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Statistical trend analyses of observed precipitation (P) time series are key to validate theoretical arguments and climate projections suggesting that extreme P will increase in a warmer climate. Recent work warned about possible misinterpretation of trend tests if the presence of serial correlation and field significance are not considered. Here, we investigate these two aspects focusing on extreme P frequencies derived from 100‐year daily records of 1,087 worldwide gauges of the Global Historical Climatology Network. For this aim, we perform Monte Carlo experiments based on count time series generated with the Poisson integer autoregressive model and characterized by different sample size, level of autocorrelation, and trend magnitude. The main results are as follows. (a) Empirical autocorrelations are consistent with those of uncorrelated and stationary or nonstationary count time series, while empirical trends cannot be explained as the exclusive effect of autocorrelation; incorporating the impact of serial correlation in trend tests on extreme P frequency has then limited impacts on tests' performance. (b) Accounting for field significance improves interpretation of test results by limiting type‐I errors, but it also decreases test power; results of local tests could complement field significance outcomes and help identify weak trend signals where several trends of coherent sign are detected. (c) Based on these findings, evident patterns of statistically significant increasing (decreasing) trends emerge in central and eastern North America, northern Eurasia, and central Australia (southwestern America, southern Europe, and southern Australia). The methodological insights of this work support trend analyses of any hydroclimatic variable. Key Points: Monte Carlo simulations based on the integer autoregressive model allow assessing trends on observed extreme precipitation frequencyAccounting for serial correlation in observed extreme precipitation frequency has limited impact on statistical trend analysesAccounting for field significance limits type‐I error of statistical trend tests, but reduces power when the trend signal is low [ABSTRACT FROM AUTHOR]