Complex-Valued Time Series Models and Their Relations to Directional Statistics

Takayuki Shiohama ()
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Takayuki Shiohama: Nanzan University

Chapter Chapter 21 in Research Papers in Statistical Inference for Time Series and Related Models, 2023, pp 475-496 from Springer

Abstract: Abstract The fluctuation of stationary time series often shows a certain periodic behavior and this pattern is usually summarized via a spectral density. Since spectral density is a periodic function, it can be modeled by using a circular distribution function. In this paper, several time series models are studied in relation to a circular distribution. As an introduction, we illustrate how to model bivariate time series data using complex-valued time series in the context of circular distribution functions. These models are extended to have a skewed spectrum by incorporating a sine-skewing transformation. Two parameter estimation methods are considered and their asymptotic properties are investigated. These theoretical results are verified via a Monte Carlo simulation. Real data analyses illustrate the applicability of the proposed model.

Keywords: Circular statistics; Maximum likelihood estimation; Sine-skewed model; Spectral density; Time series analysis (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-99-0803-5_21

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DOI: 10.1007/978-981-99-0803-5_21

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