Abstract

This paper applies methods of seasonal ARIMA time series analysis to U. S. monthly birth and death rates for January 1950–December 1978. For model selection, the conventional Box-Jenkins (1970, 1976) diagnostic checks are used in conjunction with some suggestions of Nerlove et al. (1979). This results in final models that contain significant second-order autoregressive components, as well as seasonal moving-average components, for both series. In addition, some evidence is found in the birth rate series for weekly periodicities. These findings imply the existence of a seasonal adjustment procedure that improves on the Census X-11 program currently used by vital statistics agencies.

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References

Anderson, R. L. (
1942
).
Distribution of the Serial Correlation Coefficient
.
Annals of Mathematical Statistics
,
13
,
1
13
. 10.1214/aoms/1177731638
Becker, Stan (
1981
).
Seasonal Patterns of Fertility Measures: Theory and Data
.
Journal of the American Statistical Association
,
76
,
249
259
. 10.2307/2287819
Box, George E. P., & Jenkins, Gwilym M. (
1970
).
Times Series Analysis
.
San Francisco
:
Holden-Day
.
Box, George E. P. (
1976
).
Time Series Analysis. Revised Edition
.
San Francisco
:
Holden-Day
.
Box, George E. P., Jenkins, Gwilym M., & Bacon, David W. (
1967
).
Models for Forecasting Seasonal and Non-seasonal Time Series
. In Harris, B. (Ed.),
Advanced Seminar on Spectral Analysis of Time Series
(pp.
271
300
).
New York
:
Wiley
.
Box, George E. P., & Pierce, David A. (
1970
).
Distribution of Residual Autocorrelations in Autoregressive Integrated Moving Average Time Series Models
.
Journal of the American Statistical Association
,
65
,
1509
1526
. 10.2307/2284333
Carvalho, Jose L. 1971. An Alternative Method for Identifying ARIMA Models. Center for Mathematical Studies in Business and Economics. Report 7152, University of Chicago.
Choi, K., & Thacker, S. B. (
1981
).
An Evaluation of Influenza Mortality Surveillance, 1962–1979
.
American Journal of Epidemiology
,
11
,
215
226
.
Cleveland, William S., & Devlin, Susan J. (
1980
).
Calendar Effects in Monthly Time Series: Detection by Spectrum Analysis and Graphical Methods
.
Journal of the American Statistical Association
,
75
,
487
496
. 10.2307/2287636
Cleveland, William S., & Terpenning, Irma J. (
1982
).
Graphical methods for seasonal adjustment
.
Journal of the American Statistical Association
,
77
,
52
62
. 10.2307/2287769
Cleveland, W. S., & Tiao, G. C. (
1976
).
Decomposition of seasonal time series: a model for the Census X-11 program
.
Journal of the American Statistical Association
,
71
,
581
587
. 10.2307/2285586
Granger, Clive W. J., & Newbold, Paul (
1977
).
Forecasting Economic Time Series
.
New York
:
Academic Press
.
Hannan, E. J. (
1960
).
Time Series Analysis
.
London
:
Methuen
.
Henry, Louis (
1976
). van de Walle, E., & Jones, E. F.
Population: Analysis and Models
.
New York
:
Academic Press
.
Hillmer, S. C., & Tiao, G. C. (
1982
).
AN ARIMA-model-based approach to seasonal adjustment
.
Journal of the American Statistical Association
,
77
,
63
70
. 10.2307/2287770
Lee, Ronald Demos (
1974
).
Forecasting Births in Post-Transition Populations: Stochastic Renewal with Serially Correlated Fertility
.
Journal of the American Statistical Association
,
69
,
607
617
. 10.2307/2285990
Lee, Ronald Demos (
1981
).
Short-Term Variation: Vital Rates, Prices, and Weather
. In Wrigley, E. A., & Schofield, R. S. (Eds.),
The Population History of England, 1541-1871: A Reconstruction
(pp.
356
401
).
Cambridge
:
Harvard University Press
.
Manton, Kenneth G., & Stallard, Eric (
1982
).
Temporal Trends in U. S. Multiple Cause of Death Mortality Data: 1968 to 1977
.
Demography
,
19
,
527
548
. 10.2307/2061017
McCleary, Richard, & Hay, Richard A. (
1980
).
Applied Time Series Analysis for the Social Sciences
.
Beverly Hills
:
Sage
.
McDonald, John (
1979
).
A Time Series Approach to Forecasting Australian Total Live-Births
.
Demography
,
16
,
575
601
. 10.2307/2060937
McDonald, John (
1980
).
On Births Time Series Models and Structural Interpretations
.
Journal of the American Statistical Association
,
75
,
39
41
. 10.2307/2287376
McDonald, John (
1981
).
Modeling Demographic Relation-ships: An Analysis of Forecast Functions for Australian Births
.
Journal of the American Statistical Association
,
76
,
782
792
. 10.2307/2287568
National Office of Vital Statistics. 1947. Seasonal Variation in the Crude Birth Rate. Vital Statistics—Special Reports, 23, No. 17.
National Office of Vital Statistics. 1959. Seasonal Variation of Births in the United States, 1948–54. Vital Statistics—Special Reports, 47, No. 4.
Nerlove, Marc, Grether, David M., & Carvalho, Jose L. (
1979
).
Analysis of Economic Time Series
.
New York
:
Academic Press
.
Rindfuss, Ronald R., & Ladinsky, Jack (
1976
).
Patterns of Births: Implications for the Incidence of Elective Induction
.
Medical Care
,
14
,
685
693
. 10.1097/00005650-197608000-00005
Rosenberg, Harry M. (
1966
).
Recent Developments in Seasonally Adjusting Vital Statistics
.
Demography
,
3
,
305
318
. 10.2307/2060160
Rosenwaike, Ira (
1966
).
Seasonal Variation of Deaths in the United States, 1951–1960
.
Journal of the American Statistical Association
,
61
,
706
719
. 10.2307/2282781
Saboia, Joao Luis Maurity (
1977
).
Autoregressive Integrated Moving Average (ARIMA) Models for Birth Forecasting
.
Journal of the American Statistical Association
,
72
,
264
270
. 10.2307/2286787
Serfling, Robert E. (
1963
).
Methods for Current Statistical Analysis of Excess Pneumonia-Influenza Deaths
.
Public Health Reports
,
78
,
494
506
.
Sheps, Mindel C, & Menken, Jane A. (
1973
).
Mathematical Models of Conception and Birth
.
Chicago
:
University of Chicago Press
.
Shiskin, Julius, Young, Allan H., & Musgrave, John C. (
1967
).
The X-11 Variant of the Census Method II Seasonal Adjustment Program
.
Washington, D.C.
:
U. S. Bureau of the Census
.
Shryock, Henry S., & Siegel, Jacob S. (
1973
).
The Methods and Materials of Demography
.
U.S. Government Printing Office
:
Washington, D.C.
.
U. S. National Center for Health Statistics. 1966. Seasonal Variation of Births, United States, 1933–63. Vital and Health Statistics, Series 21, No. 9.
Arnold, Zellner (
1978
).
Seasonal Analysis of Economic Time Series
.
Washington, D.C.
:
U. S. Government Printing Office
.