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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 13 Dec 2016 22:26:28 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/13/t14816645647yi89bfukq3rbvq.htm/, Retrieved Sun, 05 May 2024 01:12:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299238, Retrieved Sun, 05 May 2024 01:12:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-13 21:26:28] [130d73899007e5ff8a4f636b9bcfb397] [Current]
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Dataseries X:
3765
3680
3265
2950
2975
3225
3270
3425
3575
3455
3335
3725
3895
4145
4490
4280
3785
3295
3290
3530
4345
4340
4950
5395
4895
4255
3910
3895
3910
3300
3780
3830
3505
3505
3440
3065
3085
3240
2930
2900
2375
2875
3575
3725
3600
3695
3245
3700
3350
2670
2960
2830
2825
2920
2930
3385
3350
3485
3140
2960
2850
2995
2695
2950
2890
3040
2945
3650
3995
3540
3435
3345
3005
2760
2890
2745
3180
3365
3660
3890
3685
4150
3930
3675
3380
3195
2985
2555
2830
2595
2940
3185
3090
2615
2785
2695
3015
3185
3050
2970
3295
3680
3715
3785
3655
3725
3545
3440
3575
3570
3355
3500
3275
3395
3485
3390




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299238&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299238&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299238&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299238&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.999933893038648[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299238&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299238&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
236803765-85
332653680.00561909172-415.005619091715
429503265.02743476042-315.027434760422
529752950.0208255064524.9791744935455
632252974.99834870268250.001651297323
732703224.983473150545.0165268495002
834253269.9970240942155.002975905801
935753424.98975322426150.010246775738
1034553574.99008327841-119.990083278414
1133353455.0079321798-120.007932179798
1237253335.00793335973389.992066640265
1338953724.97421880952170.025781190477
1441453894.98876011225250.011239887746
1544904144.98347251663345.016527483373
1642804489.97719200575-209.977192005752
1737854280.01388095412-495.013880954117
1832953785.0327238635-490.032723863497
1932903295.03239457434-5.03239457433756
2035303290.00033267631239.999667323686
2143453529.98413435127815.015865648732
2243404344.94612177767-4.94612177766885
2349504340.00032697308609.999673026919
2453954949.95967477519445.04032522481
2548955394.97057973642-499.97057973642
2642554895.03305153579-640.033051535792
2739104255.0423106402-345.042310640201
2838953910.02280969869-15.0228096986943
2939103895.000993112314.9990068876996
3033003909.99900846123-609.999008461231
3137803300.04032518088479.959674819123
3238303779.9682713243350.0317286756735
3335053829.99669255445-324.996692554446
3435053505.02148454379-0.0214845437944859
3534403505.00000142028-65.0000014202778
3630653440.00429695258-375.004296952582
3730853065.0247903945719.9752096054344
3832403084.99867949959155.001320500409
3929303239.9897533337-309.989753333696
4029002930.02049248064-30.0204924806435
4123752900.00198456354-525.001984563537
4228752375.0347062859499.965293714097
4335752874.96694881365700.033051186349
4437253574.95372294214150.04627705786
4536003724.99008089656-124.990080896562
4636953600.0082627144594.991737285553
4732453694.99372038489-449.993720384894
4837003245.02974771748454.970252282518
4933503699.96992329912-349.969923299116
5026703350.02313544819-680.023135448194
5129602670.04495426313289.955045736866
5228302959.980831953-129.980831952998
5328252830.00859263783-5.00859263783423
5429202825.0003311028494.9996688971601
5529302919.9937198605610.0062801394402
5633852929.99933851523455.000661484774
5733503384.96992128886-34.9699212888563
5834853350.00231175524134.997688244765
5931403484.99107571304-344.991075713041
6029603140.02280631171-180.022806311709
