@article{RO_1977__11_2_129_0, author = {Young, Warren L.}, title = {The {Box-Jenkins} approach to time series analysis and forecasting : principles and applications}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {129--143}, publisher = {EDP-Sciences}, volume = {11}, number = {2}, year = {1977}, mrnumber = {443909}, zbl = {0359.62070}, language = {en}, url = {http://archive.numdam.org/item/RO_1977__11_2_129_0/} }

TY - JOUR AU - Young, Warren L. TI - The Box-Jenkins approach to time series analysis and forecasting : principles and applications JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 1977 SP - 129 EP - 143 VL - 11 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/item/RO_1977__11_2_129_0/ LA - en ID - RO_1977__11_2_129_0 ER -

%0 Journal Article %A Young, Warren L. %T The Box-Jenkins approach to time series analysis and forecasting : principles and applications %J RAIRO - Operations Research - Recherche Opérationnelle %D 1977 %P 129-143 %V 11 %N 2 %I EDP-Sciences %U http://archive.numdam.org/item/RO_1977__11_2_129_0/ %G en %F RO_1977__11_2_129_0

Young, Warren L. The Box-Jenkins approach to time series analysis and forecasting : principles and applications. RAIRO - Operations Research - Recherche Opérationnelle, Volume 11 (1977) no. 2, pp. 129-143. http://archive.numdam.org/item/RO_1977__11_2_129_0/

1. On these and related points, see Time Series Analysis, Forecasting, and Control, Holden-Day, San Francisco, 1970; | MR | Zbl

and ,1. Applied Time Series Analysis, Holden-Day, San Francisco, 1973; | Zbl

,1. Seminar on Time Series Analysis, in: The Statistician, vol. 17, No. 3, 1967;

1. Exponential Smoothing, Seasonality, and Projection Sensitivity: the Case of Exports, Bull. Econ. Res. Yorkshire, vol. 26, No. 1, May 1974,

,1. and, by the same author, Seasonality, Autoregression, and Exponential Smoothing: the Case of Economic Time Series, Metron, International Statistical Journal, Gini Institute, Rome, vol. 31, n° 1-4, December 1973;

1. Box-Jenkins Seasonal Forecasting: Problems in a Case Study, J. Roy.Stat. Soc A, No. 136, 1973, p. 295;

and ,1. Box-Jenkins Models: an Alternative to Econometric Models, Int. Stat. Rev., vol. 40, 1972, p. 123; | Zbl

, and ,1. The Combination of Forecasts, Op. Res. Q., vol. 20, 1969.

and ,2. The constant ?o can take on a nonzero value, for example, in cases which require "differencing". This introduces a polynomial of degree d, which is, by nature, deterministic, into the forecast function eventually generated. On this point,see and , ibid., pp. 91-94 and 194-195.

3. See

, op. cit, Chapter 2, 3 ff.4. Ibid, Chapter 5 ff.

5. An intuitive explanation regarding the nature of the partial: autocorrelation function could be given as follows: if, for example, x1, x2,..., xt is a time series, then the partial autocorrelation function at, say, lag j would be the auto correlation of xt and xt +?, under the condition that we already know the values of the observations xt + l, xt + 2,..., xt + ? - 1.

6. It should be noted that the minimum sample for reliable Box-Jenkins analysesis about fifty observations. In addition, given a time series of length T, the autocorrelation and partial autocorrelation functions should be computed only to about K ? T/4 lags, due to the fact that for larger values of K, or as it approaches T, these estimates become quite bad. On these and related points, see Distribution of the Serial Correlation Coefficient, Annals Math. Stats., vol. 13, 1942, p. 1;

,6. On the Theoretical Specification of Sampling Properties of Autocorrelated Time Series, J. Roy. Stat. Soc, B, No. 8, 1946, p. 27; | MR | Zbl

,6. The Fitting of Time Series Models, Rev. Int. Inst. Stats., vol. 28, 1960, p. 223; | Zbl

,6. Approximate Test of Correlation in Time Series, J. Roy. Stat. Soc. B, vol. 11, 1949, p. 68. | MR | Zbl

,7. An Algorithm for Least Squares Estimation of Non-Linear Parameters, J. Soc. Ind. Appl. Math., vol. 2, 1963, p. 431. | Zbl

and , op. cit; ,8.

, op. cit, pp. 82 ff.9. Distribution of Residual Autocorrelations in Autoregressive Integrated Moving Average Time Series Models, J. Amer. Stat. Assn., vol. 65, 1970, p. 1509. | MR | Zbl

and ,10. For a classification of this type of forecast and forecasting types in general, see Forecasting Types and Forecasting Techniques: a Taxonomic Approach in Quality and Quantity, Europ. Amer. J. Method., Elsevier, 1976. Also see , op. cit, Ch. 6 ff;

,10. Experience with Forecasting Univariate Time Series and the Combination of Forecasts, J. Roy. Stats. Soc, A, No. 137, 1974. | MR

and ,11. Practically speaking, however, seasonal modeling using the Box-Jenkins approach can prove difficult. This is due to the fact that at present, we do not know much about the theoretical behaviour of seasonal autocorrelation and partial autocorrelation functions. On these and related points, see A Comparison of Some Models for Predicting Time Series Subject to Seasonal Variation, in: Seminar on Time Series Analysis, op. cit.

and , op. cit; , Ibid, Ch. 7 ff; ,12. On these and related points, see An Economie Analysis of the Effects of Regulating Hire Purchase, H. M. Treasury, Gov't. Economic Service Occasional Papers, 9, London: HMSO, 1974;

,12. Hire Purchase Controls and Consumer Durable Purchases, Queen Mary College, Univ. of London, Dept. of Economics Discussion Paper, March 1975 (25-39-75).

,12. Also see Impact of Credit Controlon Consumer Durable Goods Spending in the United Kingdom, 1957-1961, Rev. Econ. Stud. vol. 30, No. 3, 1963, for an alternative view of the problem.

and ,13. On the principle of "overfitting" and "parameter redundancy", see , op. cit, p. 114.

14.

, op. cit, Appendix H, 1974, pp. 95 ff. The large forecasting error for 1971 III is due to the fact that hire-purchase credit controls were abolished in July, 1971, and were also distorted by strikes earlier that year, in addition to the fact that an increasing number of automobiles were purchased with credit from sources other than finance houses, e. g. personal bank loans and overdrafts, etc.15. An Analysis of Transformations, J. Roy. Stat. Soc, B, No. 26, 1964; | Zbl

and , op. cit; and ,15. Some Recent Advances in Forecasting and Control, Applied Stats., 17, 1968; | MR

and ,15. Forecasting Transformed Series, J. Roy. Stat. Soa, B, No. 38 1976. | MR | Zbl

and ,16. Design and Analysis of Time Series Experiments, Colorado Associated Univ. Press; Boulder, Colo., 1975;

et al.,Estimating the Effects of Intervention Into a Non-Stationary Time Series, Amer. Educ. Res. J., vol. 9, No. 3, 1972;

,A Change in a Level of a Non-Stationary Time Series, Biometrika, vol. 52, June 1965; | MR | Zbl

and ,Intervention Analysis with Applications to Economic and Environmental Problems, J. Amer. Stat. Assn., vol. 70, No. 349, March 1975, pp. 70 ff, 72. | MR | Zbl

and ,