A time series is a continuation of numerical values representing the evolution of a specific Quantité during the Temps. Such continuations of values can be expressed mathematically in order to analyze the Comportement of it, to generally include/understand its evolution Passé E and to envisage the behavior Futur of it. Such a mathematical transposition generally uses Concept S of probabilities and statistical.

Use

The time serieses are considered wrongly as being an exclusive branch of the econometrics. The latter is a discipline which is relatively young whereas the time serieses were used quite front, for example in Astronomie (1906) and in Météorologie (1968).

The object of the time serieses is the study of the variables during time. Consequently, even if they were not at the origin of this discipline, in fact the econometer S ensured the large projections that this discipline knew (many “Nobel Prize” of economy are econometers).

Among its main objectives appear the determination of tendency S within these series as well as the stability of the values (and of their variation) during time.

It is disappointment of the forecasts resulting from the models structural of inspiration keynésienne which from the time serieses such as one was born the theory knows it today. And on this point, it is the publication of the work of Box and Jenkins into 1970 which was decisive. Indeed, in the work the two authors develop the very popular model ARMED ( Regressive Auto Moving Average ). To give an example, to envisage GDP French in 2020 for example, it is not a question any more of using a structural model which explains the GDP (example via consumption, of the investment, the public expenditure and commercial balance etc) and of then projecting the last tendencies. But with the model ARMED, it acts to envisage the GDP in 2020 by exploiting the statistical properties of the GDP (average, variance etc) This model often uses delayed values of the GDP (from where Regressive the Auto term) and random shocks which are in general of null average, constant variance and not autocorrélés (white Bruit); when the variable which represents these shocks is delayed, one speaks about Moving average.

The model ARMED is a particular case of a model much more general named ARIMA where the I indicates Integrated in English or Integrated in French. Indeed, the model ARMED makes it possible to treat only the series known as stationary (of the first order moments which are invariants during time). Models ARIMA make it possible to treat the nonstationary series after having determined the level of integration (the number of times that it is necessary to differentiate the series before making it stationary).

Although having excellent estimated qualities, model ARIMA or ARMED suffers from a major gap: it is unable to treat simultaneously more than one variable (series). For example, if the structural models are able to answer an equation of the kind which is the effect of the rise of interest rates on the GDP? A model ARIMA is unable to answer it. To circumvent this problem, it is necessary to be able to generalize model ARIMA in the case with several variables. It is what with fact partly Sims by proposing in 1980 the model Vector Auto Regressive (VAR) which makes it possible to treat concomitantly several variables. But, contrary to the structural model with several variables, in the models VAR, all the variables are endogenous. This manner of modelling by disregarding economic theory gave rise to so that one called the Econométrie without theory.

These models (ARIMA and VAR) make it possible to treat only phenomena which are linear or roughly (for example GDP) but do not allow " capturer" properties of the phenomena which are nonlinear (financial variables for example, inflation, course of action etc). To take into account with time it not linearity and the strong variability of these variables, the English econometer Engel R. which was the first to develop the model known as ARCH ( Regressive Auto Conditional Heteroscedasticity ) in 1982.

References

• Bourbonnais Governed, Terraza Michel: Analysis of the time serieses in economy , University Presses of France, 1998.
• Bourbonnais Governed, Terraza Michel: Analysis of the time serieses: Applications to the economy and management , Dunod, 2004.
• Box, George and Jenkins, Gwilym: Time series analysis: Forecasting and control , San Francisco: Holden-Day, 1970.
• Bresson Georges, Pirotte Alain: Econometrics of the time serieses: Theory and applications, University Presses of France, 1995.
• Gourieroux Christian and Monfort Alain: Dynamic Time serieses and models , Economica, 1995.
• Alain Pirotte: Econometrics: origins with the recent developments , CNRS Editions, 2004.
• Ralf Vandenhouten: Non-stationary Time Series Analysis off Complex Systems and Applications in Physiology , Aachen, Shaker Verlag GMBH 1998, ISBN 3826538145.

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