Copyright 1996 (c) by Marne C. Cario and Barry L. Nelson 

**********************
ARTA PROGRAM HELP FILE
**********************

Marne C. Cario
Updates:  1/3/96, 1/17/96, 2/12/96

The ARTA program consists of a series of Fortran subroutines which
implement the theory in Cario and Nelson [1].  The program performs
two different functions.  First, given an empirical time series, the 
program calculates the sample average, sample variance, and sample 
autocorrelations up to a user-specified lag.  Second, given a
marginal distribution along with a finite number of autocorrelations to
match and their respective desired relative errors, the program outputs
the parameters of the AR process that result in an ARTA process with
the desired properties.

*************
PROGRAM INPUT
*************

The main input for the ARTA program is in the user-created file
"input.dat".  The format of input.dat is:

Line 1:         Name of the file to which program output will go
		(Not to exceed ten characters)
Line 2:		0 if the user does not want the ARTA program to
		  read an empirical time series and calculate
		  sample statistics
		1 if the user does want the ARTA program to
		  read an empirical time series and calculate
		  sample statistics

If the value on Line 2 is 1, then
 
Line 3:		number of observations in the empirical time series
Line 4:		number of sample autocorrelations to calculate 
		(currently, not to exceed 20).

In addition, the user must create a file called "tsdata.dat", which
contains the observations from the empirical time series.  The 
ARTA program will read the observations from this file using a
free format.  No other input is required for this option.

If the value on Line 2 is 0, then

Line 3:		ARTA marginal distribution
		1 = Normal
		2 = Student's t
		3 = Continuous Uniform
		4 = Exponential
		5 = Gamma
		6 = Weibull
		7 = Lognormal
		8 = Johnson Unbounded
		9 = Johnson Bounded
		10 = Empirical
		11 = Discrete Distribution with Finite Support

Line 4:		Number of autocorrelation lags to match (p)
		(currently, not to exceed 5)

Next 2p lines:  Lag-1 autocorrelation (a.c.)
		Desired relative error for lag-1 a.c.
		(e.g., 0.05 for no more than 5% relative error) 
		Lag-2 a.c..
		Desired relative error for lag-2 a.c.
		.
		.
		.
		Lag-p a.c.
		Desired relative error for lag-p a.c.

Next lines:     Parameters of the ARTA marginal distribution
		All non-integer parameters are read in using
		an f10.5 format (5 places before and after 
		the decimal).  All integer parameters are read
		in using an i4 format (four places, no decimal
		point). 

		Distribution         Parameters (in order)
		************         *********************
		1 (Normal)	     mean
				     variance (must be > 0)
		2 (Student's t)	     degrees of freedom
				     (must be an integer > 2)
		3 (Cont. Uniform)    left endpoint
				     right endpoint
		4 (Exponential)	     rate parameter
				     (must be > 0)
		5 (Gamma)	     scale parameter
				     (must be > 0)
				     shape parameter
				     (must be > 0)
		6 (Weibull)	     scale parameter
				     (must be > 0)
				     shape parameter
				     (must be > 0)
		7 (Lognormal)        mean
				     variance
		8 (Johnson Unb.)     first shape parameter
				     second shape parameter
				     location parameter
				     scale parameter
				     (as given in Swain, Venkatraman,
				      and Wilson [2])
		9  (Johnson Bnd.)    first shape parameter
				     second shape parameter
				     location parameter
				     scale parameter
				     (as given in Swain, Venkatraman,
				      and Wilson [2])
		10 (Empirical)	     number of points in cumulative
				     distribution function (c.d.f.)
				     (currently, not to exceed 300 points)
		11 (Discrete)	     number of points in probability
				     mass function
				     (currently, not to exceed 300 points)
				     first value of mass function
				     probability of first value
				     second value of mass function
				     probability of second value
					         .
						 .
						 .
				     final value of mass function
				     probability of second value

If the ARTA marginal distribution is an empirical c.d.f., then
the user must create a file "empir.dat" containing the breakpoints of
the empirical c.d.f.  The ARTA program reads the observations using
a free format, and does not assume that they are in ascending order.

No other user input is required for this option.


**************
PROGRAM OUTPUT
**************

The ARTA program output appears in the file specified on Line 1
of the input file. 

If the program terminated abnormally, then the
reason for abnormal termination will appear in this file.  Reasons
for abnormal termination are:

	1   Marginal distribution is not available
	    (user input was not one of the integers listed above)
	2   User input exceeded the maximum number of
	    autocorrelation lags that the ARTA program 
	    will match (given above)
	3   Input parameter is infeasible for the specified
	    distribution
	4   One or more input autocorrelations does not lie between the
	    minimum and maximum feasible bivariate correlations
	    for the specified marginal distribution
	5   The correlation matrix implied by the specified
	    autocorrelations is not positive definite.
	6   The AR process is not stationary.
 	7   Numerical integration failed (computations too intensive).
	8   Numerical integration failed (computations too intensive).
        9   Number of points in empirical c.d.f. exceeds the 
	    program's limit.


REFERENCES

1  Cario, M. and B.L. Nelson.  1995.  Autoregressive to anything:
   Time-series input processes for simulation.  Operations Research
   Letters, forthcoming.

2  Swain, J.J., Venkatraman, S., and J.R. Wilson.  1988.  Least-squares
   estimation of distribution functions in Johnson's translation
   system.  Journal of Statistical Computation and Simulation 29, 
   271-297.