6128502960.0119007607-110.0119007607
6229952850.00727255247144.992727447528
6326952994.99041497137-299.99041497137
6429502695.01983145477254.980168545231
6528902949.98314403585-59.9831440358525
6630402890.00396530338149.996034696615
6729453039.99008421793-94.9900842179313
6836502945.00627950583704.993720494174
6939953649.95339500737345.046604992634
7035403994.97719001742-454.977190017419
7134353540.03007715952-105.030077159517
7233453435.00694321925-90.0069432192513
7330053345.00595008552-340.005950085517
7427603005.0224767602-245.022476760202
7528902760.0161976914129.983802308599
7627452889.9914071658-144.991407165805
7731802745.00958494135434.99041505865
7833653179.97124410544185.028755894557
7936603364.98776831118295.012231688815
8038903659.9804976378230.019502362199
8136853889.98479410965-204.984794109647
8241503685.01355092186464.986449078138
8339304149.96926115878-219.969261158782
8436753930.01454149945-255.014541499446
8533803675.01685823644-295.016858236439
8631953380.01950266805-185.019502668046
8729853195.01223107711-210.012231077112
8825552985.01388327044-430.013883270443
8928302555.02842691116274.971573088838
9025952829.98182246484-234.981822464845
9129402595.01553393426344.984466065744
9231852939.97719412523245.022805874765
9330903184.98380228684-94.9838022868416
9426153090.00627909055-475.006279090547
9527852615.03140122173169.968598778266
9626952784.98876389241-89.9887638924097
9730152695.00594888374319.994051116263
9831853014.97884616563170.02115383437
9930503184.98876041815-134.988760418154
10029703050.00892369677-80.0089236967683
10132952970.00528914683324.994710853173
10236803294.97851558721385.02148441279
10337153679.9745473996135.0254526003896
10437853714.9976845737670.0023154262412
10536553784.99537235964-129.99537235964
10637253655.0085935990669.9914064009436
10735453724.9953730808-179.995373080802
10834403545.01189894717-105.011898947172
10935753440.00694201755134.993057982455
11035703574.99107601913-4.99107601913329
11133553570.00032994487-215.000329944869
11235003355.0142130185144.985786981498
11332753499.99041543018-224.990415430183
11433953275.0148734327119.985126567303
11534853394.9920681478890.0079318521248
11633903484.99404984913-94.9940498491278

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 3680 & 3765 & -85 \tabularnewline
3 & 3265 & 3680.00561909172 & -415.005619091715 \tabularnewline
4 & 2950 & 3265.02743476042 & -315.027434760422 \tabularnewline
5 & 2975 & 2950.02082550645 & 24.9791744935455 \tabularnewline
6 & 3225 & 2974.99834870268 & 250.001651297323 \tabularnewline
7 & 3270 & 3224.9834731505 & 45.0165268495002 \tabularnewline
8 & 3425 & 3269.9970240942 & 155.002975905801 \tabularnewline
9 & 3575 & 3424.98975322426 & 150.010246775738 \tabularnewline
10 & 3455 & 3574.99008327841 & -119.990083278414 \tabularnewline
11 & 3335 & 3455.0079321798 & -120.007932179798 \tabularnewline
12 & 3725 & 3335.00793335973 & 389.992066640265 \tabularnewline
13 & 3895 & 3724.97421880952 & 170.025781190477 \tabularnewline
14 & 4145 & 3894.98876011225 & 250.011239887746 \tabularnewline
15 & 4490 & 4144.98347251663 & 345.016527483373 \tabularnewline
16 & 4280 & 4489.97719200575 & -209.977192005752 \tabularnewline
17 & 3785 & 4280.01388095412 & -495.013880954117 \tabularnewline
18 & 3295 & 3785.0327238635 & -490.032723863497 \tabularnewline
19 & 3290 & 3295.03239457434 & -5.03239457433756 \tabularnewline
20 & 3530 & 3290.00033267631 & 239.999667323686 \tabularnewline
21 & 4345 & 3529.98413435127 & 815.015865648732 \tabularnewline
22 & 4340 & 4344.94612177767 & -4.94612177766885 \tabularnewline
23 & 4950 & 4340.00032697308 & 609.999673026919 \tabularnewline
24 & 5395 & 4949.95967477519 & 445.04032522481 \tabularnewline
25 & 4895 & 5394.97057973642 & -499.97057973642 \tabularnewline
26 & 4255 & 4895.03305153579 & -640.033051535792 \tabularnewline
