Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 15 Dec 2016 12:40:07 +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/15/t1481802067azn5rrunxsr2no3.htm/, Retrieved Fri, 03 May 2024 10:20:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299891, Retrieved Fri, 03 May 2024 10:20:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [ES fi comp] [2016-12-15 11:40:07] [ada7696de20b35d9f514c719a1db97fd] [Current]
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Dataseries X:
1550
1564
1812
1686
1928
1950
1876
1986
1680
1852
1604
1338
1622
1608
1816
1992
2174
2316
2320
2372
2354
2530
1938
1750
1766
1904
2198
2390
2280
2582
2392
2528
2620
2392
1886
1586
1980
1934
2362
2676
2514
2850
2556
2736
2516
2268
1974
1672
2010
2010
2406
2624
2772
2880
2766
3026
2990
2720
2572
2212
2392
2684
2766
2934
3344
3364
3198
3486
3134
3196
2722
2382
2476
2574
3126
3506
3704
3562
3752
3536
3764
3700
3040
2502
2788
2708
3036
3472
3648
3614
3612
3452
3386
3286
2602
2432
2848
3074
3460
3790
3892
3834
4102
3908
3810
3930
3178
2964
2926
3258
3786
4038
4436
4440
4128
4190
4020
3802
3488
3110
3346
3300
3936
4296
4542
4688




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=299891&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=299891&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299891&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
alpha0.374663351379588
beta0.011001404889192
gamma0.413000151576025

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.374663351379588 \tabularnewline
beta & 0.011001404889192 \tabularnewline
gamma & 0.413000151576025 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299891&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]0.374663351379588[/C][/ROW]
[ROW][C]beta[/C][C]0.011001404889192[/C][/ROW]
[ROW][C]gamma[/C][C]0.413000151576025[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299891&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299891&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
alpha0.374663351379588
beta0.011001404889192
gamma0.413000151576025







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1316221516.31489911456105.685100885436
1416081540.7801146823267.2198853176849
1518161757.64722692358.3527730770036
1619921928.3446002420163.6553997579904
1721742120.5406461838953.4593538161071
1823162282.2251681692233.774831830779
1923202225.6302053785994.3697946214061
2023722424.19451987354-52.1945198735384
2123542063.11414418476290.885855815243
2225302412.46249398523117.537506014771
2319382130.90581728838-192.905817288384
2417501717.6976117139232.3023882860789
2517662124.68820842327-358.688208423273
2619041952.0842283221-48.0842283221002
2721982158.6608140908139.3391859091935
2823902348.3044352880241.6955647119808
2922802555.7455580188-275.745558018804
3025822601.32218892696-19.3221889269553
3123922527.22793643832-135.227936438323
3225282606.51959692507-78.5195969250672
3326202295.49167876312324.508321236882
3423922621.63403101282-229.634031012822
3518862116.25018519752-230.250185197523
3615861741.0118711777-155.0118711777
3719801958.1420399345821.8579600654155
3819342005.99703710004-71.9970371000366
3923622229.43314417814132.566855821863
4026762457.83695198514218.163048014861
4125142649.18673598699-135.186735986991
4228502828.1800942925421.819905707463
4325562724.73632762024-168.736327620242
4427362813.95687562986-77.9568756298636
4525162582.34355931913-66.3435593191257
4622682614.12723812714-346.127238127141
4719742057.74151670279-83.7415167027939
4816721744.92959142604-72.9295914260415
4920102049.6929660622-39.6929660622031
5020102047.20427311786-37.204273117864
5124062343.2928283860662.7071716139376
5226242566.5206760057857.4793239942246
5327722601.91207648089170.087923519113
5428802942.39439282129-62.3943928212852
5527662748.9422072049817.0577927950203
5630262936.1991731794289.8008268205767
5729902751.77662224872238.223377751277
5827202814.73824266726-94.738242667263
