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Applied Econometric Times Series, 3rd Edition by Walter Enders

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CHAPTER 7

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NONLINEAR TIME-SERIES MODELS

Economic theory suggests that a number of important time-series variables should exhibit nonlinear behavior. The observation that wages display downward rigidity is a key feature of many macroeconomic models. Moreover, it has been established that downturns in the business cycle are sharper than recoveries in that key macroeconomic variables, such as output and employment, fall more sharply than they rise. Since the standard ARMA model relies on linear difference equations, new dynamic specifications are necessary to capture nonlinear behavior. In fact, research in this new area of time-series econometrics seems to be growing exponentially (itself a nonlinear process). This chapter has three aims:

  1. Compare the ARMA model to various types of nonlinear models. Once the assumption of linearity is abandoned, it is possible to estimate any number of potential nonlinear processes. Several nonlinear forms have proved themselves to be especially useful. The text will focus on those nonlinear models that can be estimated by OLS methods, nonlinear least squares, or maximum-likelihood techniques.
  2. Develop a number of tests that can detect the presence of nonlinear adjustment. The time-series literature contains a number of tests that are useful in determining whether or not a series is nonlinear. It will be shown that detecting nonlinearity is far simpler ...

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