Registered S3 method overwritten by 'quantmod':
  method            from
  as.zoo.data.frame zoo

#Pre-Processing

Observed that variables Value and Period are both character columns, not numeric. Conversion to numeric process and remove commas present.

[1] "numeric"
[1] 40009000 51468000 48643000 42170000 49237000 45623000

Confirming no missing values present.

[1] FALSE

Variable Period converts months to numeric by three-letter format, and the month-letters are all capital. It says for each element in Period, match its position in table in toupper(month.abb), which in turn is saying convert the list month.abb(c(Jan, Feb,…,Dec)) to uppercase, that way it matches the capitalized months in Period.

Sorting, which is important for time order.

 Time-Series [1:60] from 2018 to 2023: 41962000 35982000 39083000 35896000 39190000 ...

#Seasonal Decomposition Multiplicative Model

 [1] 1.0730029 0.9504886 1.0203860 0.9193926 0.9559208 1.0225593 1.0335956
 [8] 1.0735540 1.0108901 1.0542736 0.9393133 0.9466229
           Jan       Feb       Mar       Apr       May       Jun       Jul
2018 1.0730029 0.9504886 1.0203860 0.9193926 0.9559208 1.0225593 1.0335956
2019 1.0730029 0.9504886 1.0203860 0.9193926 0.9559208 1.0225593 1.0335956
2020 1.0730029 0.9504886 1.0203860 0.9193926 0.9559208 1.0225593 1.0335956
2021 1.0730029 0.9504886 1.0203860 0.9193926 0.9559208 1.0225593 1.0335956
2022 1.0730029 0.9504886 1.0203860 0.9193926 0.9559208 1.0225593 1.0335956
           Aug       Sep       Oct       Nov       Dec
2018 1.0735540 1.0108901 1.0542736 0.9393133 0.9466229
2019 1.0735540 1.0108901 1.0542736 0.9393133 0.9466229
2020 1.0735540 1.0108901 1.0542736 0.9393133 0.9466229
2021 1.0735540 1.0108901 1.0542736 0.9393133 0.9466229
2022 1.0735540 1.0108901 1.0542736 0.9393133 0.9466229
       1        2        3        4        5        6        7        8 
52188389 46423489 50045569 45279842 47273866 50778004 51536911 53748325 
       9       10       11       12 
50817243 53213206 47602356 48165912

#Holt-Winters Multiplicative Model

Holt-Winters exponential smoothing with trend and multiplicative seasonal component.

Call:
HoltWinters(x = chicken_time, seasonal = "multiplicative")

Smoothing parameters:
 alpha: 0.2110384
 beta : 0.0593853
 gamma: 0.7322568

Coefficients:
            [,1]
a   4.839613e+07
b   2.372964e+05
s1  1.077492e+00
s2  9.554042e-01
s3  1.066137e+00
s4  9.066157e-01
s5  9.985615e-01
s6  1.081984e+00
s7  1.010682e+00
s8  1.111475e+00
s9  1.042972e+00
s10 1.056502e+00
s11 1.039961e+00
s12 9.966623e-01

#ARIMA Mixed Model

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

Coefficients:
          ma1     ma2    sar1
      -0.9275  0.3217  0.5945
s.e.   0.1220  0.1665  0.1140

sigma^2 = 7.161e+12:  log likelihood = -958.43
AIC=1924.86   AICc=1925.6   BIC=1933.17

Training set error measures:
                 ME    RMSE     MAE       MPE     MAPE      MASE         ACF1
Training set 213901 2585176 2056380 0.1458906 4.919505 0.6712929 -0.001509238


    Ljung-Box test

data:  Residuals from ARIMA(0,1,2)(1,0,0)[12]
Q* = 14.027, df = 9, p-value = 0.1214

Model df: 3.   Total lags used: 12

         Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95
Jan 2023       51340117 47910799 54769435 46095428 56584807
Feb 2023       47421397 43983084 50859710 42162951 52679843
Mar 2023       51044573 47350122 54739025 45394397 56694750
Apr 2023       46136789 42202840 50070738 40120334 52153245
May 2023       49865778 45706099 54025457 43504097 56227458
Jun 2023       51964189 47590413 56337964 45275076 58653301
Jul 2023       49474035 44896165 54051905 42472787 56475282
Aug 2023       52948599 48175354 57721844 45648550 60248647
Sep 2023       51391733 46430800 56352665 43804641 58978824
Oct 2023       51622379 46480607 56764152 43758716 59486042
Nov 2023       52457583 47141117 57774048 44326750 60588415
Dec 2023       51269276 45783678 56754874 42879777 59658774
Jan 2024       52872579 46423907 59321250 43010186 62734971
Feb 2024       50543093 43922400 57163786 40417617 60668569
Mar 2024       52696893 45734260 59659525 42048465 63345320
Apr 2024       49779457 42490909 57068005 38632585 60926330
May 2024       51996157 44395656 59596658 40372194 63620120
Jun 2024       53243558 45343413 61143703 41161329 65325787
Jul 2024       51763285 43574453 59952117 39239547 64287023
Aug 2024       53828742 45361059 62296424 40878538 66778945
Sep 2024       52903262 44165623 61640900 39540196 66266327
Oct 2024       53040370 44040869 62039870 39276821 66803918
Nov 2024       53536857 44282901 62790812 39384153 67689560
Dec 2024       52830467 43328869 62332065 38299027 67361907