Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 08 Aug 2011 09:42:26 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Aug/08/t1312810992go06ix9iv552ii2.htm/, Retrieved Wed, 15 May 2024 03:57:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123457, Retrieved Wed, 15 May 2024 03:57:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsNick Verbeke
Estimated Impact225
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [Standard Deviatio...] [2011-05-08 16:13:36] [1cb322a33a2333c24d08c776e1f699d5]
- RMPD    [Exponential Smoothing] [TIJDREEKS A - STA...] [2011-08-08 13:42:26] [af5734c86e7bdbdfefb37d9aed9dbb03] [Current]
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Dataseries X:
588264
577918
567562
546859
756344
745987
588264
483527
493873
493873
504229
526055
462824
399492
347630
347630
546859
567562
409838
231412
325803
325803
399492
442021
431664
325803
378790
357986
536412
493873
325803
200263
315447
347630
378790
420195
336150
263595
294755
305101
577918
577918
420195
399492
462824
431664
515709
620447
641250
493873
452367
409838
694135
714939
661953
714939
704481
620447
714939
819676
862205
735641
651596
714939
987746
1071790
1051088
1092483
1082137
977399
1155825
1198354
1260562
1071790
998102
1082137
1282389
1460814
1418286
1418286
1439089
1366423
1555307
1555307
1523124
1344597
1376780
1397583
1534503
1712929
1586355
1649698
1596712
1565653
1807421
1754435
1680746
1576009
1680746
1733732
1796963
1880998
1796963
1848826
1785585
1775239
2037699
2059525
1975491
1828123
1953664
2006549
2069882
2164273
2069882
2143570
2111388
1996193
2237951
2237951




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time11 seconds
R Server'AstonUniversity' @ aston.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 11 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123457&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]11 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123457&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123457&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time11 seconds
R Server'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.653615272505321
beta0.052931792854034
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.653615272505321 \tabularnewline
beta & 0.052931792854034 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123457&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]0.653615272505321[/C][/ROW]
[ROW][C]beta[/C][C]0.052931792854034[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123457&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123457&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
alpha0.653615272505321
beta0.052931792854034
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13462824558671.733707265-95847.7337072651
14399492431689.970568831-32197.9705688309
15347630356235.210612933-8605.21061293338
16347630344263.449170433366.55082957039
17546859536823.21149955910035.7885004407
18567562552061.79788420215500.2021157981
19409838400070.8110596639767.1889403367
20231412295363.638310808-63951.6383108082
21325803259280.34423134466522.6557686558
22325803301299.319296524503.6807035003
23399492326622.51338994272869.4866100576