5925722359.31979229152212.68020770848
6022122097.08329758483114.91670241517
6123922566.23282841577-174.232828415765
6226842514.00812045243169.991879547567
6327663001.92078460231-235.920784602312
6429343152.33360634768-218.333606347684
6533443116.315559575227.684440425
6633643453.7035886148-89.7035886148019
6731983240.31527065375-42.3152706537489
6834863453.661008748432.3389912516041
6931343251.92546735799-117.925467357987
7031963079.88454433984116.115455660165
7127222732.39742993524-10.3974299352421
7223822323.6609292964358.3390707035719
7324762721.25749642097-245.257496420968
7425742734.40462798629-160.404627986295
7531262994.78256645366131.217433546339
7635063298.56296020148207.437039798524
7737043551.56013292253152.439867077469
7835623793.24537087057-231.245370870571
7937523520.4199720748231.580027925202
8035363882.77552520586-346.775525205863
8137643476.20904845318287.790951546818
8237003504.69701818026195.302981819737
8330403094.81252623764-54.8125262376361
8425022635.52853432715-133.528534327154
8527882906.31848209757-118.318482097573
8627083000.18558088545-292.185580885447
8730363321.87133801864-285.871338018643
8834723496.54540019483-24.5454001948297
8936483646.704504545791.29549545420923
9036143727.29116732841-113.291167328408
9136123612.33208567351-0.33208567351312
9234523729.46668805806-277.466688058062
9333863507.92739582364-121.927395823639
9432863359.54069590174-73.5406959017355
9526022825.36199533687-223.361995336875
9624322326.59067077978105.409329220224
9728482663.60745097904184.392549020958
9830742817.04128012311256.958719876893
9934603356.07433201154103.925667988463
10037903770.2966691711819.7033308288223
10138923955.63059681202-63.6305968120246
10238343983.55591965624-149.555919656241
10341023878.66457797486223.335422025144
10439084008.23431367122-100.234313671225
10538103882.11511894952-72.1151189495235
10639303752.10215102013177.897848979871
10731783187.29926334696-9.29926334695892
10829642791.21578750281172.78421249719
10929263233.53433720456-307.534337204556
11032583230.2349994192827.765000580725
11137863676.99729644943109.002703550565
11240384099.9090042913-61.9090042912994
11344364242.97050478195193.029495218051
11444404345.4892758779394.5107241220721
11541284431.6131212729-303.613121272904
11641904274.91110340418-84.9111034041816
11740204153.39356116728-133.393561167284
11838024059.3026348785-257.302634878501
11934883263.45486302739224.545136972606
12031102981.1616650142128.838334985796
12133463289.2048226385556.7951773614486
12233003525.33940592746-225.339405927462
12339363923.0567345114412.9432654885618
12442964279.7396053433116.2603946566869
12545424527.5448375030714.4551624969299
12646884535.01574842208152.984251577916

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1622 & 1516.31489911456 & 105.685100885436 \tabularnewline
14 & 1608 & 1540.78011468232 & 67.2198853176849 \tabularnewline
15 & 1816 & 1757.647226923 & 58.3527730770036 \tabularnewline
16 & 1992 & 1928.34460024201 & 63.6553997579904 \tabularnewline
17 & 2174 & 2120.54064618389 & 53.4593538161071 \tabularnewline
18 & 2316 & 2282.22516816922 & 33.774831830779 \tabularnewline
19 & 2320 & 2225.63020537859 & 94.3697946214061 \tabularnewline
20 & 2372 & 2424.19451987354 & -52.1945198735384 \tabularnewline
21 & 2354 & 2063.11414418476 & 290.885855815243 \tabularnewline
22 & 2530 & 2412.46249398523 & 117.537506014771 \tabularnewline
23 & 1938 & 2130.90581728838 & -192.905817288384 \tabularnewline
24 & 1750 & 1717.69761171392 & 32.3023882860789 \tabularnewline
25 & 1766 & 2124.68820842327 & -358.688208423273 \tabularnewline
26 & 1904 & 1952.0842283221 & -48.0842283221002 \tabularnewline
27 & 2198 & 2158.66081409081 & 39.3391859091935 \tabularnewline
28 & 2390 & 2348.30443528802 & 41.6955647119808 \tabularnewline
29 & 2280 & 2555.7455580188 & -275.745558018804 \tabularnewline
30 & 2582 & 2601.32218892696 & -19.3221889269553 \tabularnewline
31 & 2392 & 2527.22793643832 & -135.227936438323 \tabularnewline
