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.