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Erschienen in:
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2024 | OriginalPaper | Buchkapitel

7. An Introduction to Time Series Models

verfasst von : Valérie Mignon

Erschienen in: Principles of Econometrics

Verlag: Springer Nature Switzerland

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Abstract

Time series econometrics is a branch of econometrics that has undergone many developments over the last 40 years. This chapter offers an introduction to time series models. After laying down a number of definitions, it focuses on the essential concept of stationarity. It presents the Dickey-Fuller unit root test for testing the non-stationary nature of a time series. The chapter then exposes the basic models of time series – the autoregressive moving-average models (ARMA models) – and the related Box and Jenkins methodology. A multivariate extension is proposed through the presentation of VAR (vector autoregressive) models. Finally, the concepts of non-stationary time series econometrics are presented by studying the notions of cointegration and error-correction models. Several empirical applications illustrate all the notions.

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Vorheriges Kapitel Distributed Lag Models
Nächstes Kapitel Simultaneous Equations Models
Fußnoten
1
This chapter takes up a number of developments appearing in the work by Lardic and Mignon (2002), which interested readers may refer to for further details.
 
2
There are continuous and discrete random variables. We are only interested in discrete variables here.
 
3
For a more detailed study of stationarity and a definition of the various concepts, see in particular Lardic and Mignon (2002).
 
4
By introducing the lag operator L, we can write \(\left ( 1-L\right ) Y_{t}=\beta +\varepsilon _{t}\). If we posit \(1-L=0\), we deduce \(L=1\), hence the name of unit root.
 
5
The first-difference models allow us to reduce to usual tests of significance of the coefficients, the critical values being tabulated by Dickey and Fuller (see below).
 
6
One of the causes of error autocorrelation lies in the omission of explanatory variables. The correction provided by Dickey and Fuller thus consists in adding explanatory variables represented by the lagged values of the endogenous variable.
 
7
For robustness, we also conducted the analysis with two lags. The results are identical to those presented here.
 
8
Bartlett showed that the standard deviation is given by \(\hat {\sigma }\left ( \hat {\rho } _{h}\right ) =\left [{\frac {1}{T}}\left ( 1+2\sum \limits _{i=1}^{h-1}\hat {\rho }_{i}^{2}\right ) \right ]^{1/2}.\)
 
9
See also Akaike (1969, 1974).
 
10
It is assumed here that the constant c in the expression of the HQ criterion is equal to 1.
 
11
Strictly speaking, it is possible to estimate VAR processes in which non-stationary variables are involved using OLS. In this case, the estimators are super-consistent, but they are no longer asymptotically normal, which poses a problem for statistical inference since the usual tests can no longer be implemented.
 
12
We have assumed here that the constant c involved in the expression of the HQ criterion is equal to 1.
 
13
The data come from Robert Shiller’s website: http://​www.​econ.​yale.​edu/​~shiller/​data.​htm.
 
14
These examples are taken from the website of J. Gonzalo, Universidad Carlos III, Madrid.
 
15
Note that the cointegrating relationship can include a constant term, for example: \(Y_{t}=\alpha +\beta X_{t}.\)
 
16
We assume here that the long-term relationship includes a constant term.
 
17
In the MacKinnon table, critical values are distinguished according to whether or not a trend is included in the cointegration relationship.
 
