data <- read.csv(file = "C:/Users/LENOVO/Downloads/DATA METRAMAL.csv")
data.ts <- ts(data, start =c (2006,1), frequency = 12)
data.ts
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2006 2976 3176 2895 3259 2794 2699 3076 2998 3110 3032 3009 2791
## 2007 3993 4143 3668 3033 3384 3116 2884 2925 2717 2837 3046 2990
## 2008 3290 3238 3644 3176 3130 2793 3080 3353 3487 3448 3361 3243
## 2009 2927 3334 3793 3846 3447 3488 3151 3350 3571 2798 3160 3135
ft_additive = HoltWinters(data.ts,seasonal = "additive")
ft_additive$SSE
## [1] 4719524
ft_multiplicative = HoltWinters(data.ts,seasonal = "multiplicative")
ft_multiplicative$SSE
## [1] 4546624
#Error
ft_additive$fitted
## xhat level trend season
## Jan 2007 3777.540 3120.834 12.49403 644.21181
## Feb 2007 3954.704 3136.956 12.49403 805.25347
## Mar 2007 3514.786 3152.621 12.49403 349.67014
## Apr 2007 2919.360 3167.696 12.49403 -260.82986
## May 2007 3291.351 3182.103 12.49403 96.75347
## Jun 2007 3027.572 3196.158 12.49403 -181.07986
## Jul 2007 3194.305 3210.141 12.49403 -28.32986
## Aug 2007 3040.907 3217.409 12.49403 -188.99653
## Sep 2007 3090.949 3227.951 12.49403 -149.49653
## Oct 2007 2996.354 3234.148 12.49403 -250.28819
## Nov 2007 2967.998 3243.958 12.49403 -288.45486
## Dec 2007 2721.847 3257.766 12.49403 -548.41319
## Jan 2008 4055.710 3274.776 12.49403 768.43997
## Feb 2008 4200.689 3274.375 12.49403 913.81960
## Mar 2008 3721.160 3270.657 12.49403 438.00920
## Apr 2008 3099.038 3281.852 12.49403 -195.30815
## May 2008 3458.308 3295.642 12.49403 150.17233
## Jun 2008 3185.007 3302.607 12.49403 -130.09467
## Jul 2008 3113.751 3308.500 12.49403 -207.24277
## Aug 2008 3077.094 3320.425 12.49403 -255.82499
## Sep 2008 2984.955 3337.566 12.49403 -365.10467
## Oct 2008 3028.841 3358.514 12.49403 -342.16701
## Nov 2008 3147.080 3378.067 12.49403 -243.48091
## Dec 2008 3012.854 3394.164 12.49403 -393.80380
## Jan 2009 3749.981 3410.533 12.49403 326.95369
## Feb 2009 3780.423 3409.168 12.49403 358.76093
## Mar 2009 3820.159 3414.144 12.49403 393.52070
## Apr 2009 3287.741 3426.181 12.49403 -150.93391
## May 2009 3421.449 3448.076 12.49403 -39.12080
## Jun 2009 3117.380 3461.000 12.49403 -356.11438
## Jul 2009 3265.527 3479.736 12.49403 -226.70261
## Aug 2009 3406.049 3490.301 12.49403 -96.74575
## Sep 2009 3438.705 3501.851 12.49403 -75.63999
## Oct 2009 3428.575 3516.573 12.49403 -100.49215
## Nov 2009 3410.801 3518.448 12.49403 -120.14088
## Dec 2009 3278.105 3526.719 12.49403 -261.10810
fitted_a = ft_additive$fitted[,1]
error_a = data.ts - fitted_a
error_a
## Jan Feb Mar Apr May Jun
## 2007 215.46020 188.29611 153.21446 113.64027 92.64918 88.42825
## 2008 -765.70981 -962.68873 -77.16045 76.96227 -328.30829 -392.00653
## 2009 -822.98101 -446.42308 -27.15900 558.25895 25.55060 370.61987
## Jul Aug Sep Oct Nov Dec
## 2007 -310.30493 -115.90668 -373.94881 -159.35378 78.00241 268.15314
## 2008 -33.75098 275.90559 502.04493 419.15868 213.91982 230.14622
## 2009 -114.52725 -56.04947 132.29462 -630.57511 -250.80137 -143.10463
MSE_a = mean(error_a^2)