27 & 3910 & 4255.0423106402 & -345.042310640201 \tabularnewline
28 & 3895 & 3910.02280969869 & -15.0228096986943 \tabularnewline
29 & 3910 & 3895.0009931123 & 14.9990068876996 \tabularnewline
30 & 3300 & 3909.99900846123 & -609.999008461231 \tabularnewline
31 & 3780 & 3300.04032518088 & 479.959674819123 \tabularnewline
32 & 3830 & 3779.96827132433 & 50.0317286756735 \tabularnewline
33 & 3505 & 3829.99669255445 & -324.996692554446 \tabularnewline
34 & 3505 & 3505.02148454379 & -0.0214845437944859 \tabularnewline
35 & 3440 & 3505.00000142028 & -65.0000014202778 \tabularnewline
36 & 3065 & 3440.00429695258 & -375.004296952582 \tabularnewline
37 & 3085 & 3065.02479039457 & 19.9752096054344 \tabularnewline
38 & 3240 & 3084.99867949959 & 155.001320500409 \tabularnewline
39 & 2930 & 3239.9897533337 & -309.989753333696 \tabularnewline
40 & 2900 & 2930.02049248064 & -30.0204924806435 \tabularnewline
41 & 2375 & 2900.00198456354 & -525.001984563537 \tabularnewline
42 & 2875 & 2375.0347062859 & 499.965293714097 \tabularnewline
43 & 3575 & 2874.96694881365 & 700.033051186349 \tabularnewline
44 & 3725 & 3574.95372294214 & 150.04627705786 \tabularnewline
45 & 3600 & 3724.99008089656 & -124.990080896562 \tabularnewline
46 & 3695 & 3600.00826271445 & 94.991737285553 \tabularnewline
47 & 3245 & 3694.99372038489 & -449.993720384894 \tabularnewline
48 & 3700 & 3245.02974771748 & 454.970252282518 \tabularnewline
49 & 3350 & 3699.96992329912 & -349.969923299116 \tabularnewline
50 & 2670 & 3350.02313544819 & -680.023135448194 \tabularnewline
51 & 2960 & 2670.04495426313 & 289.955045736866 \tabularnewline
52 & 2830 & 2959.980831953 & -129.980831952998 \tabularnewline
53 & 2825 & 2830.00859263783 & -5.00859263783423 \tabularnewline
54 & 2920 & 2825.00033110284 & 94.9996688971601 \tabularnewline
55 & 2930 & 2919.99371986056 & 10.0062801394402 \tabularnewline
56 & 3385 & 2929.99933851523 & 455.000661484774 \tabularnewline
57 & 3350 & 3384.96992128886 & -34.9699212888563 \tabularnewline
58 & 3485 & 3350.00231175524 & 134.997688244765 \tabularnewline
59 & 3140 & 3484.99107571304 & -344.991075713041 \tabularnewline
60 & 2960 & 3140.02280631171 & -180.022806311709 \tabularnewline
61 & 2850 & 2960.0119007607 & -110.0119007607 \tabularnewline
62 & 2995 & 2850.00727255247 & 144.992727447528 \tabularnewline
63 & 2695 & 2994.99041497137 & -299.99041497137 \tabularnewline
64 & 2950 & 2695.01983145477 & 254.980168545231 \tabularnewline
65 & 2890 & 2949.98314403585 & -59.9831440358525 \tabularnewline
66 & 3040 & 2890.00396530338 & 149.996034696615 \tabularnewline
67 & 2945 & 3039.99008421793 & -94.9900842179313 \tabularnewline
68 & 3650 & 2945.00627950583 & 704.993720494174 \tabularnewline
69 & 3995 & 3649.95339500737 & 345.046604992634 \tabularnewline
70 & 3540 & 3994.97719001742 & -454.977190017419 \tabularnewline
71 & 3435 & 3540.03007715952 & -105.030077159517 \tabularnewline
72 & 3345 & 3435.00694321925 & -90.0069432192513 \tabularnewline
73 & 3005 & 3345.00595008552 & -340.005950085517 \tabularnewline
74 & 2760 & 3005.0224767602 & -245.022476760202 \tabularnewline
75 & 2890 & 2760.0161976914 & 129.983802308599 \tabularnewline
76 & 2745 & 2889.9914071658 & -144.991407165805 \tabularnewline
77 & 3180 & 2745.00958494135 & 434.99041505865 \tabularnewline
78 & 3365 & 3179.97124410544 & 185.028755894557 \tabularnewline
79 & 3660 & 3364.98776831118 & 295.012231688815 \tabularnewline
80 & 3890 & 3659.9804976378 & 230.019502362199 \tabularnewline
81 & 3685 & 3889.98479410965 & -204.984794109647 \tabularnewline
82 & 4150 & 3685.01355092186 & 464.986449078138 \tabularnewline
83 & 3930 & 4149.96926115878 & -219.969261158782 \tabularnewline
84 & 3675 & 3930.01454149945 & -255.014541499446 \tabularnewline
85 & 3380 & 3675.01685823644 & -295.016858236439 \tabularnewline
86 & 3195 & 3380.01950266805 & -185.019502668046 \tabularnewline
87 & 2985 & 3195.01223107711 & -210.012231077112 \tabularnewline
