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.
Highlights
The time series methodology can be applied to several areas, being an important tool when using data over time and that are correlated
The unit root tests (Dickey-Fuller, Augmented Dickey-Fuller test (ADF) and Zivot and Andrews) are parametric tests, with the ADF test being a generalization of the Dickey-Fuller test
The trend tests were applied to the four series studied and the results obtained for each series are described below
Summary
The time series methodology can be applied to several areas, being an important tool when using data over time and that are correlated. According to Morettin and Toloi (2018), a time series Z(t) is any set of observations ordered in time and spaced. A characteristic of the analysis of the series is that its study can be conducted in the time domain (parametric models) or in the frequency domain (non-parametric models).
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