166 Araújo et al: Time Series Analysis of Urban Forest Waste Figure 1. Evolution of the original series (103 2008 to 2013. tonnes) and logarithmized (Ln) series for urban pruning waste in João Pessoa, from service must also be considered (specific requests to the competent agency for the execution of pruning and removal of woody debris). The waste manage- ment policy for woody debris/UPW, enforced by the government, also influences the annual mass gener- ated through hiring or lay-offs of personnel, adminis- trative changes, reviewing and amendment of contracts with service providers, to name a few. Figure 2 shows the decomposition of data, trends, seasonality, and waste of Ln (MPA-JP) from January 2008 to December 2013. Data decomposition revealed the presence of trend and seasonal compo- nents that must be inferred within the model. In Fig- ure 2, low gray bars indicate the predominance of the component, and higher heights indicate a predomi- nance of the component of MPA-JP decomposition. Visual inspection and series decomposition cannot, on their own, confirm the stationarity of the Ln (MPA-JP). Therefore, the Augmented Dickey-Fuller (ADF), Phillips-Perron (PP), and Kwiatkowski- Phillips-Schmidt-Shin (KPSS) tests were applied to verify the presence of unit root, as shown in Table 1. The ADF test shows the presence of stationarity when there is rejection of the null hypothesis (H0) or when the series presents a unit root. Alternative ©2020 International Society of Arboriculture hypothesis (H1) refers to the nonstationarity of the series and does not incur in the unit root region. The ADF test shows that, if |α| < |t|, H0 is accepted (where α is the significance level). Thus, Ln (MPA-JP) at 5% significance level accepts H0, due to the presence of a unit root (i.e., nonstationary, requiring transforma- tion by the first difference to be stationary). Application of the ADF test to the first differential of the 1ºDiff(Ln [MPA-JP]) revealed that, for the sig- nificance levels studied, the value of t was higher than any of the critical values. It can be concluded that there is no unit root, and therefore 1ºDiff(Ln [MPA-JP]) is stationary. The KPSS test states that the null hypothesis is the nonexistence of a root unit, and (Ln [MPA-JP]) presented t = 0.40, which was higher than the 10% critical value for the test. This demonstrated the rejection of the null hypothesis, showing that the (Ln [MPA-JP]) is not stationary. For the 1ºDiff(Ln [MPA-JP]) with t = 0.09, which was lower than any of the critical val- ues, a possible stationarity is characterized. The PP test of 1ºDiff(Ln [MPA-JP]) confirmed stationarity, with t = -13.98, well above t = -6.29 for MPA-JP. Figure 3 shows the identification of the order of the model using autocorrelation functions (ACF) and partial autocorrelation functions (PACF) for Ln (MPA-JP).
May 2020
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