Definition
Neurobiological data are often collected in the form of time series. Spectral analysis is the systematic study of time series in the frequency domain. In parametric spectral analysis, time series are treated as realizations of a stochastic process, and a model, typically an autoregressive model, is fit to the data, from which spectral quantities of interest such as power, coherence, and Granger causality spectra are then derived.
Detailed Description
We start by reviewing the basic concepts in the theory of stochastic processes which is the mathematical foundation of time series analysis. From this review one can clearly see that parametric modeling of time series is not an ad hoc approach but arises naturally from the theory of stochastic processes.
Stochastic Processes
If only one variable is being recorded over time, the time series is said to be univariate. An example of a univariate EEG time series demonstrating the alpha rhythm is shown in Fig. 1. If multiple...
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Ding, M., Rangarajan, G. (2014). Parametric Spectral Analysis. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_416-1
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DOI: https://doi.org/10.1007/978-1-4614-7320-6_416-1
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Publisher Name: Springer, New York, NY
Online ISBN: 978-1-4614-7320-6
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