32 & 2528 & 2606.51959692507 & -78.5195969250672 \tabularnewline
33 & 2620 & 2295.49167876312 & 324.508321236882 \tabularnewline
34 & 2392 & 2621.63403101282 & -229.634031012822 \tabularnewline
35 & 1886 & 2116.25018519752 & -230.250185197523 \tabularnewline
36 & 1586 & 1741.0118711777 & -155.0118711777 \tabularnewline
37 & 1980 & 1958.14203993458 & 21.8579600654155 \tabularnewline
38 & 1934 & 2005.99703710004 & -71.9970371000366 \tabularnewline
39 & 2362 & 2229.43314417814 & 132.566855821863 \tabularnewline
40 & 2676 & 2457.83695198514 & 218.163048014861 \tabularnewline
41 & 2514 & 2649.18673598699 & -135.186735986991 \tabularnewline
42 & 2850 & 2828.18009429254 & 21.819905707463 \tabularnewline
43 & 2556 & 2724.73632762024 & -168.736327620242 \tabularnewline
44 & 2736 & 2813.95687562986 & -77.9568756298636 \tabularnewline
45 & 2516 & 2582.34355931913 & -66.3435593191257 \tabularnewline
46 & 2268 & 2614.12723812714 & -346.127238127141 \tabularnewline
47 & 1974 & 2057.74151670279 & -83.7415167027939 \tabularnewline
48 & 1672 & 1744.92959142604 & -72.9295914260415 \tabularnewline
49 & 2010 & 2049.6929660622 & -39.6929660622031 \tabularnewline
50 & 2010 & 2047.20427311786 & -37.204273117864 \tabularnewline
51 & 2406 & 2343.29282838606 & 62.7071716139376 \tabularnewline
52 & 2624 & 2566.52067600578 & 57.4793239942246 \tabularnewline
53 & 2772 & 2601.91207648089 & 170.087923519113 \tabularnewline
54 & 2880 & 2942.39439282129 & -62.3943928212852 \tabularnewline
55 & 2766 & 2748.94220720498 & 17.0577927950203 \tabularnewline
56 & 3026 & 2936.19917317942 & 89.8008268205767 \tabularnewline
57 & 2990 & 2751.77662224872 & 238.223377751277 \tabularnewline
58 & 2720 & 2814.73824266726 & -94.738242667263 \tabularnewline
59 & 2572 & 2359.31979229152 & 212.68020770848 \tabularnewline
60 & 2212 & 2097.08329758483 & 114.91670241517 \tabularnewline
61 & 2392 & 2566.23282841577 & -174.232828415765 \tabularnewline
62 & 2684 & 2514.00812045243 & 169.991879547567 \tabularnewline
63 & 2766 & 3001.92078460231 & -235.920784602312 \tabularnewline
64 & 2934 & 3152.33360634768 & -218.333606347684 \tabularnewline
65 & 3344 & 3116.315559575 & 227.684440425 \tabularnewline
66 & 3364 & 3453.7035886148 & -89.7035886148019 \tabularnewline
67 & 3198 & 3240.31527065375 & -42.3152706537489 \tabularnewline
68 & 3486 & 3453.6610087484 & 32.3389912516041 \tabularnewline
69 & 3134 & 3251.92546735799 & -117.925467357987 \tabularnewline
70 & 3196 & 3079.88454433984 & 116.115455660165 \tabularnewline
71 & 2722 & 2732.39742993524 & -10.3974299352421 \tabularnewline
72 & 2382 & 2323.66092929643 & 58.3390707035719 \tabularnewline
73 & 2476 & 2721.25749642097 & -245.257496420968 \tabularnewline
74 & 2574 & 2734.40462798629 & -160.404627986295 \tabularnewline
75 & 3126 & 2994.78256645366 & 131.217433546339 \tabularnewline
76 & 3506 & 3298.56296020148 & 207.437039798524 \tabularnewline
77 & 3704 & 3551.56013292253 & 152.439867077469 \tabularnewline
78 & 3562 & 3793.24537087057 & -231.245370870571 \tabularnewline
79 & 3752 & 3520.4199720748 & 231.580027925202 \tabularnewline
80 & 3536 & 3882.77552520586 & -346.775525205863 \tabularnewline
81 & 3764 & 3476.20904845318 & 287.790951546818 \tabularnewline
82 & 3700 & 3504.69701818026 & 195.302981819737 \tabularnewline
83 & 3040 & 3094.81252623764 & -54.8125262376361 \tabularnewline
84 & 2502 & 2635.52853432715 & -133.528534327154 \tabularnewline
85 & 2788 & 2906.31848209757 & -118.318482097573 \tabularnewline
86 & 2708 & 3000.18558088545 & -292.185580885447 \tabularnewline
87 & 3036 & 3321.87133801864 & -285.871338018643 \tabularnewline
88 & 3472 & 3496.54540019483 & -24.5454001948297 \tabularnewline
89 & 3648 & 3646.70450454579 & 1.29549545420923 \tabularnewline
90 & 3614 & 3727.29116732841 & -113.291167328408 \tabularnewline
91 & 3612 & 3612.33208567351 & -0.33208567351312 \tabularnewline
92 & 3452 & 3729.46668805806 & -277.466688058062 \tabularnewline