88 & 2555 & 2985.01388327044 & -430.013883270443 \tabularnewline
89 & 2830 & 2555.02842691116 & 274.971573088838 \tabularnewline
90 & 2595 & 2829.98182246484 & -234.981822464845 \tabularnewline
91 & 2940 & 2595.01553393426 & 344.984466065744 \tabularnewline
92 & 3185 & 2939.97719412523 & 245.022805874765 \tabularnewline
93 & 3090 & 3184.98380228684 & -94.9838022868416 \tabularnewline
94 & 2615 & 3090.00627909055 & -475.006279090547 \tabularnewline
95 & 2785 & 2615.03140122173 & 169.968598778266 \tabularnewline
96 & 2695 & 2784.98876389241 & -89.9887638924097 \tabularnewline
97 & 3015 & 2695.00594888374 & 319.994051116263 \tabularnewline
98 & 3185 & 3014.97884616563 & 170.02115383437 \tabularnewline
99 & 3050 & 3184.98876041815 & -134.988760418154 \tabularnewline
100 & 2970 & 3050.00892369677 & -80.0089236967683 \tabularnewline
101 & 3295 & 2970.00528914683 & 324.994710853173 \tabularnewline
102 & 3680 & 3294.97851558721 & 385.02148441279 \tabularnewline
103 & 3715 & 3679.97454739961 & 35.0254526003896 \tabularnewline
104 & 3785 & 3714.99768457376 & 70.0023154262412 \tabularnewline
105 & 3655 & 3784.99537235964 & -129.99537235964 \tabularnewline
106 & 3725 & 3655.00859359906 & 69.9914064009436 \tabularnewline
107 & 3545 & 3724.9953730808 & -179.995373080802 \tabularnewline
108 & 3440 & 3545.01189894717 & -105.011898947172 \tabularnewline
109 & 3575 & 3440.00694201755 & 134.993057982455 \tabularnewline
110 & 3570 & 3574.99107601913 & -4.99107601913329 \tabularnewline
111 & 3355 & 3570.00032994487 & -215.000329944869 \tabularnewline
112 & 3500 & 3355.0142130185 & 144.985786981498 \tabularnewline
113 & 3275 & 3499.99041543018 & -224.990415430183 \tabularnewline
114 & 3395 & 3275.0148734327 & 119.985126567303 \tabularnewline
115 & 3485 & 3394.99206814788 & 90.0079318521248 \tabularnewline
116 & 3390 & 3484.99404984913 & -94.9940498491278 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299238&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]3680[/C][C]3765[/C][C]-85[/C][/ROW]
[ROW][C]3[/C][C]3265[/C][C]3680.00561909172[/C][C]-415.005619091715[/C][/ROW]
[ROW][C]4[/C][C]2950[/C][C]3265.02743476042[/C][C]-315.027434760422[/C][/ROW]
[ROW][C]5[/C][C]2975[/C][C]2950.02082550645[/C][C]24.9791744935455[/C][/ROW]
[ROW][C]6[/C][C]3225[/C][C]2974.99834870268[/C][C]250.001651297323[/C][/ROW]
[ROW][C]7[/C][C]3270[/C][C]3224.9834731505[/C][C]45.0165268495002[/C][/ROW]
[ROW][C]8[/C][C]3425[/C][C]3269.9970240942[/C][C]155.002975905801[/C][/ROW]
[ROW][C]9[/C][C]3575[/C][C]3424.98975322426[/C][C]150.010246775738[/C][/ROW]
[ROW][C]10[/C][C]3455[/C][C]3574.99008327841[/C][C]-119.990083278414[/C][/ROW]
[ROW][C]11[/C][C]3335[/C][C]3455.0079321798[/C][C]-120.007932179798[/C][/ROW]
[ROW][C]12[/C][C]3725[/C][C]3335.00793335973[/C][C]389.992066640265[/C][/ROW]
[ROW][C]13[/C][C]3895[/C][C]3724.97421880952[/C][C]170.025781190477[/C][/ROW]
[ROW][C]14[/C][C]4145[/C][C]3894.98876011225[/C][C]250.011239887746[/C][/ROW]
[ROW][C]15[/C][C]4490[/C][C]4144.98347251663[/C][C]345.016527483373[/C][/ROW]
[ROW][C]16[/C][C]4280[/C][C]4489.97719200575[/C][C]-209.977192005752[/C][/ROW]
[ROW][C]17[/C][C]3785[/C][C]4280.01388095412[/C][C]-495.013880954117[/C][/ROW]
[ROW][C]18[/C][C]3295[/C][C]3785.0327238635[/C][C]-490.032723863497[/C][/ROW]
[ROW][C]19[/C][C]3290[/C][C]3295.03239457434[/C][C]-5.03239457433756[/C][/ROW]
[ROW][C]20[/C][C]3530[/C][C]3290.00033267631[/C][C]239.999667323686[/C][/ROW]
[ROW][C]21[/C][C]4345[/C][C]3529.98413435127[/C][C]815.015865648732[/C][/ROW]
[ROW][C]22[/C][C]4340[/C][C]4344.94612177767[/C][C]-4.94612177766885[/C][/ROW]
[ROW][C]23[/C][C]4950[/C][C]4340.00032697308[/C][C]609.999673026919[/C][/ROW]
[ROW][C]24[/C][C]5395[/C][C]4949.95967477519[/C][C]445.04032522481[/C][/ROW]
[ROW][C]25[/C][C]4895[/C][C]5394.97057973642[/C][C]-499.97057973642[/C][/ROW]
[ROW][C]26[/C][C]4255[/C][C]4895.03305153579[/C][C]-640.033051535792[/C][/ROW]
