164 The analysis of temporal series is an important instrument to understand the market and to formulate action plans and strategies. The history of a variable can interfere on its behavior and generate information on probable future behavior through the construction of models that predict the future movements (Fischer 1982; Rezende et al. 2005; Coelho Jr., Melquíades, et al. 2018). The use of time series forecasting models is an alternative in the decision-making process, involv- ing activities that require planning, policy evaluation, and reduction of uncertainties. Time series forecast models present wide applicability, with different resources and knowledge fields such as administra- tion, economics, forestry, and health sectors to name a few (Bressan 2004; Coelho Jr., Rezende, Sáfadi, et al. 2006; Antunes and Cardoso 2015). In the forestry sector, there are several applications of time series analysis: Floriano et al. (2006) devel- oped height growth equations in a population of Pinus elliottii; Coelho Jr., Rezende, Calegario, et al. (2006) forecasted charcoal prices in the state of Minas Gerais; Soares et al. (2008) forecasted natural rubber prices in the domestic market; Coelho Jr. et al. (2009) forecasted natural rubber prices in the international market; and Almeida et al. (2009) forecasted the price paid for exports of wood composites from the Paraná state, where graphical analysis and statistics indicated the Autoregressive Integrated Moving Average (ARIMA)(1,1,3) as the best fit to wood composite price series. Finally, Soares et al. (2010) elaborated a model to forecast the price of standing timber for Eucalyptus spp. Decision makers and urban afforestation managers that wish to carry out reliable predictions of the amount of urban pruning waste are usually faced with limited budget for its maintenance. Urban forestry management techniques can generate these data, pro- viding significant elements for the prediction of future behavior. However, there are limited data on the fore- cast of woody residues from urban pruning activities. The study presented herein analyzed the forecast model for urban pruning waste in the municipality of João Pessoa, Paraíba. MATERIALS AND METHODS Study Object This study utilized the UPW historical series in tonnes (t) for João Pessoa, collected monthly by the Munici- pal Urban Cleaning Autarchy (EMLUR). The period ©2020 International Society of Arboriculture Araújo et al: Time Series Analysis of Urban Forest Waste analyzed was January 2008 to December 2014, encompassing 84 data sets. Data between January 2008 and December 2013 were utilized to adjust the model, and data between January and December 2014 were utilized to validate the model. Time Series Analysis A specific time series {Yt , t = 1, 2, 3, ..., n} is defined as a set of observations of a variable, sequentially arranged in time (Morettin and Toloi 2006). Wold (1938) affirmed that a temporal series presents the following components: trend (T), seasonality (S), and irregular or random variations (at variable (Y) that evolves in time (t), combined actions determine these movements, in which Yt where the trend (Tt ). When observing a = f (Tt , St ) + at , ) is the result of a complex of causes in which the series of prices acts continuously in the same sense throughout time. Seasonality (S) is the fluctuation caused, with specific regularity, within the annual period and can be caused by climatic vari- ations, for example. The random or irregular compo- nent (at ) is caused by exogenous factors, including catastrophic factors, such as war and epidemics, gov- ernment plans, and random factors. The values of at represent a sequence of random and independent shocks, and at is a noncontrollable portion of the model, usually referred to as white noise. The Autoregressive Integrated Moving Average (ARIMA), introduced by Box and Jenkins (1976), is based on the idea that a nonstationary time series, homogeneous, can be modeled from (d) differentia- tions with the addition of an autoregressive compo- nent (p) and an average moving component (q). Considering that (B) is a difference operator (i.e., B = Yt – Yt-1 ), {Yt } is a process that can be described by an ARIMA model (P,D,Q), and data backward (B) are the lag times or lag, in time (sequence), as follows: Zt = { Øp (B)Zt Yt (1 − B)d Yt = Ɵ0 + Ɵq (B)at , if the process is stationary, The pondering of differentiation Yt ARIMA model (p,d,q) with: Øp Øp (B)(1 − B)d Yt gressive component of p order (AR [p]), Ø0 µ(1 − Ø1 (B) = 1 − Ø1B − Ø2B2 − Ø2 − ... − Øp when d = 0 , if the process is nonstationary, when d ≥ 1 } corresponds to an = Ø0 + Øq(B)at − ... − ØpBp is the autore- = ) is the intercept or constant, µ is a periodic deterministic function (mean), and
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