93 & 3386 & 3507.92739582364 & -121.927395823639 \tabularnewline
94 & 3286 & 3359.54069590174 & -73.5406959017355 \tabularnewline
95 & 2602 & 2825.36199533687 & -223.361995336875 \tabularnewline
96 & 2432 & 2326.59067077978 & 105.409329220224 \tabularnewline
97 & 2848 & 2663.60745097904 & 184.392549020958 \tabularnewline
98 & 3074 & 2817.04128012311 & 256.958719876893 \tabularnewline
99 & 3460 & 3356.07433201154 & 103.925667988463 \tabularnewline
100 & 3790 & 3770.29666917118 & 19.7033308288223 \tabularnewline
101 & 3892 & 3955.63059681202 & -63.6305968120246 \tabularnewline
102 & 3834 & 3983.55591965624 & -149.555919656241 \tabularnewline
103 & 4102 & 3878.66457797486 & 223.335422025144 \tabularnewline
104 & 3908 & 4008.23431367122 & -100.234313671225 \tabularnewline
105 & 3810 & 3882.11511894952 & -72.1151189495235 \tabularnewline
106 & 3930 & 3752.10215102013 & 177.897848979871 \tabularnewline
107 & 3178 & 3187.29926334696 & -9.29926334695892 \tabularnewline
108 & 2964 & 2791.21578750281 & 172.78421249719 \tabularnewline
109 & 2926 & 3233.53433720456 & -307.534337204556 \tabularnewline
110 & 3258 & 3230.23499941928 & 27.765000580725 \tabularnewline
111 & 3786 & 3676.99729644943 & 109.002703550565 \tabularnewline
112 & 4038 & 4099.9090042913 & -61.9090042912994 \tabularnewline
113 & 4436 & 4242.97050478195 & 193.029495218051 \tabularnewline
114 & 4440 & 4345.48927587793 & 94.5107241220721 \tabularnewline
115 & 4128 & 4431.6131212729 & -303.613121272904 \tabularnewline
116 & 4190 & 4274.91110340418 & -84.9111034041816 \tabularnewline
117 & 4020 & 4153.39356116728 & -133.393561167284 \tabularnewline
118 & 3802 & 4059.3026348785 & -257.302634878501 \tabularnewline
119 & 3488 & 3263.45486302739 & 224.545136972606 \tabularnewline
120 & 3110 & 2981.1616650142 & 128.838334985796 \tabularnewline
121 & 3346 & 3289.20482263855 & 56.7951773614486 \tabularnewline
122 & 3300 & 3525.33940592746 & -225.339405927462 \tabularnewline
123 & 3936 & 3923.05673451144 & 12.9432654885618 \tabularnewline
124 & 4296 & 4279.73960534331 & 16.2603946566869 \tabularnewline
125 & 4542 & 4527.54483750307 & 14.4551624969299 \tabularnewline
126 & 4688 & 4535.01574842208 & 152.984251577916 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299891&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]13[/C][C]1622[/C][C]1516.31489911456[/C][C]105.685100885436[/C][/ROW]
[ROW][C]14[/C][C]1608[/C][C]1540.78011468232[/C][C]67.2198853176849[/C][/ROW]
[ROW][C]15[/C][C]1816[/C][C]1757.647226923[/C][C]58.3527730770036[/C][/ROW]
[ROW][C]16[/C][C]1992[/C][C]1928.34460024201[/C][C]63.6553997579904[/C][/ROW]
[ROW][C]17[/C][C]2174[/C][C]2120.54064618389[/C][C]53.4593538161071[/C][/ROW]
[ROW][C]18[/C][C]2316[/C][C]2282.22516816922[/C][C]33.774831830779[/C][/ROW]
[ROW][C]19[/C][C]2320[/C][C]2225.63020537859[/C][C]94.3697946214061[/C][/ROW]
[ROW][C]20[/C][C]2372[/C][C]2424.19451987354[/C][C]-52.1945198735384[/C][/ROW]
[ROW][C]21[/C][C]2354[/C][C]2063.11414418476[/C][C]290.885855815243[/C][/ROW]
[ROW][C]22[/C][C]2530[/C][C]2412.46249398523[/C][C]117.537506014771[/C][/ROW]
[ROW][C]23[/C][C]1938[/C][C]2130.90581728838[/C][C]-192.905817288384[/C][/ROW]
[ROW][C]24[/C][C]1750[/C][C]1717.69761171392[/C][C]32.3023882860789[/C][/ROW]
[ROW][C]25[/C][C]1766[/C][C]2124.68820842327[/C][C]-358.688208423273[/C][/ROW]
[ROW][C]26[/C][C]1904[/C][C]1952.0842283221[/C][C]-48.0842283221002[/C][/ROW]
[ROW][C]27[/C][C]2198[/C][C]2158.66081409081[/C][C]39.3391859091935[/C][/ROW]
[ROW][C]28[/C][C]2390[/C][C]2348.30443528802[/C][C]41.6955647119808[/C][/ROW]
[ROW][C]29[/C][C]2280[/C][C]2555.7455580188[/C][C]-275.745558018804[/C][/ROW]
[ROW][C]30[/C][C]2582[/C][C]2601.32218892696[/C][C]-19.3221889269553[/C][/ROW]
[ROW][C]31[/C][C]2392[/C][C]2527.22793643832[/C][C]-135.227936438323[/C][/ROW]
[ROW][C]32[/C][C]2528[/C][C]2606.51959692507[/C][C]-78.5195969250672[/C][/ROW]
[ROW][C]33[/C][C]2620[/C][C]2295.49167876312[/C][C]324.508321236882[/C][/ROW]