MSE_a
## [1] 131097.9
MAPE_a= mean(abs((error_a/data.ts)*100))
MAPE_a
## [1] 8.68438
ft_multiplicative$fitted
## xhat level trend season
## Jan 2007 3736.709 3120.834 12.49403 1.1925686
## Feb 2007 3976.004 3189.935 12.49403 1.2415588
## Mar 2007 3594.233 3237.858 12.49403 1.1057980
## Apr 2007 3022.342 3267.924 12.49403 0.9213283
## May 2007 3395.032 3283.465 12.49403 1.0300591
## Jun 2007 3125.758 3293.138 12.49403 0.9455856
## Jul 2007 3291.825 3302.914 12.49403 0.9928870
## Aug 2007 3032.915 3207.216 12.49403 0.9419840
## Sep 2007 3057.653 3189.534 12.49403 0.9549114
## Oct 2007 2884.459 3108.062 12.49403 0.9243413
## Nov 2007 2848.155 3107.032 12.49403 0.9130089
## Dec 2007 2665.988 3176.604 12.49403 0.8359691
## Jan 2008 4135.386 3291.190 12.49403 1.2517496
## Feb 2008 4015.592 3125.792 12.49403 1.2795496
## Mar 2008 3356.846 2978.214 12.49403 1.1224253
## Apr 2008 2836.363 3058.095 12.49403 0.9237193
## May 2008 3267.671 3167.438 12.49403 1.0275914
## Jun 2008 2978.473 3144.643 12.49403 0.9434095
## Jul 2008 2803.637 3105.352 12.49403 0.8992223
## Aug 2008 2944.955 3198.800 12.49403 0.9170619
## Sep 2008 2920.619 3328.494 12.49403 0.8741781
## Oct 2008 3217.858 3511.647 12.49403 0.9130900
## Nov 2008 3454.889 3590.531 12.49403 0.9588855
## Dec 2008 3261.218 3577.234 12.49403 0.9084859
## Jan 2009 3785.900 3584.446 12.49403 1.0525333
## Feb 2009 3690.587 3381.996 12.49403 1.0872288
## Mar 2009 3956.791 3308.099 12.49403 1.1915914
## Apr 2009 3305.793 3284.387 12.49403 1.0027030
## May 2009 3435.213 3438.790 12.49403 0.9953435
## Jun 2009 3118.179 3454.403 12.49403 0.8994148
## Jul 2009 3454.454 3575.203 12.49403 0.9628612
## Aug 2009 3543.072 3504.683 12.49403 1.0073624
## Sep 2009 3454.768 3466.693 12.49403 0.9929813
## Oct 2009 3382.682 3510.020 12.49403 0.9603036
## Nov 2009 3170.647 3362.140 12.49403 0.9395526
## Dec 2009 3061.778 3371.650 12.49403 0.9047422
fitted_m = ft_multiplicative$fitted[,1]
error_m = data.ts - fitted_m
error_m
## Jan Feb Mar Apr May Jun
## 2007 256.291474 166.995876 73.767098 10.658490 -11.032489 -9.757633
## 2008 -845.385623 -777.592335 287.153875 339.637349 -137.671199 -185.473055
## 2009 -858.899624 -356.587022 -163.790652 540.207155 11.787119 369.821353
## Jul Aug Sep Oct Nov Dec
## 2007 -407.825007 -107.915162 -340.653021 -47.459176 197.844888 324.012072
## 2008 276.362898 408.045166 566.381257 230.141876 -93.888782 -18.217549
## 2009 -303.454440 -193.072361 116.232157 -584.682384 -10.646679 73.222412
MSE_m = mean(error_m^2)
MSE_m
## [1] 126295.1
MAPE_m= mean(abs((error_m/data.ts)*100))
MAPE_m
## [1] 8.364667
df_a <- data.frame(ft_additive[["fitted"]])
df_m <- data.frame(ft_multiplicative[["fitted"]])
library("writexl")