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Macroeconomics, Non-linear Time Series in

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Encyclopedia of Complexity and Systems Science

Definition of the Subject

Nonlinear time series in macroeconomics is a broad field of study in economics. It refers to the use of statistical analysis of data to make inferences about nonlinearities in the nature of aggregate phenomena in the economy. This analysis is relevant for forecasting, the formulation of economic policy, and the development and testing of macroeconomic theories.

Introduction

In macroeconomics, the primary aggregate phenomenon is the flow of total production for the entire economy over the course of a year, which is measured by real gross domestic product (GDP ). A collection of data corresponding to the values of a variable such as real GDP at different points of time is referred to as a time series. Figure 1 presents the time series for US real GDP for each year from 1929 to 2006.

Figure 1
figure 1_316

US real GDP 1929–2006 (Source: St. Louis Fed website)

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Abbreviations

Nonlinear time series in macroeconomics:

A field of study in economics pertaining to the use of statistical analysis of data in order to make inferences about nonlinearities in the nature of aggregate phenomena in the economy.

Time series:

A collection of data corresponding to the values of a variable at different points of time.

Linear:

Refers to a class of models for which the dependence between two random variables can be completely described by a fixed correlation parameter.

Nonlinear:

Refers to the class of models for which the dependence between two random variables has a more general functional form than a linear equation and/or can change over time.

Structural change :

A change in the model describing a time series, with no expected reversal of the change.

Level:

Refers to a definition of the business cycle that links the cycle to alternation between phases of expansion and recession in the level of economic activity.

Deviations:

Refers to a definition of the business cycle that links the cycle to transitory deviations of economic activity from a trend level.

Fluctuations:

Refers to a definition of the business cycle that links the cycle to any short‐run changes in economic activity.

Deepness:

A characteristic of a process with a skewed unconditional distribution.

Steepness:

A characteristic of a process with a skewed unconditional distribution for its first‐differences.

Sharpness:

A characteristic of a process for which the probability of a peak when increasing is different than the probability of a trough when decreasing.

Time reversibility :

The ability to substitute −t and t in the equations of motion for a process without changing the process.

Markov‐switching models :

Models that assume the prevailing regime governing the conditional distribution of a variable or variables being modeled depends on an unobserved discrete Markov process.

Self‐exciting threshold models :

Models that assume the prevailing regime governing the conditional distribution of a variable or variables being modeled is observable and depends on whether realized values of the time series being modeled exceed or fall below certain “threshold” values.

Nuisance parameters:

Parameters that are not of direct interest in a test, but influence the distribution of a test statistic.

Pivotal:

Refers to the invariance of the distribution of a test statistic with respect to values of parameters in the data generating process under the null hypothesis.

Size:

Probability of false rejection of a null hypothesis in repeated experiments.

Power:

Probability of correct rejection of a null hypothesis in repeated experiments.

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  1. Washington University, St. Louis, USA

    James Morley

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  1. James Morley
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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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© 2009 Springer-Verlag

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Morley, J. (2009). Macroeconomics, Non-linear Time Series in. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_316

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