[ROW][C]34[/C][C]2392[/C][C]2621.63403101282[/C][C]-229.634031012822[/C][/ROW]
[ROW][C]35[/C][C]1886[/C][C]2116.25018519752[/C][C]-230.250185197523[/C][/ROW]
[ROW][C]36[/C][C]1586[/C][C]1741.0118711777[/C][C]-155.0118711777[/C][/ROW]
[ROW][C]37[/C][C]1980[/C][C]1958.14203993458[/C][C]21.8579600654155[/C][/ROW]
[ROW][C]38[/C][C]1934[/C][C]2005.99703710004[/C][C]-71.9970371000366[/C][/ROW]
[ROW][C]39[/C][C]2362[/C][C]2229.43314417814[/C][C]132.566855821863[/C][/ROW]
[ROW][C]40[/C][C]2676[/C][C]2457.83695198514[/C][C]218.163048014861[/C][/ROW]
[ROW][C]41[/C][C]2514[/C][C]2649.18673598699[/C][C]-135.186735986991[/C][/ROW]
[ROW][C]42[/C][C]2850[/C][C]2828.18009429254[/C][C]21.819905707463[/C][/ROW]
[ROW][C]43[/C][C]2556[/C][C]2724.73632762024[/C][C]-168.736327620242[/C][/ROW]
[ROW][C]44[/C][C]2736[/C][C]2813.95687562986[/C][C]-77.9568756298636[/C][/ROW]
[ROW][C]45[/C][C]2516[/C][C]2582.34355931913[/C][C]-66.3435593191257[/C][/ROW]
[ROW][C]46[/C][C]2268[/C][C]2614.12723812714[/C][C]-346.127238127141[/C][/ROW]
[ROW][C]47[/C][C]1974[/C][C]2057.74151670279[/C][C]-83.7415167027939[/C][/ROW]
[ROW][C]48[/C][C]1672[/C][C]1744.92959142604[/C][C]-72.9295914260415[/C][/ROW]
[ROW][C]49[/C][C]2010[/C][C]2049.6929660622[/C][C]-39.6929660622031[/C][/ROW]
[ROW][C]50[/C][C]2010[/C][C]2047.20427311786[/C][C]-37.204273117864[/C][/ROW]
[ROW][C]51[/C][C]2406[/C][C]2343.29282838606[/C][C]62.7071716139376[/C][/ROW]
[ROW][C]52[/C][C]2624[/C][C]2566.52067600578[/C][C]57.4793239942246[/C][/ROW]
[ROW][C]53[/C][C]2772[/C][C]2601.91207648089[/C][C]170.087923519113[/C][/ROW]
[ROW][C]54[/C][C]2880[/C][C]2942.39439282129[/C][C]-62.3943928212852[/C][/ROW]
[ROW][C]55[/C][C]2766[/C][C]2748.94220720498[/C][C]17.0577927950203[/C][/ROW]
[ROW][C]56[/C][C]3026[/C][C]2936.19917317942[/C][C]89.8008268205767[/C][/ROW]
[ROW][C]57[/C][C]2990[/C][C]2751.77662224872[/C][C]238.223377751277[/C][/ROW]
[ROW][C]58[/C][C]2720[/C][C]2814.73824266726[/C][C]-94.738242667263[/C][/ROW]
[ROW][C]59[/C][C]2572[/C][C]2359.31979229152[/C][C]212.68020770848[/C][/ROW]
[ROW][C]60[/C][C]2212[/C][C]2097.08329758483[/C][C]114.91670241517[/C][/ROW]
[ROW][C]61[/C][C]2392[/C][C]2566.23282841577[/C][C]-174.232828415765[/C][/ROW]
[ROW][C]62[/C][C]2684[/C][C]2514.00812045243[/C][C]169.991879547567[/C][/ROW]
[ROW][C]63[/C][C]2766[/C][C]3001.92078460231[/C][C]-235.920784602312[/C][/ROW]
[ROW][C]64[/C][C]2934[/C][C]3152.33360634768[/C][C]-218.333606347684[/C][/ROW]
[ROW][C]65[/C][C]3344[/C][C]3116.315559575[/C][C]227.684440425[/C][/ROW]
[ROW][C]66[/C][C]3364[/C][C]3453.7035886148[/C][C]-89.7035886148019[/C][/ROW]
[ROW][C]67[/C][C]3198[/C][C]3240.31527065375[/C][C]-42.3152706537489[/C][/ROW]
[ROW][C]68[/C][C]3486[/C][C]3453.6610087484[/C][C]32.3389912516041[/C][/ROW]
[ROW][C]69[/C][C]3134[/C][C]3251.92546735799[/C][C]-117.925467357987[/C][/ROW]
[ROW][C]70[/C][C]3196[/C][C]3079.88454433984[/C][C]116.115455660165[/C][/ROW]
[ROW][C]71[/C][C]2722[/C][C]2732.39742993524[/C][C]-10.3974299352421[/C][/ROW]
[ROW][C]72[/C][C]2382[/C][C]2323.66092929643[/C][C]58.3390707035719[/C][/ROW]
[ROW][C]73[/C][C]2476[/C][C]2721.25749642097[/C][C]-245.257496420968[/C][/ROW]
[ROW][C]74[/C][C]2574[/C][C]2734.40462798629[/C][C]-160.404627986295[/C][/ROW]
[ROW][C]75[/C][C]3126[/C][C]2994.78256645366[/C][C]131.217433546339[/C][/ROW]
[ROW][C]76[/C][C]3506[/C][C]3298.56296020148[/C][C]207.437039798524[/C][/ROW]
[ROW][C]77[/C][C]3704[/C][C]3551.56013292253[/C][C]152.439867077469[/C][/ROW]
[ROW][C]78[/C][C]3562[/C][C]3793.24537087057[/C][C]-231.245370870571[/C][/ROW]
[ROW][C]79[/C][C]3752[/C][C]3520.4199720748[/C][C]231.580027925202[/C][/ROW]
[ROW][C]80[/C][C]3536[/C][C]3882.77552520586[/C][C]-346.775525205863[/C][/ROW]
[ROW][C]81[/C][C]3764[/C][C]3476.20904845318[/C][C]287.790951546818[/C][/ROW]
[ROW][C]82[/C][C]3700[/C][C]3504.69701818026[/C][C]195.302981819737[/C][/ROW]
[ROW][C]83[/C][C]3040[/C][C]3094.81252623764[/C][C]-54.8125262376361[/C][/ROW]