Literatur
Akaike, H. (1969), “Fitting Autoregressive Models for Prediction”, Annals of the Institute of Statistical Mathematics, 21, pp. 243–247.CrossRef
Akaike, H. (1974), “A new look at the statistical model identification”, IEEE Transactions on Automatic Control, 19(6), pp. 716–723.CrossRef
Banerjee, A., Dolado, J., Galbraith, J.W. and D.F. Hendry (1993), Cointegration, Error-Correction, and the Analysis of Nonstationary Data, Oxford University Press.
Bauwens, L., Hafner, C. and S. Laurent (2012), “Volatility models”, in Bauwens, L., Hafner, C. and S. Laurent (eds), Handbook of Volatility Models and their Applications, John Wiley & Sons, Inc.
Beran, J. (1994), Statistics for Long Memory Processes, Chapman & Hall.
Bollerslev, T. (2008), “Glossary to ARCH (GARCH)”, CREATES Research Paper, 2008–49.
Bollerslev, T., Chou, R.Y. and K.F. Kroner (1992), “ARCH modeling in finance: A review of the theory and empirical evidence”, Journal of Econometrics, 52(1–2), pp. 5–59.CrossRef
Bollerslev, T., Engle, R.F. and D.B. Nelson (1994), “ARCH Models”, in Engle R.F. and D.L. McFadden (eds), Handbook of Econometrics, Vol. IV, pp. 2959–3038, Elsevier Science.
Box, G.E.P. and G.M. Jenkins (1970), Time Series Analysis: Forecasting and Control, Holden Day, San Francisco.
Brockwell, P.J. and R.A. Davis (1998), Time Series. Theory and Methods, 2nd edition, Springer Verlag.
Campbell, J.Y. and P. Perron (1991), “Pitfalls and Opportunities: What Macroeconomists Should Know about Unit Roots”, in Fisher, S. (ed.), NBER Macroeconomic Annual, MIT Press, pp. 141–201.
Dickey, D.A. and W.A. Fuller (1979), “Distribution of the Estimators for Autoregressive Time Series With a Unit Root”, Journal of the American Statistical Association, 74, pp. 427–431.
Dickey, D.A. and W.A. Fuller (1981), “Likelihood Ratio Statistics for Autoregressive Time Series With a Unit Root”, Econometrica, 49, pp. 1057–1072.CrossRef
Dufrénot, G. and V. Mignon (2002a), “La cointégration non linéaire : une note méthodologique”, Économie et Prévision, n 155, pp. 117–137.
Dufrénot, G. and V. Mignon (2002b), Recent Developments in Nonlinear Cointegration with Applications to Macroeconomics and Finance, Kluwer Academic Publishers.CrossRef
Durbin, J. (1960), “The Fitting of Time Series Models”, Review of the International Statistical Institute, 28, pp. 233–244.CrossRef
Engle, R.F. and C.W.J. Granger (1987), “Cointegration and Error Correction: Representation, Estimation and Testing”, Econometrica, 55, pp. 251–276.CrossRef
Engle, R.F. and C.W.J. Granger (1991), Long Run Economic Relationships. Readings in Cointegration, Oxford University Press.CrossRef
Engle, R.F. and S. Yoo (1987), “Forecasting and Testing in Cointegrated Systems”, Journal of Econometrics, 35, pp. 143–159.CrossRef
Gouriéroux, C. (1997), ARCH Models and Financial Applications, Springer Series in Statistics.
Gouriéroux, C. and A. Monfort (1996), Time Series and Dynamic Models, Cambridge University Press.CrossRef
Gouriéroux, C. and A. Monfort (2008), Statistics and Econometric Models, Cambridge University Press.
Granger, C.W.J. (1969), “Investigating Causal Relations by Econometric Models and Cross-Spectral Methods”, Econometrica, 36, pp. 424–438.CrossRef
Granger, C.W.J. (1981), “Some Properties of Time Series Data and their Use in Econometric Model Specification” , Journal of Econometrics, pp. 121–130.
Granger, C.W.J. and P. Newbold (1974), “Spurious Regressions in Econometrics”, Journal of Econometrics, 26, pp. 1045–1066.
Granger, C.W.J. and T. Teräsvirta (1993), Modelling Nonlinear Economic Relationships, Oxford University Press.CrossRef
Greene, W. (2020), Econometric Analysis, 8th edition, Pearson.
Hamilton, J.D. (1994), Time Series Analysis, Princeton University Press.CrossRef
Hannan, E.J. and B.G. Quinn (1979), “The Determination of the Order of an Autoregression”, Journal of the Royal Statistical Society, Series B, 41, pp. 190–195.
Harvey, A.C. (1990), The Econometric Analysis of Time Series, MIT Press.
Hurlin, C. and V. Mignon (2005), “Une synthèse des tests de racine unitaire sur données de panel”, Économie et Prévision, n 169–170-171, pp. 253–294.
Hurlin, C. and V. Mignon (2007), “Une synthèse des tests de cointégration sur données de panel”, Économie et Prévision, n 180–181, pp. 241–265.
Johansen, S. (1988), “Statistical Analysis of Cointegration Vectors”, Journal of Economic Dynamics and Control, 12, pp. 231–254.CrossRef
Johansen, S. (1991), “Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models”, Econometrica, 59, pp. 1551–1580.CrossRef
Johansen, S. (1995), Likelihood-based Inference in Cointegrated Vector Autoregression Models, Oxford University Press.CrossRef
Johansen, S. and K. Juselius (1990), “Maximum Likelihood Estimation and Inferences on Cointegration with Application to the Demand for Money”, Oxford Bulletin of Economics and Statistics, 52, pp. 169–210.CrossRef
Lardic, S. and V. Mignon (1999), “La mémoire longue en économie : une revue de la littérature”, Journal de la Société Française de Statistique, pp. 5–48.
Lardic, S. and V. Mignon (2002), Économétrie des séries temporelles macroéconomiques et financières, Economica.
Lardic, S., Mignon, V. and F. Murtin (2005), “Estimation des modèles à correction d’erreur fractionnaires : une note méthodologique”, Journal de la Société Française de Statistique, pp. 55–68.
MacKinnon, J.G. (1991), “Critical Values for Cointegration Tests”, in Engle, R.F. and C.W.J. Granger (eds), Long-Run Economic Relationships, Oxford University Press, pp. 267–276.
Maddala, G.S. and I.-M. Kim (1998), Unit Roots, Cointegration, and Structural Change, Cambridge University Press.
Mills, T.C. (1990), Time Series Techniques for Economists, Cambridge University Press.
Nelson, C.R. and C. Plosser (1982), “Trends and Random Walks in Macroeconomics Time Series: Some Evidence and Implications”, Journal of Monetary Economics, 10, pp. 139–162.CrossRef
Palm, F.C. (1996), “GARCH Models of Volatility”, in Maddala G.S. and C.R. Rao (eds), Handbook of Statistics, Vol. 14, pp. 209–240, Elsevier Science.
Schwarz, G. (1978), “Estimating the Dimension of a Model”, The Annals of Statistics, 6, pp. 461–464.CrossRef
Sims, C.A. (1980), “Macroeconomics and Reality”, Econometrica, 48, pp. 1–48.CrossRef
Teräsvirta, T., Tjøstheim, D. and C.W.J. Granger (2010), Modelling Nonlinear Economic Time Series, Oxford University Press.CrossRef
Metadaten
Titel
An Introduction to Time Series Models
verfasst von
Valérie Mignon
Copyright-Jahr
2024
Buch
Principles of Econometrics

Print ISBN: 978-3-031-52534-6

Electronic ISBN: 978-3-031-52535-3

Copyright-Jahr: 2024

DOI
https://doi.org/10.1007/978-3-031-52535-3_7

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