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The Structural Analysis of Time Series

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Multivariate Modelling of Non-Stationary Economic Time Series

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Abstract

In this chapter a number of what might be variously considered as structural models are considered. In the first case cointegrating relations with expectations are dealt with in terms of what may be viewed as regular solutions to the standard saddle point problem for a linear quadratic adjustment costs (LQAC) model.

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Notes

  1. 1.

    The interested reader is directed to Hunter and Ioannidis (2000) for the same solution method.

  2. 2.

    This may also be considered as a representation of the finite impulse response (FIR) with ν k being an FIR filter of length m. When the scree diagram has a break in the slope at k = s then this filter is optimal.

  3. 3.

    Where m defines the embedding dimension which relates to the replications that might capture certain components of the series. This may be a complete replication of the series or what might be seen as certain characteristics, such as the series being without trend or the fitted value.

  4. 4.

    When principle components are time reversed and ν k is derived for k = 1, …, m, then backward-forward filtering is applied to the data which has the property of preserving the phase relations. If the SSA filter completely reconstructs the data, then it is equivalent to a wavelet reconstruction. For further discussion of the nature of the SSA filter and comparison with other types of filter in relation to economic problems, the interested reader is directed to Groth et al. (2012).

  5. 5.

    For further details see Chap. 3 of Golyandina et al. (2001) and the article of Moskvina and Zhigljavsky (2003).

  6. 6.

    A brief introduction may also be found in Chap. 5 of Harvey (1993).

  7. 7.

    This is computed in two ways as the squares of returns and absolute values.

  8. 8.

    A number of switching routines are available, including the Markov chain Monte Carlo. Here emphasis is placed on regime switching that follows from some theoretical mechanism as compared with a more statistical procedure.

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  1. Department of Economics and Finance, Brunel University, Uxbridge, UK

    John Hunter & Alessandra Canepa

  2. Department of Economics, University of Reading, Reading, UK

    Simon P. Burke

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Hunter, J., Burke, S.P., Canepa, A. (2017). The Structural Analysis of Time Series. In: Multivariate Modelling of Non-Stationary Economic Time Series. Palgrave Texts in Econometrics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-137-31303-4_9

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