24442021396682.57124153745338.4287584628
25431664330765.167990704100898.832009296
26325803362870.606236248-37067.6062362481
27378790300680.01020105578109.9897989448
28357986360808.41210223-2822.41210222954
29536412562693.924757464-26281.9247574639
30493873565891.832511297-72018.8325112974
31325803361487.685299066-35684.6852990662
32200263206741.343205456-6478.34320545569
33315447260610.12629066554836.8737093349
34347630287224.42209439660405.5779056037
35378790360796.9775516317993.0224483696
36420195391584.19631737428610.8036826262
37336150339531.504830006-3381.50483000587
38263595257633.3332711015961.66672889888
39294755266896.85048833527858.1495116647
40305101267841.33285363337259.6671463666
41577918490881.00731319287036.9926868076
42577918559305.74117912718612.2588208735
43420195436863.036865369-16668.0368653692
44399492315458.80074851184033.1992514893
45462824463653.298693069-829.298693069024
46431664467813.697670391-36149.6976703912
47515709472246.11284500843462.8871549924
48620447532900.76699806287546.2330019382
49641250519868.621417129121381.378582871
50493873538651.229107855-44778.2291078547
51452367536477.054369802-84110.0543698024
52409838477762.255325897-67924.2553258968
53694135655923.47040402638211.5295959739
54714939673673.89061437341265.1093856266
55661953559540.63860012102412.36139988
56714939560694.126386069154244.873613931
57704481737657.675765578-33176.6757655783
58620447719594.467159476-99147.4671594764
59714939719401.204825352-4462.20482535241
60819676771317.06216605348358.9378339471
61862205750351.693204496111853.306795504
62735641710982.02780603224658.972193968
63651596748602.016135081-97006.0161350807
64714939694651.46255728820287.5374427116
65987746977871.6628639874.3371369997
661071790987816.38738000283973.6126199976
671051088933914.33953725117173.66046275
681092483974316.525497108118166.474502892
6910821371073177.011555588959.98844441678
709773991071659.79062428-94260.7906242833
7111558251119483.2229969736341.7770030291
7211983541229802.47915639-31448.479156395
7312605621189342.9998345971219.0001654108
7410717901102481.27550585-30691.2755058485
759981021069135.57899307-71033.5789930653
7610821371081043.247948621093.75205137627
7712823891355700.6208607-73311.6208606965
7814608141341652.10060816119161.899391844
7914182861328178.5645777390107.4354222682
8014182861356226.2577916762059.7422083342
8114390891383638.4513068955450.5486931051
8213664231381413.88786527-14990.8878652719
8315553071533690.3959042521616.6040957454
8415553071617796.41930744-62489.4193074438
8515231241598429.50454818-75305.5045481764
8613445971381246.6009227-36649.6009226954
8713767801330575.9916140846204.0083859221
8813975831448695.31371395-51112.313713948
8915345031666250.51478704-131747.514787039
9017129291681448.9762766231480.0237233771
9115863551598339.35888899-11984.3588889856
9216496981544149.08517122105548.914828781
9315967121593407.820135433304.17986457003
9415656531526606.3241521139046.6758478915
9518074211722658.9927033284762.0072966805
9617544351816865.52477902-62430.5247790213
9716807461791060.59651405-110314.596514049
9815760091561136.6081288514872.3918711522
9916807461571374.87068301109371.129316992
10017337321697791.7803175935940.2196824111
