A Série

Descritiva

── Data Summary ────────────────────────
                           Values                
Name                       precomediacanadeacucar
Number of rows             403                   
Number of columns          2                     
_______________________                          
Column type frequency:                           
  character                1                     
  numeric                  1                     
________________________                         
Group variables            None                  
     Data               valor1         
 Length:403         Min.   :  0.00006  
 Class :character   1st Qu.: 15.54500  
 Mode  :character   Median : 28.53630  
                    Mean   : 37.41690  
                    3rd Qu.: 54.02315  
                    Max.   :122.64300

Transformando em Série

Plot da Série

forecast::autoplot(precomediacanadeacucar,xlab="Ano",ylab="Preço Médio")

Teste de Tendência


    Cox Stuart test

data:  precomediacanadeacucar
statistic = 201, n = 201, p-value < 2.2e-16
alternative hypothesis: increasing trend


    Cox Stuart test

data:  precomediacanadeacucar
statistic = 201, n = 201, p-value = 1
alternative hypothesis: decreasing trend

Há evidência estatística com 5% de significância e 95% de confiança que a série segue uma tendência crescente.

Teste de Estacionaridade


    Augmented Dickey-Fuller Test

data:  precomediacanadeacucar
Dickey-Fuller = -0.71394, Lag order = 7, p-value = 0.9689
alternative hypothesis: stationary


    Phillips-Perron Unit Root Test

data:  precomediacanadeacucar
Dickey-Fuller Z(alpha) = -0.00274, Truncation lag parameter = 5,
p-value = 0.99
alternative hypothesis: stationary


    KPSS Test for Level Stationarity

data:  precomediacanadeacucar
KPSS Level = 5.955, Truncation lag parameter = 5, p-value = 0.01

Há evidência estatística com 5% de significância e 95% de confiança que a série é não estacionária.

Teste de Sazonalidade

[1] TRUE
Test used:  WO 
 
Test statistic:  1 
P-value:  0.0002115736 0.0005069643 0.6737711

Há evidência estatística com 5% de significância e 95% de confiança, que a série não é sazonal.

Diferença para transformar a série em estacionária

[1] 2
Series: precomediacanadeacucar 
ARIMA(0,2,1)(0,0,2)[12] 

Coefficients:
          ma1    sma1    sma2
      -0.8056  0.1793  0.1070
s.e.   0.0542  0.0512  0.0632

sigma^2 = 1.497:  log likelihood = -649.13
AIC=1306.26   AICc=1306.36   BIC=1322.23

Ajustando o Modelo

initial  value 0.338325 
iter   2 value 0.214499
iter   3 value 0.171934
iter   4 value 0.144200
iter   5 value 0.142066
iter   6 value 0.135690
iter   7 value 0.135405
iter   8 value 0.134739
iter   9 value 0.134685
iter  10 value 0.134683
iter  11 value 0.134683
iter  11 value 0.134683
iter  11 value 0.134683
final  value 0.134683 
converged
initial  value 0.138743 
iter   2 value 0.138728
iter   3 value 0.138712
iter   4 value 0.138711
iter   5 value 0.138711
iter   5 value 0.138711
iter   5 value 0.138711
final  value 0.138711 
converged

     Estimate     SE  t.value p.value
ma1   -0.5987 0.0453 -13.2289       0
ma2   -0.3855 0.0453  -8.5039       0
sma1   0.2014 0.0483   4.1676       0