[ROW][C]84[/C][C]2502[/C][C]2635.52853432715[/C][C]-133.528534327154[/C][/ROW]
[ROW][C]85[/C][C]2788[/C][C]2906.31848209757[/C][C]-118.318482097573[/C][/ROW]
[ROW][C]86[/C][C]2708[/C][C]3000.18558088545[/C][C]-292.185580885447[/C][/ROW]
[ROW][C]87[/C][C]3036[/C][C]3321.87133801864[/C][C]-285.871338018643[/C][/ROW]
[ROW][C]88[/C][C]3472[/C][C]3496.54540019483[/C][C]-24.5454001948297[/C][/ROW]
[ROW][C]89[/C][C]3648[/C][C]3646.70450454579[/C][C]1.29549545420923[/C][/ROW]
[ROW][C]90[/C][C]3614[/C][C]3727.29116732841[/C][C]-113.291167328408[/C][/ROW]
[ROW][C]91[/C][C]3612[/C][C]3612.33208567351[/C][C]-0.33208567351312[/C][/ROW]
[ROW][C]92[/C][C]3452[/C][C]3729.46668805806[/C][C]-277.466688058062[/C][/ROW]
[ROW][C]93[/C][C]3386[/C][C]3507.92739582364[/C][C]-121.927395823639[/C][/ROW]
[ROW][C]94[/C][C]3286[/C][C]3359.54069590174[/C][C]-73.5406959017355[/C][/ROW]
[ROW][C]95[/C][C]2602[/C][C]2825.36199533687[/C][C]-223.361995336875[/C][/ROW]
[ROW][C]96[/C][C]2432[/C][C]2326.59067077978[/C][C]105.409329220224[/C][/ROW]
[ROW][C]97[/C][C]2848[/C][C]2663.60745097904[/C][C]184.392549020958[/C][/ROW]
[ROW][C]98[/C][C]3074[/C][C]2817.04128012311[/C][C]256.958719876893[/C][/ROW]
[ROW][C]99[/C][C]3460[/C][C]3356.07433201154[/C][C]103.925667988463[/C][/ROW]
[ROW][C]100[/C][C]3790[/C][C]3770.29666917118[/C][C]19.7033308288223[/C][/ROW]
[ROW][C]101[/C][C]3892[/C][C]3955.63059681202[/C][C]-63.6305968120246[/C][/ROW]
[ROW][C]102[/C][C]3834[/C][C]3983.55591965624[/C][C]-149.555919656241[/C][/ROW]
[ROW][C]103[/C][C]4102[/C][C]3878.66457797486[/C][C]223.335422025144[/C][/ROW]
[ROW][C]104[/C][C]3908[/C][C]4008.23431367122[/C][C]-100.234313671225[/C][/ROW]
[ROW][C]105[/C][C]3810[/C][C]3882.11511894952[/C][C]-72.1151189495235[/C][/ROW]
[ROW][C]106[/C][C]3930[/C][C]3752.10215102013[/C][C]177.897848979871[/C][/ROW]
[ROW][C]107[/C][C]3178[/C][C]3187.29926334696[/C][C]-9.29926334695892[/C][/ROW]
[ROW][C]108[/C][C]2964[/C][C]2791.21578750281[/C][C]172.78421249719[/C][/ROW]
[ROW][C]109[/C][C]2926[/C][C]3233.53433720456[/C][C]-307.534337204556[/C][/ROW]
[ROW][C]110[/C][C]3258[/C][C]3230.23499941928[/C][C]27.765000580725[/C][/ROW]
[ROW][C]111[/C][C]3786[/C][C]3676.99729644943[/C][C]109.002703550565[/C][/ROW]
[ROW][C]112[/C][C]4038[/C][C]4099.9090042913[/C][C]-61.9090042912994[/C][/ROW]
[ROW][C]113[/C][C]4436[/C][C]4242.97050478195[/C][C]193.029495218051[/C][/ROW]
[ROW][C]114[/C][C]4440[/C][C]4345.48927587793[/C][C]94.5107241220721[/C][/ROW]
[ROW][C]115[/C][C]4128[/C][C]4431.6131212729[/C][C]-303.613121272904[/C][/ROW]
[ROW][C]116[/C][C]4190[/C][C]4274.91110340418[/C][C]-84.9111034041816[/C][/ROW]
[ROW][C]117[/C][C]4020[/C][C]4153.39356116728[/C][C]-133.393561167284[/C][/ROW]
[ROW][C]118[/C][C]3802[/C][C]4059.3026348785[/C][C]-257.302634878501[/C][/ROW]
[ROW][C]119[/C][C]3488[/C][C]3263.45486302739[/C][C]224.545136972606[/C][/ROW]
[ROW][C]120[/C][C]3110[/C][C]2981.1616650142[/C][C]128.838334985796[/C][/ROW]
[ROW][C]121[/C][C]3346[/C][C]3289.20482263855[/C][C]56.7951773614486[/C][/ROW]
[ROW][C]122[/C][C]3300[/C][C]3525.33940592746[/C][C]-225.339405927462[/C][/ROW]
[ROW][C]123[/C][C]3936[/C][C]3923.05673451144[/C][C]12.9432654885618[/C][/ROW]
[ROW][C]124[/C][C]4296[/C][C]4279.73960534331[/C][C]16.2603946566869[/C][/ROW]
[ROW][C]125[/C][C]4542[/C][C]4527.54483750307[/C][C]14.4551624969299[/C][/ROW]
[ROW][C]126[/C][C]4688[/C][C]4535.01574842208[/C][C]152.984251577916[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299891&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299891&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
1316221516.31489911456105.685100885436
1416081540.7801146823267.2198853176849
1518161757.64722692358.3527730770036
1619921928.3446002420163.6553997579904
1721742120.5406461838953.4593538161071
1823162282.2251681692233.774831830779
1923202225.6302053785994.3697946214061
2023722424.19451987354-52.1945198735384
2123542063.11414418476290.885855815243
2225302412.46249398523117.537506014771
