Single-step and multiple-step forecasting in one-dimensional single chirp signal using MCMC-based Bayesian analysis

Abstract

Chirp signals are frequently used in different areas of science and engineering. MCMC based Bayesian inference is done here for purpose of one step and multiple step prediction in case of one dimensional single chirp signal with i. i. d. error structure as well as dependent error structure with exponentially decaying covariances. We use Gibbs sampling technique and random walk MCMC to update the parameters. We perform total five simulation studies for illustration purpose. We also do some real data analysis to show how the method is working in practice.

Chirp-like model and its parameters estimation

“…Proof of Theorm 6: Consider the error sum of squares, defined in (12). Let us denote Q ′ (ϑ) as the 3(p + q) × 1 first derivative vector and Q ′′ (ϑ) as the 3(p + q) × 3(p + q) second derivative matrix.…”

“…One major issue related to chirp model is the efficient estimation of the unknown parameters. Some of the references in this area are Abatzoglou [1], Djuric and Kay [2], Peleg and Porat [14], Ikram et al [5], Saha and Kay [18], Nandi and Kundu [13], Kundu and Nandi [6], Lahiri et al [10], [11], Mazumder [12], Grover et al [4] and the references cited therein. One of the widely used methods for estimation of parameters of both linear and nonlinear models, is the least squares estimation method.…”