10117969631948046.28381767-151083.283817667
10218809982010208.39690216-129210.396902159
10317969631804516.53619833-7553.53619832802
10418488261791590.2082237257235.7917762827
10517855851769839.4043333515745.5956666484
10617752391719965.5693678155273.4306321882
10720376991939435.8896952898263.1103047156
10820595251988925.3062218870599.6937781177
10919754912035530.70203704-60039.7020370427
11018281231885615.42797153-57492.4279715323
11119536641882569.6653978871094.334602119
11220065491958490.4753489548058.5246510531
11320698822152260.40364543-82378.403645433
11421642732269659.29524441-105386.295244413
11520698822125257.33846222-55375.3384622186
11621435702105439.5203239138130.4796760916
11721113882058092.171803753295.8281962997
11819961932049015.25652076-52822.2565207582
11922379512211545.439645826405.5603542044
12022379512200821.3077362537129.6922637504

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 462824 & 558671.733707265 & -95847.7337072651 \tabularnewline
14 & 399492 & 431689.970568831 & -32197.9705688309 \tabularnewline
15 & 347630 & 356235.210612933 & -8605.21061293338 \tabularnewline
16 & 347630 & 344263.44917043 & 3366.55082957039 \tabularnewline
17 & 546859 & 536823.211499559 & 10035.7885004407 \tabularnewline
18 & 567562 & 552061.797884202 & 15500.2021157981 \tabularnewline
19 & 409838 & 400070.811059663 & 9767.1889403367 \tabularnewline
20 & 231412 & 295363.638310808 & -63951.6383108082 \tabularnewline
21 & 325803 & 259280.344231344 & 66522.6557686558 \tabularnewline
22 & 325803 & 301299.3192965 & 24503.6807035003 \tabularnewline
23 & 399492 & 326622.513389942 & 72869.4866100576 \tabularnewline
24 & 442021 & 396682.571241537 & 45338.4287584628 \tabularnewline
25 & 431664 & 330765.167990704 & 100898.832009296 \tabularnewline
26 & 325803 & 362870.606236248 & -37067.6062362481 \tabularnewline
27 & 378790 & 300680.010201055 & 78109.9897989448 \tabularnewline
28 & 357986 & 360808.41210223 & -2822.41210222954 \tabularnewline
29 & 536412 & 562693.924757464 & -26281.9247574639 \tabularnewline
30 & 493873 & 565891.832511297 & -72018.8325112974 \tabularnewline
31 & 325803 & 361487.685299066 & -35684.6852990662 \tabularnewline
32 & 200263 & 206741.343205456 & -6478.34320545569 \tabularnewline
33 & 315447 & 260610.126290665 & 54836.8737093349 \tabularnewline
34 & 347630 & 287224.422094396 & 60405.5779056037 \tabularnewline
35 & 378790 & 360796.97755163 & 17993.0224483696 \tabularnewline
36 & 420195 & 391584.196317374 & 28610.8036826262 \tabularnewline
37 & 336150 & 339531.504830006 & -3381.50483000587 \tabularnewline
38 & 263595 & 257633.333271101 & 5961.66672889888 \tabularnewline
39 & 294755 & 266896.850488335 & 27858.1495116647 \tabularnewline
40 & 305101 & 267841.332853633 & 37259.6671463666 \tabularnewline
41 & 577918 & 490881.007313192 & 87036.9926868076 \tabularnewline
42 & 577918 & 559305.741179127 & 18612.2588208735 \tabularnewline
43 & 420195 & 436863.036865369 & -16668.0368653692 \tabularnewline
44 & 399492 & 315458.800748511 & 84033.1992514893 \tabularnewline
45 & 462824 & 463653.298693069 & -829.298693069024 \tabularnewline
46 & 431664 & 467813.697670391 & -36149.6976703912 \tabularnewline
