**1. NAME AND TITLE**

MESA: Non-Linear Least Squares Spectral Analysis.

**2. CONTRIBUTOR**

Oak Ridge National Laboratory, Oak Ridge, Tennessee.

**3. CODING LANGUAGE AND COMPUTER**

Fortran 77; IBM 3033.

**4. NATURE OF PROBLEM SOLVED**

MESA is a non-linear least squares spectral analysis program which can be used to determine the
dominant cycles or characteristics of time series. Assuming that there are cycles in nature, selected
time series were analyzed and expressed as cyclic mathematical functions. In addition, the exponential
behavior of population growth has been incorporated into the models. Polynomial and autoregressive
expressions are also considered. MESA attempts to fit a mathematical model to a time series with the
ultimate purpose of driving the residual time series to white noise.

**5. METHOD OF SOLUTION**

Analysis of time series data is aimed at constructing mathematical functions which describe as many major features of the data as possible. A trend function is fit to the data, removed, and the resulting residuals analyzed for any significant behavior. This is repeated until the residuals are driven to white noise.

In analysis, (a) obvious or hidden trends in the data are removed by fitting the appropriate mathematical functions and (b) the periodogram, Fourier, and MESA spectra of the residual time series are studied to detect other trends. Steps (a) and (b) are repeated until the residuals resemble white noise.

The subroutine VARPRO is employed to estimate the parameters, whether linear or nonlinear.
The subroutine SPECTR determines cyclic behavior in time series.

**6. RESTRICTIONS OR LIMITATIONS**

The total number of time series that can be analyzed is five. There should be no more than 300
points per time series. The same time series can be detrended and analyzed by subroutine SPECTR
using as many as six different detrending models.

**7. TYPICAL RUNNING TIME**

On the IBM 3033, the sample problem runs in about 37 seconds for example 1.

**8. COMPUTER HARDWARE REQUIREMENTS**

MESA is operable on the IBM 3033 computer.

**9. COMPUTER SOFTWARE REQUIREMENTS**

MESA requires a VS Fortran compiler. The DISSPLA plotting routines from ISSCO are used.
Should these not be available, they can be written as dummy subroutines.

**10. REFERENCE**

B. L. Kirk and B. W. Rust, "Inductive Time Series Modeling Program," ORNL/TM-7534 (October
1985).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced document and one (1.2MB) DOS diskette which contains the source
code plus sample problem input and output.

**12. DATE OF ABSTRACT**

February 1986.

**KEYWORDS: ** DATA PROCESSING, SPECTRA; EXPERIMENTAL DATA ANALYSIS;
PLOTTING