Copyright 1996 (c) by Marne C. Cario and Barry L. Nelson
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ARTA PROGRAM HELP FILE
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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.
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PROGRAM INPUT
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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)
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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.
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PROGRAM OUTPUT
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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.