[ROW][C]27[/C][C]3910[/C][C]4255.0423106402[/C][C]-345.042310640201[/C][/ROW]
[ROW][C]28[/C][C]3895[/C][C]3910.02280969869[/C][C]-15.0228096986943[/C][/ROW]
[ROW][C]29[/C][C]3910[/C][C]3895.0009931123[/C][C]14.9990068876996[/C][/ROW]
[ROW][C]30[/C][C]3300[/C][C]3909.99900846123[/C][C]-609.999008461231[/C][/ROW]
[ROW][C]31[/C][C]3780[/C][C]3300.04032518088[/C][C]479.959674819123[/C][/ROW]
[ROW][C]32[/C][C]3830[/C][C]3779.96827132433[/C][C]50.0317286756735[/C][/ROW]
[ROW][C]33[/C][C]3505[/C][C]3829.99669255445[/C][C]-324.996692554446[/C][/ROW]
[ROW][C]34[/C][C]3505[/C][C]3505.02148454379[/C][C]-0.0214845437944859[/C][/ROW]
[ROW][C]35[/C][C]3440[/C][C]3505.00000142028[/C][C]-65.0000014202778[/C][/ROW]
[ROW][C]36[/C][C]3065[/C][C]3440.00429695258[/C][C]-375.004296952582[/C][/ROW]
[ROW][C]37[/C][C]3085[/C][C]3065.02479039457[/C][C]19.9752096054344[/C][/ROW]
[ROW][C]38[/C][C]3240[/C][C]3084.99867949959[/C][C]155.001320500409[/C][/ROW]
[ROW][C]39[/C][C]2930[/C][C]3239.9897533337[/C][C]-309.989753333696[/C][/ROW]
[ROW][C]40[/C][C]2900[/C][C]2930.02049248064[/C][C]-30.0204924806435[/C][/ROW]
[ROW][C]41[/C][C]2375[/C][C]2900.00198456354[/C][C]-525.001984563537[/C][/ROW]
[ROW][C]42[/C][C]2875[/C][C]2375.0347062859[/C][C]499.965293714097[/C][/ROW]
[ROW][C]43[/C][C]3575[/C][C]2874.96694881365[/C][C]700.033051186349[/C][/ROW]
[ROW][C]44[/C][C]3725[/C][C]3574.95372294214[/C][C]150.04627705786[/C][/ROW]
[ROW][C]45[/C][C]3600[/C][C]3724.99008089656[/C][C]-124.990080896562[/C][/ROW]
[ROW][C]46[/C][C]3695[/C][C]3600.00826271445[/C][C]94.991737285553[/C][/ROW]
[ROW][C]47[/C][C]3245[/C][C]3694.99372038489[/C][C]-449.993720384894[/C][/ROW]
[ROW][C]48[/C][C]3700[/C][C]3245.02974771748[/C][C]454.970252282518[/C][/ROW]
[ROW][C]49[/C][C]3350[/C][C]3699.96992329912[/C][C]-349.969923299116[/C][/ROW]
[ROW][C]50[/C][C]2670[/C][C]3350.02313544819[/C][C]-680.023135448194[/C][/ROW]
[ROW][C]51[/C][C]2960[/C][C]2670.04495426313[/C][C]289.955045736866[/C][/ROW]
[ROW][C]52[/C][C]2830[/C][C]2959.980831953[/C][C]-129.980831952998[/C][/ROW]
[ROW][C]53[/C][C]2825[/C][C]2830.00859263783[/C][C]-5.00859263783423[/C][/ROW]
[ROW][C]54[/C][C]2920[/C][C]2825.00033110284[/C][C]94.9996688971601[/C][/ROW]
[ROW][C]55[/C][C]2930[/C][C]2919.99371986056[/C][C]10.0062801394402[/C][/ROW]
[ROW][C]56[/C][C]3385[/C][C]2929.99933851523[/C][C]455.000661484774[/C][/ROW]
[ROW][C]57[/C][C]3350[/C][C]3384.96992128886[/C][C]-34.9699212888563[/C][/ROW]
[ROW][C]58[/C][C]3485[/C][C]3350.00231175524[/C][C]134.997688244765[/C][/ROW]
[ROW][C]59[/C][C]3140[/C][C]3484.99107571304[/C][C]-344.991075713041[/C][/ROW]
[ROW][C]60[/C][C]2960[/C][C]3140.02280631171[/C][C]-180.022806311709[/C][/ROW]
[ROW][C]61[/C][C]2850[/C][C]2960.0119007607[/C][C]-110.0119007607[/C][/ROW]
[ROW][C]62[/C][C]2995[/C][C]2850.00727255247[/C][C]144.992727447528[/C][/ROW]
[ROW][C]63[/C][C]2695[/C][C]2994.99041497137[/C][C]-299.99041497137[/C][/ROW]
[ROW][C]64[/C][C]2950[/C][C]2695.01983145477[/C][C]254.980168545231[/C][/ROW]
[ROW][C]65[/C][C]2890[/C][C]2949.98314403585[/C][C]-59.9831440358525[/C][/ROW]
[ROW][C]66[/C][C]3040[/C][C]2890.00396530338[/C][C]149.996034696615[/C][/ROW]
[ROW][C]67[/C][C]2945[/C][C]3039.99008421793[/C][C]-94.9900842179313[/C][/ROW]
[ROW][C]68[/C][C]3650[/C][C]2945.00627950583[/C][C]704.993720494174[/C][/ROW]
[ROW][C]69[/C][C]3995[/C][C]3649.95339500737[/C][C]345.046604992634[/C][/ROW]
[ROW][C]70[/C][C]3540[/C][C]3994.97719001742[/C][C]-454.977190017419[/C][/ROW]
[ROW][C]71[/C][C]3435[/C][C]3540.03007715952[/C][C]-105.030077159517[/C][/ROW]
[ROW][C]72[/C][C]3345[/C][C]3435.00694321925[/C][C]-90.0069432192513[/C][/ROW]
[ROW][C]73[/C][C]3005[/C][C]3345.00595008552[/C][C]-340.005950085517[/C][/ROW]
[ROW][C]74[/C][C]2760[/C][C]3005.0224767602[/C][C]-245.022476760202[/C][/ROW]
[ROW][C]75[/C][C]2890[/C][C]2760.0161976914[/C][C]129.983802308599[/C][/ROW]
