# Accession Number:

## ADA048218

# Title:

## Harmonic Regression.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## YALE UNIV NEW HAVEN CONN DEPT OF STATISTICS

# Personal Author(s):

# Report Date:

## 1977-12-01

# Pagination or Media Count:

## 26.0

# Abstract:

Ordinary linear regression, by the method of least squares, is used to determine a linear relation subsisting between given independent observations of two or more variables. An analogous problem for time series is to determine a linear relation subsisting between two or more given stationary series. The linear relation may take the form that one series is a linear filtering of the other series, plus a stationary error process. The coefficients of the filter can be determined directly by multiple regression in the time domain, but there are difficulties. An easier procedure, leading to more intelligible results, is to estimate the Fourier transform of the coefficients of the filter for each predictor series conveniently expressed as a gain function and a phase-shift function by simpler regression calculations in the frequency domain. The procedure is illustrated by a study of interrelationship of an annual series of output of U.S. copper mines from 1860 to 1975, and two annual economic series relating to the same time period, namely a series of copper prices at New York and a series of total dollar value of general imports of merchandise into the U.S. Author

# Descriptors:

# Subject Categories:

- Mining Engineering
- Statistics and Probability