Resíduos

  [1] -0.054153294 -0.054153309 -0.054121998 -0.054177691 -0.054183012
  [6] -0.054174109 -0.054162872 -0.054138117 -0.054143823 -0.054138147
 [11] -0.054125579 -0.054124853 -0.054117191 -0.053958408 -0.054245313
 [16] -0.054163959 -0.054184879 -0.054124708 -0.054121494 -0.054073636
 [21] -0.054080900 -0.053847805 -0.053926096 -0.053533529 -0.053639546
 [26] -0.053648365 -0.053761935 -0.053201205 -0.053182201 -0.053406145
 [31] -0.052327862 -0.051737705 -0.052524845 -0.051333302 -0.054118680
 [36] -0.049153912 -0.048332504 -0.044583098 -0.047234475 -0.041173298
 [41] -0.041625591 -0.013574249 -0.030046463 -0.007658350  0.016774857
 [46]  0.052663822  0.067456982  0.127779506  0.231150180  0.372718332
 [51]  0.749545423  0.698899690  0.682243183  1.861318817  0.699364010
 [56] -0.533737014 -0.012685926 -0.248848533 -0.212241338 -0.262439302
 [61]  0.163568100 -0.340241941 -0.203399999 -0.240616754 -0.140172608
 [66] -0.696908381  0.049260912 -0.167265952  0.129542635  0.385911922
 [71] -0.042917478 -0.185398177 -0.112538097 -0.027859686  0.013030362
 [76]  0.369643157  0.303270089  0.067213389 -0.272797791  0.197868327
 [81] -0.573211384 -0.367892624  0.009430922  0.047514944 -0.366082334
 [86] -0.048197094 -0.404138852 -0.169313556 -0.133247829  0.667121141
 [91] -0.286380414 -0.175488328 -0.071551140 -0.116923233 -0.145082049
 [96] -0.222157839 -0.100536794 -0.098354720 -0.147562734 -0.188960957
[101] -0.134160027 -0.291199331 -0.195398207 -0.369814217 -0.001846473
[106] -0.134451091  0.023822489 -0.607213262  0.372320947 -0.442469935
[111]  0.071993157 -0.755130354 -0.904382949 -0.269527477 -0.726397131
[116] -0.448883734 -0.345238798  0.266301649 -0.171309561  0.315275782
[121]  0.194036790  0.209071456 -0.558775340  0.783103338  0.558807991
[126] -0.521354201  0.270446323  1.501355419  0.661482925  0.053717711
[131] -0.270326866 -0.643562055  0.477013377 -0.282345226 -0.271513639
[136] -0.226843737 -0.276651854  0.066789226  0.927372670 -0.292105458
[141]  0.565321281 -0.396515442 -0.828291997  1.283607434 -0.711085487
[146]  0.036117155 -0.388485163 -0.245921982 -1.342031359 -0.962758896
[151] -0.952293474  0.741520440  0.638166673  0.922998744  0.197332756
[156] -0.056799533  0.432295888  0.391263683  0.295477943 -0.220173918
[161]  1.295882325  1.570113936 -2.298025924 -0.277083240  1.227263034
[166] -0.415480719 -1.398398290 -0.057622484 -0.505287560 -0.998008628
[171] -0.053366874 -0.166209309 -1.207037182 -0.253547786  0.875755935
[176]  0.999822844 -0.517693107  0.472437525  0.724454802  0.031967539
[181] -0.544561230  0.405501133 -0.686192307  0.154237159 -0.011813666
[186] -0.242511241  0.029200163  0.017012458 -0.248350181 -0.240259190
[191] -0.134371046 -0.184742660  0.145569318 -0.144778612  0.092280951
[196] -0.399559214  5.237903596 -1.805062294  1.549792226 -0.028219093
[201] -1.077748888 -0.483635917 -0.424216397 -0.087054069 -0.547683991
[206] -0.863684972 -0.312747057 -0.081185240 -2.578008775 -1.977081205
[211] -1.011029623  0.036007913  0.353591711 -0.387698657 -0.330770632
[216]  0.608157773  0.052225193 -0.031984604  0.084330771 -0.559441285
[221]  0.532160745 -0.167280260 -0.882152076 -0.089139025  0.513691387
[226]  0.577345536  0.933523723 -0.517791311  0.131090647 -0.513367070
[231]  0.072427061 -0.456472386 -0.287021725  0.224389530  0.444937813
