Computational explosion in the frequency estimation of sinusoidal data

Abstract

This paper highlights the computational explosion issues in the autoregressive moving average approach of frequency estimation of sinusoidal data with a large sample size. A new algorithm is proposed to circumvent the computational explosion difficulty in the conditional least-square estimation method. Notice that sinusoidal pattern can be generated by a non-invertible non-stationary autoregressive moving average (ARMA) model. The computational explosion is shown to be closely related to the non-invertibility of the equivalent ARMA model. Simulation studies illustrate the computational explosion phenomenon and show that the proposed algorithm can efficiently overcome computational explosion difficulty. Real data example of sunspot number is provided to illustrate the application of the proposed algorithm to the time series data exhibiting sinusoidal pattern.

Real time prediction of irregular periodic time series data

“…with 𝜃 1 = 𝜙 1 and 𝜃 2 = 𝜙 2 . See Zhang et al (2018) and Platonov et al (1992) for a more detailed discussion on the frequency estimation problem. It is natural to expect that r should be close to one if the data exhibit a sine or cosine function pattern.…”

“…Then, putting f t = y t − ϵ t , Equation is equivalent to the ARMA model with θ 1 = ϕ 1 and θ 2 = ϕ 2 . See Zhang et al () and Platonov et al () for a more detailed discussion on the frequency estimation problem. It is natural to expect that r should be close to one if the data exhibit a sine or cosine function pattern.…”

“…In spite of its simplicity, the time-varying ARMA model is flexible enough to describe the periodic pattern of the time series data with unknown frequency cases. The frequency estimation problem based on the time-constant ARMA model is discussed in Zhang, Ng, and Na (2018), B. Chen and Gel (2010), Stoica, Friedlander, andSoderstrom (1987), andPlatonov, Gajo, andSzabatin (1992).…”