, B.P, Teukolsky, S.A. & Vetterling, W.T.:     1986, Numerical Recipes, Cambridge University Press, Cambridge.

Press, W.H. & Rybicki, G.B.:     1989, Astrophys. J. 338, 277.

Press, W.H. et al.:     1992, Astrophys. J. 385, 404.

Renson, P.:     1978, Astron. Astroph. 63, 125.

Roberts, D.H. et al.:     1987, Astron. J. 93, 968.

Scargle, J.H.:     1982, Astrophys. J. 263, 835.

Schwarzenberg-Czerny, A.:     1989, Mon. Not. R. astr. Soc. 241, 153.

Schwarzenberg-Czerny, A.:     1991, Mon. Not. R. astr. Soc. 253, 198.

Schwarzenberg-Czerny, A.:     1996, Astrophys. J. 460, L107.

Stellingwerf, R.F.:     1978, Astrophys. J. 224, 953.

=31 =1 =1993

Next: PEPSYS general photometry package Up: Examples Previous: Period analysis
Petra Nass
1999-06-15