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.)

Modeling water table depth using singular spectrum analysis

Pages: 279 – 286



Rahim Mahmoudvand (Department of Statistics, Bu-Ali Sina University, Hamadan, Iran)

Mehrdad Barati (Department of Geology, Bu-Ali Sina University, Hamadan, Iran)

Asghar Seif (Department of Statistics, Bu-Ali Sina University, Hamadan, Iran)

Sahar Ranjbaran (Department of Geology, Bu-Ali Sina University, Hamadan, Iran)

Paulo Canas Rodrigues (Department of Statistics, Federal University of Bahia, Salvadore, Bahia, Brazil)


The majority of countries are facing or will face a serious water crisis. As a consequence, we observe a deterioration in the water quality such as the drop in the water table and a salinity increase. Therefore, it is highly recommended to conduct a regular monitoring program on groundwater levels in order to sustain this source. Water table depth (WTD) is an index of water availability that influences many soil characteristics. Consequently, there are concerns with WTD in both time and space. This paper shows how to build a model for water table depth using Singular Spectrum Analysis (SSA). The study area is located in the Ghahavand plain in the Hamedan province, western Iran. We used water table depth records that were collected by Hamedan regional water authority as part of their monitoring system program. The data were obtained monthly by measuring WTD of about 200 wells within the study area in the period between 1988 and 2016. There were many errors, inconsistencies and missing cells in the data file. So, we started with improving data quality and filling the missing cells. The other problem with the data was related to the well samples that have changed during the study horizon. Classically, we take a simple average on the observations at each time point to build a univariate time series. However, a descriptive analysis revealed that the heterogeneity in the value of the WTD in the study area has increased over time. So, we used box plot components to build model for WTD. We used both univariate SSA and multivariate SSA to capture the information within the box plot components. The performance of the proposal was accessed by using both in sample fitting errors and out of sample forecasting errors. The results suggest that the new approach provides an attractive alternative to the classical approach.


Hamedan, water table depth, singular spectrum analysis

2010 Mathematics Subject Classification

Primary 62M10, 62-xx. Secondary 86A05, 86-xx.

Received 10 June 2021

Accepted 31 March 2022

Published 13 April 2023