Work

An Improved Version of the Prewhitening Method for Trend Analysis in the Autocorrelated Time Series

Year: 2024

Type: article

Abstract: Nonparametric tests like Mann-Kendall (MK) require independent observations, but serial autocorrelation in the datasets inflates/deflates the variance and alters the type I and type II errors. Prewhitening (PW) techniques help address this issue by removing autocorrelation prior to applying MK. We evaluate several PW schemes - von Storch (PW-S), Slope corrected PW (PW-Cor), trend-free prewhitening (TFPW) proposed by Yue (TFPW-Y), iterative TFPW (TFPW-WS), variance-corrected TFPW (VCTFPW), and newly proposed trend-free prewhitening scheme (TFPW-New). Through Monte Carlo simulations, we constructed a lag-1 autoregressive (AR(1)) time series and systematically assessed the performance of different PW methods relative to sample size, autocorrelation, and trend slope. Results indicate the magnitude of trend and series length substantially impact autocorrelation. Strong trends significantly increase correlation, especially in large samples, posing challenges even after prewhitening. All methods tend to overestimate weak trends in small samples. For moderate trends, VCTFPW and TFPW-New provide most accurate slope estimation. VCTFPW shows slightly lower RMSE than TFPW-New at mid-range autocorrelation but fluctuates at higher levels. TFPW-New exhibits stable RMSE for low to high lag-1 autocorrelation (ρ1). TFPW-WS shows high power of test but only strong autocorrelated data combined with strong trends. In contrast, VCTFPW failed to preserve the power of the test at high autocorrelation due to slope underestimation. TFPW-New restores the test power across a wide range of ρ1 for moderate to strong trends. Overall, proposed TFPW-New approach demonstrates clear advantages, providing unbiased slope estimates, reasonable Type I error control, and sufficient power in detecting linear trends in AR(1) series.

Source: Atmosphere

DOI: 10.3390/atmos15101159

Authors: Rahul sheoran, Umesh C. Dumka, Rakesh Tiwari, Rakesh Hooda

Institutions: Aryabhatta Research Institute of Observational Sciences, Deen Dayal Upadhyaya Gorakhpur University, Graphic Era University, Finnish Meteorological Institute

Language: English

Topic: Statistical and numerical algorithms

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,728

Funders: Department of Biotechnology, Ministry of Science and Technology, India, Council of Scientific and Industrial Research, India, Business Finland