Study of Tests for Trend in Time Series

Abstract

The time series methodology is an important tool when using data over time. The time series can be composed of the components trend (Tt), seasonality (St) and the random error (at). The aim of this study was to evaluate the tests used to analyze the trend component, which were: Pettitt, Run, Mann-Kendall, Cox-Stuart and the unit root tests (Dickey-Fuller, Dickey-Fuller Augmented and Zivot and Andrews), given that there is a discrepancy between the test results found in the literature. The four series analyzed were the maximum temperature in the Lavras city, MG, Brazil, the unemployment rate in the Metropolitan Region of S~ao Paulo (RMSP), the Broad Consumer Price Index (IPCA) and the nominal Gross Domestic Product (GDP) of Brazil. It was found that the unit root tests showed similar results in relation to the presence of the stochastic trend for all series. Furthermore, the turning point of the Pettitt test diverged from all the structural breaks found through the Zivot and Andrews test, except for the GDP series. Therefore, it was found that the trend tests diverged, obtaining similar results only in relation to the unemployment series.

Investigation of the Historical Trends and Variability of Rainfall Patterns during the March–May Season in Rwanda

“…These metrics collectively indicate that the CHIRPS dataset closely mirrors the actual rainfall measurements recorded at ground stations across Rwanda, capturing the wide variance in rainfall with a high level of precision. The strong positive correlation suggests that the CHIRPS dataset effectively replicates the trends and fluctuations in rainfall observed during this critical agricultural season as was previously reported [36,37]. The RMSE, when considered against the backdrop of the broad range of rainfall amounts, points to a relatively minor average deviation from the station data, underscoring the dataset's reliability for practical applications.…”

“…previously reported [36,37]. The RMSE, when considered against the backdrop of the broad range of rainfall amounts, points to a relatively minor average deviation from the station data, underscoring the dataset's reliability for practical applications.…”

“…An effective method for identifying change points, the start of a substantial trend, and sudden changes in a series is the sequential MK test [35]. In case the intersection happens outside of the computed α-value of 1.96, an unanticipated shift at that moment is acknowledged [36]. The study used a 95% confidence level, or α = 0.05, to evaluate the significant trend, with ±1.96-tabulated valves serving as the equivalent.…”

Shift in hospital opioid use during the COVID-19 pandemic in Brazil: a time-series analysis of one million prescriptions

“…Non-significant values represent a stationary (stable) trend. Since the observed data correspond only to two years being used for comparison, seasonality was not verified because it does not apply to relatively short periods with no discernible seasonal pattern 34 . The Student t-test was used to test the hypothesis of a significant difference between the average consumption of each opioid in 2019 and 2020.…”