Using Periodic Copula to Assess the Relationship Between Two Meteorological Cyclostationary Time Series Datasets

In environmental, hydrological, and meteorological research, one of the main aims is to study the relationship between some variables. This issue has an influential role in various fields such as predicting stochastic variables, reconstructing missing data (especially in studies related to assessing the changes in climate conditions and drought characteristics), etc. For this purpose, statisticians have proposed different parametric and non-parametric techniques. Most of the proposed methods are applicable for stationary and some special non-stationary time series datasets. This work was devoted to introducing and applying a novel copula-based approach, called the periodic copula model (in 5 methods, including Gaussian, t, Clayton, Gumbel, and Frank periodic copula models) to study the relationship between some cyclostationary processes. For assessing the performance of the introduced model, two numerical studies, including the first-order periodic autoregressive (PAR (1)) and the first-order periodic moving average (PMA (1)) time series were considered. Moreover, the comparison of the relationship between observed and simulated drought severities (based on the 3month standardized precipitation evapotranspiration index (SPEI)) using the periodic copula was used. To comput SPEI, data series of 10 stations over Iran during 1967–2019 (5 groups, each group includes two stations with a short spatial distance) were used. The ability and performance of the method was evaluated based on three indices, including Willmott’s index (WI), Nash-Sutcliff’s coefficient (NSC), and correlation of coefficient (r). The results of numerical studies verify the ability of the proposed technique. In all five copula models studied in 6month (with T = 2) and 3month (with T = 4) periods with n equal to 100, 200, 500, and 1000, the r, NSE, and WI indices in the periodic form of data series were more than the non-periodic form. The results of testing the performance of the proposed model based on actual data also verified the greater ability of periodic copula models compared to non-periodic copula models. So that in all chosen groups and all periods, including winter, spring, summer, and autumn, the R-Square between observed drought indices and predicted data using the periodic copula models was more than the R-Square between observed drought indices and predicted data using the non-periodic copula models.