2319382130.90581728838-192.905817288384
2417501717.6976117139232.3023882860789
2517662124.68820842327-358.688208423273
2619041952.0842283221-48.0842283221002
2721982158.6608140908139.3391859091935
2823902348.3044352880241.6955647119808
2922802555.7455580188-275.745558018804
3025822601.32218892696-19.3221889269553
3123922527.22793643832-135.227936438323
3225282606.51959692507-78.5195969250672
3326202295.49167876312324.508321236882
3423922621.63403101282-229.634031012822
3518862116.25018519752-230.250185197523
3615861741.0118711777-155.0118711777
3719801958.1420399345821.8579600654155
3819342005.99703710004-71.9970371000366
3923622229.43314417814132.566855821863
4026762457.83695198514218.163048014861
4125142649.18673598699-135.186735986991
4228502828.1800942925421.819905707463
4325562724.73632762024-168.736327620242
4427362813.95687562986-77.9568756298636
4525162582.34355931913-66.3435593191257
4622682614.12723812714-346.127238127141
4719742057.74151670279-83.7415167027939
4816721744.92959142604-72.9295914260415
4920102049.6929660622-39.6929660622031
5020102047.20427311786-37.204273117864
5124062343.2928283860662.7071716139376
5226242566.5206760057857.4793239942246
5327722601.91207648089170.087923519113
5428802942.39439282129-62.3943928212852
5527662748.9422072049817.0577927950203
5630262936.1991731794289.8008268205767
5729902751.77662224872238.223377751277
5827202814.73824266726-94.738242667263
5925722359.31979229152212.68020770848
6022122097.08329758483114.91670241517
6123922566.23282841577-174.232828415765
6226842514.00812045243169.991879547567
6327663001.92078460231-235.920784602312
6429343152.33360634768-218.333606347684
6533443116.315559575227.684440425
6633643453.7035886148-89.7035886148019
6731983240.31527065375-42.3152706537489
6834863453.661008748432.3389912516041
6931343251.92546735799-117.925467357987
7031963079.88454433984116.115455660165
7127222732.39742993524-10.3974299352421
7223822323.6609292964358.3390707035719
7324762721.25749642097-245.257496420968
7425742734.40462798629-160.404627986295
7531262994.78256645366131.217433546339
7635063298.56296020148207.437039798524
7737043551.56013292253152.439867077469
7835623793.24537087057-231.245370870571
7937523520.4199720748231.580027925202
8035363882.77552520586-346.775525205863
8137643476.20904845318287.790951546818
8237003504.69701818026195.302981819737
8330403094.81252623764-54.8125262376361
8425022635.52853432715-133.528534327154
8527882906.31848209757-118.318482097573
8627083000.18558088545-292.185580885447
8730363321.87133801864-285.871338018643
8834723496.54540019483-24.5454001948297
8936483646.704504545791.29549545420923
9036143727.29116732841-113.291167328408
9136123612.33208567351-0.33208567351312
9234523729.46668805806-277.466688058062
9333863507.92739582364-121.927395823639
9432863359.54069590174-73.5406959017355
9526022825.36199533687-223.361995336875
9624322326.59067077978105.409329220224
9728482663.60745097904184.392549020958
9830742817.04128012311256.958719876893
9934603356.07433201154103.925667988463
10037903770.2966691711819.7033308288223
10138923955.63059681202-63.6305968120246
10238343983.55591965624-149.555919656241
10341023878.66457797486223.335422025144
10439084008.23431367122-100.234313671225
10538103882.11511894952-72.1151189495235
10639303752.10215102013177.897848979871
10731783187.29926334696-9.29926334695892
10829642791.21578750281172.78421249719
10929263233.53433720456-307.534337204556
11032583230.2349994192827.765000580725
11137863676.99729644943109.002703550565
11240384099.9090042913-61.9090042912994
11344364242.97050478195193.029495218051
11444404345.4892758779394.5107241220721
11541284431.6131212729-303.613121272904
11641904274.91110340418-84.9111034041816
11740204153.39356116728-133.393561167284
11838024059.3026348785-257.302634878501
11934883263.45486302739224.545136972606
12031102981.1616650142128.838334985796
12133463289.2048226385556.7951773614486
12233003525.33940592746-225.339405927462