47 & 515709 & 472246.112845008 & 43462.8871549924 \tabularnewline
48 & 620447 & 532900.766998062 & 87546.2330019382 \tabularnewline
49 & 641250 & 519868.621417129 & 121381.378582871 \tabularnewline
50 & 493873 & 538651.229107855 & -44778.2291078547 \tabularnewline
51 & 452367 & 536477.054369802 & -84110.0543698024 \tabularnewline
52 & 409838 & 477762.255325897 & -67924.2553258968 \tabularnewline
53 & 694135 & 655923.470404026 & 38211.5295959739 \tabularnewline
54 & 714939 & 673673.890614373 & 41265.1093856266 \tabularnewline
55 & 661953 & 559540.63860012 & 102412.36139988 \tabularnewline
56 & 714939 & 560694.126386069 & 154244.873613931 \tabularnewline
57 & 704481 & 737657.675765578 & -33176.6757655783 \tabularnewline
58 & 620447 & 719594.467159476 & -99147.4671594764 \tabularnewline
59 & 714939 & 719401.204825352 & -4462.20482535241 \tabularnewline
60 & 819676 & 771317.062166053 & 48358.9378339471 \tabularnewline
61 & 862205 & 750351.693204496 & 111853.306795504 \tabularnewline
62 & 735641 & 710982.027806032 & 24658.972193968 \tabularnewline
63 & 651596 & 748602.016135081 & -97006.0161350807 \tabularnewline
64 & 714939 & 694651.462557288 & 20287.5374427116 \tabularnewline
65 & 987746 & 977871.662863 & 9874.3371369997 \tabularnewline
66 & 1071790 & 987816.387380002 & 83973.6126199976 \tabularnewline
67 & 1051088 & 933914.33953725 & 117173.66046275 \tabularnewline
68 & 1092483 & 974316.525497108 & 118166.474502892 \tabularnewline
69 & 1082137 & 1073177.01155558 & 8959.98844441678 \tabularnewline
70 & 977399 & 1071659.79062428 & -94260.7906242833 \tabularnewline
71 & 1155825 & 1119483.22299697 & 36341.7770030291 \tabularnewline
72 & 1198354 & 1229802.47915639 & -31448.479156395 \tabularnewline
73 & 1260562 & 1189342.99983459 & 71219.0001654108 \tabularnewline
74 & 1071790 & 1102481.27550585 & -30691.2755058485 \tabularnewline
75 & 998102 & 1069135.57899307 & -71033.5789930653 \tabularnewline
76 & 1082137 & 1081043.24794862 & 1093.75205137627 \tabularnewline
77 & 1282389 & 1355700.6208607 & -73311.6208606965 \tabularnewline
78 & 1460814 & 1341652.10060816 & 119161.899391844 \tabularnewline
79 & 1418286 & 1328178.56457773 & 90107.4354222682 \tabularnewline
80 & 1418286 & 1356226.25779167 & 62059.7422083342 \tabularnewline
81 & 1439089 & 1383638.45130689 & 55450.5486931051 \tabularnewline
82 & 1366423 & 1381413.88786527 & -14990.8878652719 \tabularnewline
83 & 1555307 & 1533690.39590425 & 21616.6040957454 \tabularnewline
84 & 1555307 & 1617796.41930744 & -62489.4193074438 \tabularnewline
85 & 1523124 & 1598429.50454818 & -75305.5045481764 \tabularnewline
86 & 1344597 & 1381246.6009227 & -36649.6009226954 \tabularnewline
87 & 1376780 & 1330575.99161408 & 46204.0083859221 \tabularnewline
88 & 1397583 & 1448695.31371395 & -51112.313713948 \tabularnewline
89 & 1534503 & 1666250.51478704 & -131747.514787039 \tabularnewline
90 & 1712929 & 1681448.97627662 & 31480.0237233771 \tabularnewline
91 & 1586355 & 1598339.35888899 & -11984.3588889856 \tabularnewline
92 & 1649698 & 1544149.08517122 & 105548.914828781 \tabularnewline
93 & 1596712 & 1593407.82013543 & 3304.17986457003 \tabularnewline
94 & 1565653 & 1526606.32415211 & 39046.6758478915 \tabularnewline