[ROW][C]76[/C][C]2745[/C][C]2889.9914071658[/C][C]-144.991407165805[/C][/ROW]
[ROW][C]77[/C][C]3180[/C][C]2745.00958494135[/C][C]434.99041505865[/C][/ROW]
[ROW][C]78[/C][C]3365[/C][C]3179.97124410544[/C][C]185.028755894557[/C][/ROW]
[ROW][C]79[/C][C]3660[/C][C]3364.98776831118[/C][C]295.012231688815[/C][/ROW]
[ROW][C]80[/C][C]3890[/C][C]3659.9804976378[/C][C]230.019502362199[/C][/ROW]
[ROW][C]81[/C][C]3685[/C][C]3889.98479410965[/C][C]-204.984794109647[/C][/ROW]
[ROW][C]82[/C][C]4150[/C][C]3685.01355092186[/C][C]464.986449078138[/C][/ROW]
[ROW][C]83[/C][C]3930[/C][C]4149.96926115878[/C][C]-219.969261158782[/C][/ROW]
[ROW][C]84[/C][C]3675[/C][C]3930.01454149945[/C][C]-255.014541499446[/C][/ROW]
[ROW][C]85[/C][C]3380[/C][C]3675.01685823644[/C][C]-295.016858236439[/C][/ROW]
[ROW][C]86[/C][C]3195[/C][C]3380.01950266805[/C][C]-185.019502668046[/C][/ROW]
[ROW][C]87[/C][C]2985[/C][C]3195.01223107711[/C][C]-210.012231077112[/C][/ROW]
[ROW][C]88[/C][C]2555[/C][C]2985.01388327044[/C][C]-430.013883270443[/C][/ROW]
[ROW][C]89[/C][C]2830[/C][C]2555.02842691116[/C][C]274.971573088838[/C][/ROW]
[ROW][C]90[/C][C]2595[/C][C]2829.98182246484[/C][C]-234.981822464845[/C][/ROW]
[ROW][C]91[/C][C]2940[/C][C]2595.01553393426[/C][C]344.984466065744[/C][/ROW]
[ROW][C]92[/C][C]3185[/C][C]2939.97719412523[/C][C]245.022805874765[/C][/ROW]
[ROW][C]93[/C][C]3090[/C][C]3184.98380228684[/C][C]-94.9838022868416[/C][/ROW]
[ROW][C]94[/C][C]2615[/C][C]3090.00627909055[/C][C]-475.006279090547[/C][/ROW]
[ROW][C]95[/C][C]2785[/C][C]2615.03140122173[/C][C]169.968598778266[/C][/ROW]
[ROW][C]96[/C][C]2695[/C][C]2784.98876389241[/C][C]-89.9887638924097[/C][/ROW]
[ROW][C]97[/C][C]3015[/C][C]2695.00594888374[/C][C]319.994051116263[/C][/ROW]
[ROW][C]98[/C][C]3185[/C][C]3014.97884616563[/C][C]170.02115383437[/C][/ROW]
[ROW][C]99[/C][C]3050[/C][C]3184.98876041815[/C][C]-134.988760418154[/C][/ROW]
[ROW][C]100[/C][C]2970[/C][C]3050.00892369677[/C][C]-80.0089236967683[/C][/ROW]
[ROW][C]101[/C][C]3295[/C][C]2970.00528914683[/C][C]324.994710853173[/C][/ROW]
[ROW][C]102[/C][C]3680[/C][C]3294.97851558721[/C][C]385.02148441279[/C][/ROW]
[ROW][C]103[/C][C]3715[/C][C]3679.97454739961[/C][C]35.0254526003896[/C][/ROW]
[ROW][C]104[/C][C]3785[/C][C]3714.99768457376[/C][C]70.0023154262412[/C][/ROW]
[ROW][C]105[/C][C]3655[/C][C]3784.99537235964[/C][C]-129.99537235964[/C][/ROW]
[ROW][C]106[/C][C]3725[/C][C]3655.00859359906[/C][C]69.9914064009436[/C][/ROW]
[ROW][C]107[/C][C]3545[/C][C]3724.9953730808[/C][C]-179.995373080802[/C][/ROW]
[ROW][C]108[/C][C]3440[/C][C]3545.01189894717[/C][C]-105.011898947172[/C][/ROW]
[ROW][C]109[/C][C]3575[/C][C]3440.00694201755[/C][C]134.993057982455[/C][/ROW]
[ROW][C]110[/C][C]3570[/C][C]3574.99107601913[/C][C]-4.99107601913329[/C][/ROW]
[ROW][C]111[/C][C]3355[/C][C]3570.00032994487[/C][C]-215.000329944869[/C][/ROW]
[ROW][C]112[/C][C]3500[/C][C]3355.0142130185[/C][C]144.985786981498[/C][/ROW]
[ROW][C]113[/C][C]3275[/C][C]3499.99041543018[/C][C]-224.990415430183[/C][/ROW]
[ROW][C]114[/C][C]3395[/C][C]3275.0148734327[/C][C]119.985126567303[/C][/ROW]
[ROW][C]115[/C][C]3485[/C][C]3394.99206814788[/C][C]90.0079318521248[/C][/ROW]
[ROW][C]116[/C][C]3390[/C][C]3484.99404984913[/C][C]-94.9940498491278[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299238&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299238&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
236803765-85
332653680.00561909172-415.005619091715
429503265.02743476042-315.027434760422
529752950.0208255064524.9791744935455
632252974.99834870268250.001651297323
732703224.983473150545.0165268495002
834253269.9970240942155.002975905801
935753424.98975322426150.010246775738
1034553574.99008327841-119.990083278414
1133353455.0079321798-120.007932179798
1237253335.00793335973389.992066640265
1338953724.97421880952170.025781190477
1441453894.98876011225250.011239887746
