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

In: Research Papers in Statistical Inference for Time Series and Related Models

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  • Takayuki Shiohama

    (Nanzan University)

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.

Suggested Citation

  • Takayuki Shiohama, 2023. "Complex-Valued Time Series Models and Their Relations to Directional Statistics," Springer Books, in: Yan Liu & Junichi Hirukawa & Yoshihide Kakizawa (ed.), Research Papers in Statistical Inference for Time Series and Related Models, chapter 0, pages 475-496, Springer.
    • Handle: RePEc:spr:sprchp:978-981-99-0803-5_21
    DOI: 10.1007/978-981-99-0803-5_21
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