95 & 1807421 & 1722658.99270332 & 84762.0072966805 \tabularnewline
96 & 1754435 & 1816865.52477902 & -62430.5247790213 \tabularnewline
97 & 1680746 & 1791060.59651405 & -110314.596514049 \tabularnewline
98 & 1576009 & 1561136.60812885 & 14872.3918711522 \tabularnewline
99 & 1680746 & 1571374.87068301 & 109371.129316992 \tabularnewline
100 & 1733732 & 1697791.78031759 & 35940.2196824111 \tabularnewline
101 & 1796963 & 1948046.28381767 & -151083.283817667 \tabularnewline
102 & 1880998 & 2010208.39690216 & -129210.396902159 \tabularnewline
103 & 1796963 & 1804516.53619833 & -7553.53619832802 \tabularnewline
104 & 1848826 & 1791590.20822372 & 57235.7917762827 \tabularnewline
105 & 1785585 & 1769839.40433335 & 15745.5956666484 \tabularnewline
106 & 1775239 & 1719965.56936781 & 55273.4306321882 \tabularnewline
107 & 2037699 & 1939435.88969528 & 98263.1103047156 \tabularnewline
108 & 2059525 & 1988925.30622188 & 70599.6937781177 \tabularnewline
109 & 1975491 & 2035530.70203704 & -60039.7020370427 \tabularnewline
110 & 1828123 & 1885615.42797153 & -57492.4279715323 \tabularnewline
111 & 1953664 & 1882569.66539788 & 71094.334602119 \tabularnewline
112 & 2006549 & 1958490.47534895 & 48058.5246510531 \tabularnewline
113 & 2069882 & 2152260.40364543 & -82378.403645433 \tabularnewline
114 & 2164273 & 2269659.29524441 & -105386.295244413 \tabularnewline
115 & 2069882 & 2125257.33846222 & -55375.3384622186 \tabularnewline
116 & 2143570 & 2105439.52032391 & 38130.4796760916 \tabularnewline
117 & 2111388 & 2058092.1718037 & 53295.8281962997 \tabularnewline
118 & 1996193 & 2049015.25652076 & -52822.2565207582 \tabularnewline
119 & 2237951 & 2211545.4396458 & 26405.5603542044 \tabularnewline
120 & 2237951 & 2200821.30773625 & 37129.6922637504 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123457&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]462824[/C][C]558671.733707265[/C][C]-95847.7337072651[/C][/ROW]
[ROW][C]14[/C][C]399492[/C][C]431689.970568831[/C][C]-32197.9705688309[/C][/ROW]
[ROW][C]15[/C][C]347630[/C][C]356235.210612933[/C][C]-8605.21061293338[/C][/ROW]
[ROW][C]16[/C][C]347630[/C][C]344263.44917043[/C][C]3366.55082957039[/C][/ROW]
[ROW][C]17[/C][C]546859[/C][C]536823.211499559[/C][C]10035.7885004407[/C][/ROW]
[ROW][C]18[/C][C]567562[/C][C]552061.797884202[/C][C]15500.2021157981[/C][/ROW]
[ROW][C]19[/C][C]409838[/C][C]400070.811059663[/C][C]9767.1889403367[/C][/ROW]
[ROW][C]20[/C][C]231412[/C][C]295363.638310808[/C][C]-63951.6383108082[/C][/ROW]
[ROW][C]21[/C][C]325803[/C][C]259280.344231344[/C][C]66522.6557686558[/C][/ROW]
[ROW][C]22[/C][C]325803[/C][C]301299.3192965[/C][C]24503.6807035003[/C][/ROW]
[ROW][C]23[/C][C]399492[/C][C]326622.513389942[/C][C]72869.4866100576[/C][/ROW]
[ROW][C]24[/C][C]442021[/C][C]396682.571241537[/C][C]45338.4287584628[/C][/ROW]
[ROW][C]25[/C][C]431664[/C][C]330765.167990704[/C][C]100898.832009296[/C][/ROW]
[ROW][C]26[/C][C]325803[/C][C]362870.606236248[/C][C]-37067.6062362481[/C][/ROW]
[ROW][C]27[/C][C]378790[/C][C]300680.010201055[/C][C]78109.9897989448[/C][/ROW]
[ROW][C]28[/C][C]357986[/C][C]360808.41210223[/C][C]-2822.41210222954[/C][/ROW]