[236]  0.482187547 -0.279867727  0.440854357 -0.136895221  0.237821172
[241] -0.017730216 -0.026456455  0.751517370  0.438130750 -0.632848455
[246]  0.208464707 -0.099824845 -0.234409510  0.328622879  0.616331208
[251]  0.290641325  1.221898658 -0.179024307  0.927938241 -0.520754452
[256]  0.553639854  1.735852890 -0.515777422  2.336543583  0.312396323
[261]  0.756524841  0.224141223 -0.200157696 -0.118788328  1.389122880
[266] -1.739482200 -1.724210781  0.166297558 -0.336353246  0.382527057
[271] -0.730406133  0.294584964 -0.196336196 -1.014417180 -0.017700735
[276] -0.727609016 -0.583428355  0.263661102  0.138480871 -1.829703552
[281] -0.066681520 -1.152951029  0.780394778 -0.193430525 -0.472303725
[286]  1.496628600 -0.529717870 -0.094716674  0.717604038 -0.486353750
[291] -0.501704373  0.245741062 -0.072206380 -0.850542388  0.172124899
[296] -0.480251797  0.026338728 -0.372874226 -0.137095812 -0.484968349
[301] -0.099421355  0.380410723 -0.339823153  0.446601211  0.348615518
[306] -0.323150522 -0.303956145  0.390822075  0.231360321  0.849507337
[311]  1.737831519  0.410384791 -0.302807462 -0.045641407 -0.394738692
[316]  4.051947502 -1.217804744 -0.389736156  0.775729035 -0.378330759
[321] -0.251655563  0.228309369 -0.341836055  0.248763340  0.077291255
[326] -0.485666976 -0.393949233  0.689948669 -1.258935327 -0.464714614
[331] -2.391344934  1.020258989 -1.713739399 -0.556999602 -0.467088640
[336] -0.936490429  2.245850710 -0.827912977  0.279992087 -1.460855748
[341] -2.259622804  1.394929630  1.779076721  0.502626845 -1.101796343
[346]  0.367765997  0.585872595 -0.687825962 -0.668829366 -1.454243124
[351] -0.314119652  0.144868170  1.124951877  1.271303717 -1.625905893
[356] -1.499490369  0.311995626  0.089143371 -0.316729118  0.149743670
[361]  0.654468831  1.916656061 -0.311327434  0.915738766  0.712705790
[366] -1.369592354  1.563494350  1.490622906 -0.762710640 -0.393342043
[371] -1.917059847  2.602148981 -1.547822252  0.281522146 -0.047379367
[376]  2.809957375 10.114993576 -0.158933602  1.671088199 -1.027528294
[381]  1.498046347 -0.975232382  1.522016230  1.205863379  0.293612068
[386] -0.544581138 -0.648609409 -1.037812733  4.106570287  0.222634914
[391] -1.214081955 -1.443447640 -2.442360688 -2.441933871  0.874900510
[396] -0.600477967 -1.077328058  2.428099451 -1.055476679  0.795329139
[401]  0.790226630 -1.369346966 -1.487237983

    Ljung-Box test

data:  Residuals
Q* = 6.5426, df = 10, p-value = 0.7678

Model df: 0.   Total lags used: 10

Testando Normalidade


    Jarque Bera Test

data:  residuos_padronizados
X-squared = 13979, df = 2, p-value < 2.2e-16


    Lilliefors (Kolmogorov-Smirnov) normality test

data:  residuos_padronizados
D = 0.14433, p-value < 2.2e-16

Há evidência estatística com 5% de significância e 95% de confiança, que os erros não segue normalidade.

Usando o Alisamento Exponencial Holt

Prevendo com o Prophet

Comparando a Previsão

profeta<- c(104.32,105.5,106.42,106.98)
holte<- c(119.64,120.28,120.91,121.55)
mes<-c("Abril","Maio","Junho","Julho")
observado<- c(119.84,122.64,122.57,120.72)
comparacao<- data.frame(mes,observado,profeta,holte)
knitr::kable(comparacao)
mes observado profeta holte
Abril 119.84 104.32 119.64
Maio 122.64 105.50 120.28
Junho 122.57 106.42 120.91
Julho 120.72 106.98 121.55
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