1544904144.98347251663345.016527483373
1642804489.97719200575-209.977192005752
1737854280.01388095412-495.013880954117
1832953785.0327238635-490.032723863497
1932903295.03239457434-5.03239457433756
2035303290.00033267631239.999667323686
2143453529.98413435127815.015865648732
2243404344.94612177767-4.94612177766885
2349504340.00032697308609.999673026919
2453954949.95967477519445.04032522481
2548955394.97057973642-499.97057973642
2642554895.03305153579-640.033051535792
2739104255.0423106402-345.042310640201
2838953910.02280969869-15.0228096986943
2939103895.000993112314.9990068876996
3033003909.99900846123-609.999008461231
3137803300.04032518088479.959674819123
3238303779.9682713243350.0317286756735
3335053829.99669255445-324.996692554446
3435053505.02148454379-0.0214845437944859
3534403505.00000142028-65.0000014202778
3630653440.00429695258-375.004296952582
3730853065.0247903945719.9752096054344
3832403084.99867949959155.001320500409
3929303239.9897533337-309.989753333696
4029002930.02049248064-30.0204924806435
4123752900.00198456354-525.001984563537
4228752375.0347062859499.965293714097
4335752874.96694881365700.033051186349
4437253574.95372294214150.04627705786
4536003724.99008089656-124.990080896562
4636953600.0082627144594.991737285553
4732453694.99372038489-449.993720384894
4837003245.02974771748454.970252282518
4933503699.96992329912-349.969923299116
5026703350.02313544819-680.023135448194
5129602670.04495426313289.955045736866
5228302959.980831953-129.980831952998
5328252830.00859263783-5.00859263783423
5429202825.0003311028494.9996688971601
5529302919.9937198605610.0062801394402
5633852929.99933851523455.000661484774
5733503384.96992128886-34.9699212888563
5834853350.00231175524134.997688244765
5931403484.99107571304-344.991075713041
6029603140.02280631171-180.022806311709
6128502960.0119007607-110.0119007607
6229952850.00727255247144.992727447528
6326952994.99041497137-299.99041497137
6429502695.01983145477254.980168545231
6528902949.98314403585-59.9831440358525
6630402890.00396530338149.996034696615
6729453039.99008421793-94.9900842179313
6836502945.00627950583704.993720494174
6939953649.95339500737345.046604992634
7035403994.97719001742-454.977190017419
7134353540.03007715952-105.030077159517
7233453435.00694321925-90.0069432192513
7330053345.00595008552-340.005950085517
7427603005.0224767602-245.022476760202
7528902760.0161976914129.983802308599
7627452889.9914071658-144.991407165805
7731802745.00958494135434.99041505865
7833653179.97124410544185.028755894557
7936603364.98776831118295.012231688815
8038903659.9804976378230.019502362199
8136853889.98479410965-204.984794109647
8241503685.01355092186464.986449078138
8339304149.96926115878-219.969261158782
8436753930.01454149945-255.014541499446
8533803675.01685823644-295.016858236439
8631953380.01950266805-185.019502668046
8729853195.01223107711-210.012231077112
8825552985.01388327044-430.013883270443
8928302555.02842691116274.971573088838
9025952829.98182246484-234.981822464845
9129402595.01553393426344.984466065744
9231852939.97719412523245.022805874765
9330903184.98380228684-94.9838022868416
9426153090.00627909055-475.006279090547
9527852615.03140122173169.968598778266
9626952784.98876389241-89.9887638924097
9730152695.00594888374319.994051116263
9831853014.97884616563170.02115383437
9930503184.98876041815-134.988760418154
10029703050.00892369677-80.0089236967683
10132952970.00528914683324.994710853173
10236803294.97851558721385.02148441279
10337153679.9745473996135.0254526003896
10437853714.9976845737670.0023154262412
10536553784.99537235964-129.99537235964
10637253655.0085935990669.9914064009436
10735453724.9953730808-179.995373080802
10834403545.01189894717-105.011898947172
10935753440.00694201755134.993057982455
11035703574.99107601913-4.99107601913329
11133553570.00032994487-215.000329944869
11235003355.0142130185144.985786981498