12339363923.0567345114412.9432654885618
12442964279.7396053433116.2603946566869
12545424527.5448375030714.4551624969299
12646884535.01574842208152.984251577916







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1274533.343744506734332.695984424264733.9915045892
1284545.708433204014312.056868721664779.35999768636
1294433.471333363894173.478481748894693.46418497889
1304347.390514030474063.621642913214631.15938514773
1313703.502043769483420.433821924243986.57026561472
1323276.516273375592988.516958339613564.51558841156
1333533.009647533683205.941715344213860.07757972314
1343680.789519919293321.780904255594039.79813558299
1354271.104803068753846.831712047644695.37789408985
1364652.879078845774178.846810446625126.91134724492
1374913.02778907814399.344290248455426.71128790774
1384951.940240580924457.97348234485445.90699881703

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 4533.34374450673 & 4332.69598442426 & 4733.9915045892 \tabularnewline
128 & 4545.70843320401 & 4312.05686872166 & 4779.35999768636 \tabularnewline
129 & 4433.47133336389 & 4173.47848174889 & 4693.46418497889 \tabularnewline
130 & 4347.39051403047 & 4063.62164291321 & 4631.15938514773 \tabularnewline
131 & 3703.50204376948 & 3420.43382192424 & 3986.57026561472 \tabularnewline
132 & 3276.51627337559 & 2988.51695833961 & 3564.51558841156 \tabularnewline
133 & 3533.00964753368 & 3205.94171534421 & 3860.07757972314 \tabularnewline
134 & 3680.78951991929 & 3321.78090425559 & 4039.79813558299 \tabularnewline
135 & 4271.10480306875 & 3846.83171204764 & 4695.37789408985 \tabularnewline
136 & 4652.87907884577 & 4178.84681044662 & 5126.91134724492 \tabularnewline
137 & 4913.0277890781 & 4399.34429024845 & 5426.71128790774 \tabularnewline
138 & 4951.94024058092 & 4457.9734823448 & 5445.90699881703 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299891&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]127[/C][C]4533.34374450673[/C][C]4332.69598442426[/C][C]4733.9915045892[/C][/ROW]
[ROW][C]128[/C][C]4545.70843320401[/C][C]4312.05686872166[/C][C]4779.35999768636[/C][/ROW]
[ROW][C]129[/C][C]4433.47133336389[/C][C]4173.47848174889[/C][C]4693.46418497889[/C][/ROW]
[ROW][C]130[/C][C]4347.39051403047[/C][C]4063.62164291321[/C][C]4631.15938514773[/C][/ROW]
[ROW][C]131[/C][C]3703.50204376948[/C][C]3420.43382192424[/C][C]3986.57026561472[/C][/ROW]
[ROW][C]132[/C][C]3276.51627337559[/C][C]2988.51695833961[/C][C]3564.51558841156[/C][/ROW]
[ROW][C]133[/C][C]3533.00964753368[/C][C]3205.94171534421[/C][C]3860.07757972314[/C][/ROW]
[ROW][C]134[/C][C]3680.78951991929[/C][C]3321.78090425559[/C][C]4039.79813558299[/C][/ROW]
[ROW][C]135[/C][C]4271.10480306875[/C][C]3846.83171204764[/C][C]4695.37789408985[/C][/ROW]
[ROW][C]136[/C][C]4652.87907884577[/C][C]4178.84681044662[/C][C]5126.91134724492[/C][/ROW]
[ROW][C]137[/C][C]4913.0277890781[/C][C]4399.34429024845[/C][C]5426.71128790774[/C][/ROW]
[ROW][C]138[/C][C]4951.94024058092[/C][C]4457.9734823448[/C][C]5445.90699881703[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299891&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299891&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
1274533.343744506734332.695984424264733.9915045892
1284545.708433204014312.056868721664779.35999768636
1294433.471333363894173.478481748894693.46418497889
1304347.390514030474063.621642913214631.15938514773
1313703.502043769483420.433821924243986.57026561472
1323276.516273375592988.516958339613564.51558841156
1333533.009647533683205.941715344213860.07757972314
1343680.789519919293321.780904255594039.79813558299
1354271.104803068753846.831712047644695.37789408985
1364652.879078845774178.846810446625126.91134724492
1374913.02778907814399.344290248455426.71128790774
1384951.940240580924457.97348234485445.90699881703



Parameters (Session):
par1 = additive ; par2 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; 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')