Abstract
As mentioned in the introduction, the publication of the textbook by GEORGE E.P. BOX and GWILYM M. JENKINS in 1970 opened a new road to the analysis of economic time series. This chapter presents the Box-Jenkins Approach, its different models and their basic properties in a rather elementary and heuristic way. These models have become an indispensable tool for short-run forecasts. We first present the most important approaches for statistical modelling of time series. These are autoregressive (AR) processes (Section 2.1) and moving average (MA) processes (Section 2.2), as well as a combination of both types, the so-called ARMA processes (Section 2.3). In Section 2.4 we show how this class of models can be used for predicting the future development of a time series in an optimal way. Finally, we conclude this chapter with some remarks on the relation between the univariate time series models described in this chapter and the simultaneous equations systems of traditional econometrics (Section 2.5).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Since the time when HERMAN WOLD developed the class of ARMA processes in his dissertation and GEORGE E.P. BOX and GWILYM M. JENKINS (1970) popularised and further developed this model class in the textbook mentioned above, there have been quite a lot of textbooks dealing with these models at different technical levels. An introduction focusing on empirical applications is, for example, to be found in
ROBERT S. PINDYCK and DANIEL L. RUBINFELD, Econometric Models and Economic Forecasts, McGraw-Hill, Boston et al., 4th edition 1998, Chapter 17f. pp. 521 – 578,
PETER J. BROCKWELL and RICHARD A. DAVIS, Introduction to Time Series and Forecasting, Springer, New York et al. 1996, as well as
TERENCE C. MILLS, Time Series Techniques for Economists, Cambridge University Press, Cambridge (England) 1990. Contrary to this,
PETER J. BROCKWELL and RICHARD A. DAVIS, Time Series: Theory and Methods, Springer, New York et al. 1987,
give a rigorous presentation in probability theory. Along with the respective proofs of the theorems, this textbook shows, however, many empirical examples. Autoregressive processes for the residuals of an estimated regression equation were used for the first time in econometrics by
DONALD COCHRANE and GUY H. ORCUTT, Application of Least Squares Regression to Relationships Containing Autocorrelated Error Terms, Journal of the American Statistical Association 44 (1949), pp. 32 – 61.
The different information criteria to detect the order of an autoregressive process are presented in
HIROTUGU AKAIKE, Fitting Autoregressive Models for Prediction, Annals of the Institute of Statistical Mathematics AC-19 (1974), pp. 364 – 385,
HIROTUGU AKAIKE, A New Look at the Statistical Model Identification, IEEE Transactions on Automatic Control 21 (1969), pp. 234 – 237,
GIDEON SCHWARZ, Estimating the Dimensions of a Model, Annals of Statistics 6 (1978), pp. 461 – 464, as well as in
EDWARD J. HANNAN and BARRY G. QUINN, The Determination of the Order of an Autoregression, Journal of the Royal Statistical Society B 41 (1979), pp. 190 – 195.
The effect of temporal aggregation on the first differences of temporal averages have first been investigated by
HOLBROOK WORKING, Note on the Correlation of First Differences of Averages in a Random Chain, Econometrica 28 (1960), pp. 916 – 918
and later on, in more detail, by
GEORGE C. TIAO, Asymptotic Behaviour of Temporal Aggregates of Time Series, Biometrika 59 (1972), pp. 525 – 531.
The approach to check the consistency of predictions was developed by
JACOB MINCER and VICTOR ZARNOWITZ, The Evaluation of Economic Forecasts, in: J. MINCER (ed.), Economic Forecasts and Expectations, National Bureau of Economic Research, New York 1969.
The use of MA processes of the forecast errors to estimate the variances of the estimated parameters was presented by
BRYAN W. BROWN and SHLOMO MAITAL, What Do Economists Know? An Empirical Study of Experts’ Expectations, Econometrica 49 (1981), pp. 491 – 504.
The fact that measurement errors also play a role in rational forecasts and that, therefore, instrumental variable estimators should be used, was indicated by
JINOOK JEONG and GANGADHARRAO S. MADDALA, Measurement Errors and Tests for Rationality, Journal of Business and Economic Statistics 9 (1991), pp. 431 – 439.
These procedures have been applied to the common forecasts of the German economic research institutes by
GEBHARD KIRCHGÄSSNER, Testing Weak Rationality of Forecasts with Different Time Horizons, Journal of Forecasting 12 (1993), pp. 541 – 558.
Moreover, the forecasts of the German Council of Economic Experts as well as those of the German Economic Research Institutes were investigated in
HANNS MARTIN HAGEN and GEBHARD KIRCHGÄSSNER, Interest Rate Based Forecasts of German Economic Growth: A Note, Weltwirtschaftliches Archiv 132 (1996), pp. 763 – 773.
The measure of inequality (Theil’s U) was proposed by
HENRY THEIL, Economic Forecasts and Policy, North-Holland, Amsterdam 1961.
An alternative measure is given in
HENRY THEIL, Applied Economic Forecasting, North-Holland, Amsterdam 1966.
Today, both measures are used in computer programmes. Quite generally, forecasts for time series data are discussed in
CLIVE W.J. GRANGER, Forecasting in Business and Economics, Academic Press, 2nd edition 1989.
On the evaluation of the predictive accuracy of forecasts see
FRANCIS X. DIEBOLD and ROBERTO S. MARIANO, Comparing Predictive Accuracy, Journal of Business and Economic Statistics 13 (1995), pp. 253 – 263.
The relationship between time series models and econometric equation systems is analysed in
ARNOLD ZELLNER and FRANZ C. PALM, Time Series Analysis and Simultaneous Equation Econometric Models, Journal of Econometrics 2 (1974), pp. 17 – 54.
See for this also
FRANZ C. PALM, Structural Econometric Modeling and Time Series Analysis: An Integrated Approach, in: A. ZELLNER (ed.), Applied Time Series Analysis of Economic Data, U.S. Department of Commerce, Economic Research Report ER-S, Washington 1983, pp. 199 – 230.
The term final equation originates from
JAN TINBERGEN, Econometric Business Cycle Research, Review of Economic Studies 7 (1940), pp. 73 – 90.
An introduction into the solution of difference equations is given in
WALTER ENDERS, Applied Econometric Time Series, 3rd edition, Wiley, Hoboken, N.J. 2010, Chapter 1.
The permanent income hypothesis as a determinant of consumption expenditure was developed by
MILTON FRIEDMAN, A Theory of the Consumption Function, Princeton University Press, Princeton N.J. 1957.
The example of the estimated popularity function is given in
GEBHARD KIRCHGÄSSNER, Causality Testing of the Popularity Function: An Empirical Investigation for the Federal Republic of Germany, 1971 – 1982, Public Choice 45 (1985), pp. 155 – 173.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kirchgässner, G., Wolters, J., Hassler, U. (2013). Univariate Stationary Processes. In: Introduction to Modern Time Series Analysis. Springer Texts in Business and Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33436-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-33436-8_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33435-1
Online ISBN: 978-3-642-33436-8
eBook Packages: Business and EconomicsEconomics and Finance (R0)