Statistics and Its Interface

Volume 16 (2023)

Number 2

Special issue on recent developments in complex time series analysis – Part II

Guest editors: Robert T. Krafty (Emory Univ.), Guodong Li (Univ. of Hong Kong), Anatoly Zhigljavsky (Cardiff Univ.)

Modified recurrent forecasting in singular spectrum analysis using Kalman filter and its application for bicoid signal extraction

Pages: 217 – 225



Reza Zabihi Moghadam (Department of Statistics, Payame Noor University, Tehran, Iran)

Masoud Yarmohammadi (Department of Statistics, Payame Noor University, Tehran, Iran)

Hossein Hassani ( Research Institute for Energy Management and Planning, (RIEMP), University of Tehran, Iran)


One of the important topics in Drosophila melanogaster is statistical analysis of bicoid protein gradient. The bicoid protein gradient plays an important role in the segmentation stage of embryo development in the head and thorax and also has considerable noise. Therefore, it has been considered by many researchers. In this paper the state space model and Kalman filter algorithms are used for noise elimination and smoothing bicoid gene expression. The state-space allows the unobserved variables, each with a specific interpretation, to be included in the estimate with the observed model and can be analyzed using the Kalman filter algorithm. Then, the less noise bicoid gene expression are used for forecast by singular spectrum analysis (SSA) method. The results with strong evidence indicate that the proposed method can be considered as a powerful technique in the analysis and prediction of gene expression measurements.


forecasting, Kalman filter, singular spectrum analysis, state space form, recurrent forecasting, bicoid, Drosophila melanogaster

Received 23 May 2021

Accepted 6 January 2022

Published 13 April 2023