Drought is a stochastic climatic phenomenon that has detrimental and widespread effects that spread throughout the local community, the global economy, and ecological environments. Consideration of wet and dry periods' calculations through various drought indices has extensive consequences for better understanding and monitoring drought intensities over considering periods. As a high chance of implausibility could occur in predicting drought events, trend detection during wet and dry periods could play a vital role in assessing future events and providing a necessary equitable understanding of the events' variability. Although these event trend lines are statistically independent, they could be found to have a significant correlation in time lags. With the help of historical meteorological data (1980–2018) over Bangladesh, three drought monitoring indices were used to monitor wet and dry periods in this study, including SPI, PNPI, and ZSI. Besides, to detect the trend of wet and dry periods in time series, the Mann-Kendall nonparametric test has been used. The results reveal that, through the Mann-Kendall test, the trend of wet and dry periods was negative in the majority of total stations. A total of eight stations among thirty selected stations showing increasing and decreasing trends were significant at the 95% confidence level, respectively. Serial correlation was used for better understanding and detecting non-randomness in rainfall data and drought indices, and it was found that rainfall and drought indices were dependent on small serial correlation lags. Moreover, a significant correlation was found on lag-1 coefficient values, which justified the preceding claim. The Theil-Sen slope estimator remarkably captured the changes in trend lines.