[ROW][C]29[/C][C]536412[/C][C]562693.924757464[/C][C]-26281.9247574639[/C][/ROW]
[ROW][C]30[/C][C]493873[/C][C]565891.832511297[/C][C]-72018.8325112974[/C][/ROW]
[ROW][C]31[/C][C]325803[/C][C]361487.685299066[/C][C]-35684.6852990662[/C][/ROW]
[ROW][C]32[/C][C]200263[/C][C]206741.343205456[/C][C]-6478.34320545569[/C][/ROW]
[ROW][C]33[/C][C]315447[/C][C]260610.126290665[/C][C]54836.8737093349[/C][/ROW]
[ROW][C]34[/C][C]347630[/C][C]287224.422094396[/C][C]60405.5779056037[/C][/ROW]
[ROW][C]35[/C][C]378790[/C][C]360796.97755163[/C][C]17993.0224483696[/C][/ROW]
[ROW][C]36[/C][C]420195[/C][C]391584.196317374[/C][C]28610.8036826262[/C][/ROW]
[ROW][C]37[/C][C]336150[/C][C]339531.504830006[/C][C]-3381.50483000587[/C][/ROW]
[ROW][C]38[/C][C]263595[/C][C]257633.333271101[/C][C]5961.66672889888[/C][/ROW]
[ROW][C]39[/C][C]294755[/C][C]266896.850488335[/C][C]27858.1495116647[/C][/ROW]
[ROW][C]40[/C][C]305101[/C][C]267841.332853633[/C][C]37259.6671463666[/C][/ROW]
[ROW][C]41[/C][C]577918[/C][C]490881.007313192[/C][C]87036.9926868076[/C][/ROW]
[ROW][C]42[/C][C]577918[/C][C]559305.741179127[/C][C]18612.2588208735[/C][/ROW]
[ROW][C]43[/C][C]420195[/C][C]436863.036865369[/C][C]-16668.0368653692[/C][/ROW]
[ROW][C]44[/C][C]399492[/C][C]315458.800748511[/C][C]84033.1992514893[/C][/ROW]
[ROW][C]45[/C][C]462824[/C][C]463653.298693069[/C][C]-829.298693069024[/C][/ROW]
[ROW][C]46[/C][C]431664[/C][C]467813.697670391[/C][C]-36149.6976703912[/C][/ROW]
[ROW][C]47[/C][C]515709[/C][C]472246.112845008[/C][C]43462.8871549924[/C][/ROW]
[ROW][C]48[/C][C]620447[/C][C]532900.766998062[/C][C]87546.2330019382[/C][/ROW]
[ROW][C]49[/C][C]641250[/C][C]519868.621417129[/C][C]121381.378582871[/C][/ROW]
[ROW][C]50[/C][C]493873[/C][C]538651.229107855[/C][C]-44778.2291078547[/C][/ROW]
[ROW][C]51[/C][C]452367[/C][C]536477.054369802[/C][C]-84110.0543698024[/C][/ROW]
[ROW][C]52[/C][C]409838[/C][C]477762.255325897[/C][C]-67924.2553258968[/C][/ROW]
[ROW][C]53[/C][C]694135[/C][C]655923.470404026[/C][C]38211.5295959739[/C][/ROW]
[ROW][C]54[/C][C]714939[/C][C]673673.890614373[/C][C]41265.1093856266[/C][/ROW]
[ROW][C]55[/C][C]661953[/C][C]559540.63860012[/C][C]102412.36139988[/C][/ROW]
[ROW][C]56[/C][C]714939[/C][C]560694.126386069[/C][C]154244.873613931[/C][/ROW]
[ROW][C]57[/C][C]704481[/C][C]737657.675765578[/C][C]-33176.6757655783[/C][/ROW]
[ROW][C]58[/C][C]620447[/C][C]719594.467159476[/C][C]-99147.4671594764[/C][/ROW]
[ROW][C]59[/C][C]714939[/C][C]719401.204825352[/C][C]-4462.20482535241[/C][/ROW]
[ROW][C]60[/C][C]819676[/C][C]771317.062166053[/C][C]48358.9378339471[/C][/ROW]
[ROW][C]61[/C][C]862205[/C][C]750351.693204496[/C][C]111853.306795504[/C][/ROW]
[ROW][C]62[/C][C]735641[/C][C]710982.027806032[/C][C]24658.972193968[/C][/ROW]
[ROW][C]63[/C][C]651596[/C][C]748602.016135081[/C][C]-97006.0161350807[/C][/ROW]
[ROW][C]64[/C][C]714939[/C][C]694651.462557288[/C][C]20287.5374427116[/C][/ROW]
[ROW][C]65[/C][C]987746[/C][C]977871.662863[/C][C]9874.3371369997[/C][/ROW]
[ROW][C]66[/C][C]1071790[/C][C]987816.387380002[/C][C]83973.6126199976[/C][/ROW]
[ROW][C]67[/C][C]1051088[/C][C]933914.33953725[/C][C]117173.66046275[/C][/ROW]
[ROW][C]68[/C][C]1092483[/C][C]974316.525497108[/C][C]118166.474502892[/C][/ROW]
