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XploRe® — Application Guide pp 397–457Cite as

Flexible Time Series Analysis

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Abstract

In this chapter we present nonparametric methods and available quantlets for nonlinear modelling of univariate time series. A general nonlinear time series model for an univariate stochastic process Y t T t=1 is given by the heteroskedastic nonlinear autoregressive (NAR) process

$${Y_t} = f\left( {{Y_{t - i1}},{Y_{t - i2}}, \ldots ,{Y_{t - im}}} \right) + \sigma \left( {{Y_{t - i1}},{Y_{t - i2}}, \ldots ,{Y_{t - im}}} \right){\xi _t},$$
(16.1)

where ξ t denotes an i.i.d. noise with zero mean and unit variance and ƒ(·) and σ(·) denote the conditional mean function and conditional standard deviation with lags i 1,... ,i m , respectively. In practice, the conditional functions ƒ(·) and σ(·) as well as the number of lags m and the lags itself i 1,... ,i m are unknown and have to be estimated.

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Authors
  1. Wolfgang Härdle
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  2. Rolf Tschernig
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© 2000 Springer-Verlag Berlin Heidelberg

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Härdle, W., Tschernig, R. (2000). Flexible Time Series Analysis. In: XploRe® — Application Guide. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57292-0_16

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  • DOI: https://doi.org/10.1007/978-3-642-57292-0_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67545-7

  • Online ISBN: 978-3-642-57292-0

  • eBook Packages: Springer Book Archive

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