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Elements of Nonlinear Time Series Analysis and Forecasting

Part of the Springer Series in Statistics Book Series

DOI: 10.1007/978-3-319-43252-6

ISBN: 978-3-319-43251-9

Publisher: Springer International Publishing - Springer Journals

Mar 31, 2017

1 - 10 of 12 Chapters

LitStream

Chapter 1Introduction and Some Basic Concepts

De Gooijer, Jan G.

Pages: 1 –27

[Informally, a time series is a record of a fluctuating quantity observed over time that has resulted from some underlying phenomenon. The set of times at which observations are measured can be equally spaced. In that case, the resulting series is called discrete. Continuous time series, on the...
LitStream

Chapter 2Classic Nonlinear Models

De Gooijer, Jan G.

Pages: 29 –85

[In Section 1.1, we discussed in some detail the distinction between linear and nonlinear time series processes. In order to make this distinction as clear as possible, we introduce in this chapter a number of classic parametric univariate nonlinear models. By “classic” we mean that during the...
LitStream

Chapter 3Probabilistic Properties

De Gooijer, Jan G.

Pages: 87 –117

[From the previous two chapters we have seen that the richness of nonlinear models is fascinating: they can handle various nonlinear phenomena met in practice. However, before selecting a particular nonlinear model we need tools to fully understand the probabilistic and statistical...
LitStream

Chapter 4Frequency-Domain Tests

De Gooijer, Jan G.

Pages: 119 –153

[The specification and estimation of a nonlinear model may be difficult in practice and sometimes no substantial improvements in forecasting accuracy can be achieved by using a nonlinear model instead of a familiar ARMA model. Therefore, one may wish to start the model building from a linear...
LitStream

Chapter 5Time-Domain Linearity Tests

De Gooijer, Jan G.

Pages: 155 –196

[Time-domain linearity test statistics are parametric; that is, they test the null hypothesis that a time series is generated by a linear process against a pre-chosen particular nonlinear alternative. Using the classical theory of statistical hypothesis testing, time-domain test nonlinearity...
LitStream

Chapter 6Model Estimation, Selection, and Checking

De Gooijer, Jan G.

Pages: 197 –255

[Model estimation, selection, and diagnostic checking are three interwoven components of time series analysis. If, within a specified class of nonlinear models, a particular linearity test statistics indicates that the DGP underlying an observed time series is indeed a nonlinear process, one...
LitStream

Chapter 7Tests for Serial Independence

De Gooijer, Jan G.

Pages: 257 –314

[Testing for randomness of a given finite time series is one of the basic problems of statistical analysis. For instance, in many time series models the noise process is assumed to consist of i.i.d. random variables, and this hypothesis should be testable. Also, it is the first issue that gets...
LitStream

Chapter 8Time-Reversibility

De Gooijer, Jan G.

Pages: 315 –336

[Time-reversibility (TR) amounts to temporal symmetry in the probabilistic structure of a strictly stationary time series process. In other words, a stochastic process is said to be TR if its probabilistic structure is unaffected by reversing (“mirroring”) the direction of time. Otherwise, the...
LitStream

Chapter 9Semi- and Nonparametric Forecasting

De Gooijer, Jan G.

Pages: 337 –389

[The time series methods we have discussed so far can be loosely classified as parametric (see, e.g., Chapter 5), and semi- and nonparametric (see, e.g., Chapter 7). For the parametric methods, usually a quite flexible but well-structured family of finitedimensional models are considered (Chapter...
LitStream

Chapter 10Forecasting

De Gooijer, Jan G.

Pages: 391 –437

[As we saw in Chapter 9, it is fairly straightforward to forecast future values of a time series process using semi- and nonparametric methods, given data up to a certain time t. In contrast, the situation becomes more complicated when real out-of-sample forecast are computed from parametric...

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