11332753499.99041543018-224.990415430183
11433953275.0148734327119.985126567303
11534853394.9920681478890.0079318521248
11633903484.99404984913-94.9940498491278







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1173390.006279767982795.246017304333984.76654223163
1183390.006279767982548.916051650354231.09650788562
1193390.006279767982359.896686635244420.11587290073
1203390.006279767982200.544731043834579.46782849213
1213390.006279767982060.152235926184719.86032360978
1223390.006279767981933.227374116364846.7851854196
1233390.006279767981816.507699539624963.50485999634
1243390.006279767981707.867526867435072.14503266853
1253390.006279767981605.830339441765174.1822200942
1263390.006279767981509.321088655955270.69147088001
1273390.006279767981417.52819621495362.48436332106
1283390.006279767981329.821144367195450.19141516877

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 3390.00627976798 & 2795.24601730433 & 3984.76654223163 \tabularnewline
118 & 3390.00627976798 & 2548.91605165035 & 4231.09650788562 \tabularnewline
119 & 3390.00627976798 & 2359.89668663524 & 4420.11587290073 \tabularnewline
120 & 3390.00627976798 & 2200.54473104383 & 4579.46782849213 \tabularnewline
121 & 3390.00627976798 & 2060.15223592618 & 4719.86032360978 \tabularnewline
122 & 3390.00627976798 & 1933.22737411636 & 4846.7851854196 \tabularnewline
123 & 3390.00627976798 & 1816.50769953962 & 4963.50485999634 \tabularnewline
124 & 3390.00627976798 & 1707.86752686743 & 5072.14503266853 \tabularnewline
125 & 3390.00627976798 & 1605.83033944176 & 5174.1822200942 \tabularnewline
126 & 3390.00627976798 & 1509.32108865595 & 5270.69147088001 \tabularnewline
127 & 3390.00627976798 & 1417.5281962149 & 5362.48436332106 \tabularnewline
128 & 3390.00627976798 & 1329.82114436719 & 5450.19141516877 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299238&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]117[/C][C]3390.00627976798[/C][C]2795.24601730433[/C][C]3984.76654223163[/C][/ROW]
[ROW][C]118[/C][C]3390.00627976798[/C][C]2548.91605165035[/C][C]4231.09650788562[/C][/ROW]
[ROW][C]119[/C][C]3390.00627976798[/C][C]2359.89668663524[/C][C]4420.11587290073[/C][/ROW]
[ROW][C]120[/C][C]3390.00627976798[/C][C]2200.54473104383[/C][C]4579.46782849213[/C][/ROW]
[ROW][C]121[/C][C]3390.00627976798[/C][C]2060.15223592618[/C][C]4719.86032360978[/C][/ROW]
[ROW][C]122[/C][C]3390.00627976798[/C][C]1933.22737411636[/C][C]4846.7851854196[/C][/ROW]
[ROW][C]123[/C][C]3390.00627976798[/C][C]1816.50769953962[/C][C]4963.50485999634[/C][/ROW]
[ROW][C]124[/C][C]3390.00627976798[/C][C]1707.86752686743[/C][C]5072.14503266853[/C][/ROW]
[ROW][C]125[/C][C]3390.00627976798[/C][C]1605.83033944176[/C][C]5174.1822200942[/C][/ROW]
[ROW][C]126[/C][C]3390.00627976798[/C][C]1509.32108865595[/C][C]5270.69147088001[/C][/ROW]
[ROW][C]127[/C][C]3390.00627976798[/C][C]1417.5281962149[/C][C]5362.48436332106[/C][/ROW]
[ROW][C]128[/C][C]3390.00627976798[/C][C]1329.82114436719[/C][C]5450.19141516877[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299238&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299238&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1173390.006279767982795.246017304333984.76654223163
1183390.006279767982548.916051650354231.09650788562
1193390.006279767982359.896686635244420.11587290073
1203390.006279767982200.544731043834579.46782849213
1213390.006279767982060.152235926184719.86032360978
1223390.006279767981933.227374116364846.7851854196
1233390.006279767981816.507699539624963.50485999634
1243390.006279767981707.867526867435072.14503266853
1253390.006279767981605.830339441765174.1822200942
1263390.006279767981509.321088655955270.69147088001
1273390.006279767981417.52819621495362.48436332106
1283390.006279767981329.821144367195450.19141516877



Parameters (Session):
par1 = 12 ; par2 = 12 ; par3 = BFGS ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')