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Idiographic Data Analysis: Quantitative Methods—From Simple to Advanced

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Dynamic Process Methodology in the Social and Developmental Sciences

Abstract

Time series analysis is a technique which can be used to model a large number of repeated measurements taken from a single case. This makes it a valuable approach for social scientists who are interested in idiographic data analysis. A fundamental time series model is the autoregressive moving average (ARMA) model. In this chapter we introduce the reader to the ARMA model and several extensions of it, including nonstationary models, multivariate models and nonlinear models. The focus is on the utility of these techniques for social scientists and we discuss existing applications within the social sciences to illustrate this. In the discussion we indicate how these techniques can be extended to handle multiple cases, and we briefly touch upon some valuable time series techniques which could not be treated in the current chapter.

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Notes

  1. 1.

    The autocovariance is the covariance between y t and y t + k , that is, E[(y t −μ) (y t+k −μ)], where m is the mean of the series. The lag k is the distance in time. When k  =  0, we obtain the variance of the series. The autocorrelation at lag k can be obtained by dividing the autocovariance at lag k by the variance of the series.

  2. 2.

    In some texts −q 1 is replaced by y 1, such that the minus sign is omitted. However, the above notation is more conventional, as it has some important advantages for the expression of particular characteristics of an MA process.

  3. 3.

    In practice, a process of infinite order is not appealing, as there will be more parameters to estimate than observations. However, in finite samples, the parameters beyond a certain lag will be insignificant and can be omitted from the model. The important issue is that there are no fundamental differences between these processes.

  4. 4.

    One can model the trend and the VARMA relations at the same time using a VARMAX model discussed below, but the point made here remains the same: One is modelling the deviations from the deterministic trend (rather then the trend itself) as a function of another variable.

  5. 5.

    A related technique, which is popular in speech recognition for instance, is the Hidden Markov model (HMM). The difference between the HMM and the MSAR model is that the former requires categorical observations, while the latter requires continuous observations. Moreover, while the MSAR model allows for autoregressive relationships between observations, the sequential dependency in the HMM is modelled exclusively by the hidden Markov process.

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Acknowledgements

This work was supported by the Netherlands Organization for Scientific Research (NWO), VENI grant 451–05–012 awarded to Ellen L. Hamaker.

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  1. Department of Methods and Statistics Faculty of Social Sciences, Utrecht University, 80140, 3508 TC, Utrecht, The Netherland

    Ellen L. Hamaker

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  1. Ellen L. Hamaker
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Correspondence to Ellen L. Hamaker .

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    Hamaker, E., Dolan, C. (2009). Idiographic Data Analysis: Quantitative Methods—From Simple to Advanced. In: Valsiner, J., Molenaar, P., Lyra, M., Chaudhary, N. (eds) Dynamic Process Methodology in the Social and Developmental Sciences. Springer, New York, NY. https://doi.org/10.1007/978-0-387-95922-1_9

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