[ROW][C]69[/C][C]1082137[/C][C]1073177.01155558[/C][C]8959.98844441678[/C][/ROW]
[ROW][C]70[/C][C]977399[/C][C]1071659.79062428[/C][C]-94260.7906242833[/C][/ROW]
[ROW][C]71[/C][C]1155825[/C][C]1119483.22299697[/C][C]36341.7770030291[/C][/ROW]
[ROW][C]72[/C][C]1198354[/C][C]1229802.47915639[/C][C]-31448.479156395[/C][/ROW]
[ROW][C]73[/C][C]1260562[/C][C]1189342.99983459[/C][C]71219.0001654108[/C][/ROW]
[ROW][C]74[/C][C]1071790[/C][C]1102481.27550585[/C][C]-30691.2755058485[/C][/ROW]
[ROW][C]75[/C][C]998102[/C][C]1069135.57899307[/C][C]-71033.5789930653[/C][/ROW]
[ROW][C]76[/C][C]1082137[/C][C]1081043.24794862[/C][C]1093.75205137627[/C][/ROW]
[ROW][C]77[/C][C]1282389[/C][C]1355700.6208607[/C][C]-73311.6208606965[/C][/ROW]
[ROW][C]78[/C][C]1460814[/C][C]1341652.10060816[/C][C]119161.899391844[/C][/ROW]
[ROW][C]79[/C][C]1418286[/C][C]1328178.56457773[/C][C]90107.4354222682[/C][/ROW]
[ROW][C]80[/C][C]1418286[/C][C]1356226.25779167[/C][C]62059.7422083342[/C][/ROW]
[ROW][C]81[/C][C]1439089[/C][C]1383638.45130689[/C][C]55450.5486931051[/C][/ROW]
[ROW][C]82[/C][C]1366423[/C][C]1381413.88786527[/C][C]-14990.8878652719[/C][/ROW]
[ROW][C]83[/C][C]1555307[/C][C]1533690.39590425[/C][C]21616.6040957454[/C][/ROW]
[ROW][C]84[/C][C]1555307[/C][C]1617796.41930744[/C][C]-62489.4193074438[/C][/ROW]
[ROW][C]85[/C][C]1523124[/C][C]1598429.50454818[/C][C]-75305.5045481764[/C][/ROW]
[ROW][C]86[/C][C]1344597[/C][C]1381246.6009227[/C][C]-36649.6009226954[/C][/ROW]
[ROW][C]87[/C][C]1376780[/C][C]1330575.99161408[/C][C]46204.0083859221[/C][/ROW]
[ROW][C]88[/C][C]1397583[/C][C]1448695.31371395[/C][C]-51112.313713948[/C][/ROW]
[ROW][C]89[/C][C]1534503[/C][C]1666250.51478704[/C][C]-131747.514787039[/C][/ROW]
[ROW][C]90[/C][C]1712929[/C][C]1681448.97627662[/C][C]31480.0237233771[/C][/ROW]
[ROW][C]91[/C][C]1586355[/C][C]1598339.35888899[/C][C]-11984.3588889856[/C][/ROW]
[ROW][C]92[/C][C]1649698[/C][C]1544149.08517122[/C][C]105548.914828781[/C][/ROW]
[ROW][C]93[/C][C]1596712[/C][C]1593407.82013543[/C][C]3304.17986457003[/C][/ROW]
[ROW][C]94[/C][C]1565653[/C][C]1526606.32415211[/C][C]39046.6758478915[/C][/ROW]
[ROW][C]95[/C][C]1807421[/C][C]1722658.99270332[/C][C]84762.0072966805[/C][/ROW]
[ROW][C]96[/C][C]1754435[/C][C]1816865.52477902[/C][C]-62430.5247790213[/C][/ROW]
[ROW][C]97[/C][C]1680746[/C][C]1791060.59651405[/C][C]-110314.596514049[/C][/ROW]
[ROW][C]98[/C][C]1576009[/C][C]1561136.60812885[/C][C]14872.3918711522[/C][/ROW]
[ROW][C]99[/C][C]1680746[/C][C]1571374.87068301[/C][C]109371.129316992[/C][/ROW]
[ROW][C]100[/C][C]1733732[/C][C]1697791.78031759[/C][C]35940.2196824111[/C][/ROW]
[ROW][C]101[/C][C]1796963[/C][C]1948046.28381767[/C][C]-151083.283817667[/C][/ROW]
[ROW][C]102[/C][C]1880998[/C][C]2010208.39690216[/C][C]-129210.396902159[/C][/ROW]
[ROW][C]103[/C][C]1796963[/C][C]1804516.53619833[/C][C]-7553.53619832802[/C][/ROW]
[ROW][C]104[/C][C]1848826[/C][C]1791590.20822372[/C][C]57235.7917762827[/C][/ROW]
[ROW][C]105[/C][C]1785585[/C][C]1769839.40433335[/C][C]15745.5956666484[/C][/ROW]
[ROW][C]106[/C][C]1775239[/C][C]1719965.56936781[/C][C]55273.4306321882[/C][/ROW]
[ROW][C]107[/C][C]2037699[/C][C]1939435.88969528[/C][C]98263.1103047156[/C][/ROW]
[ROW][C]108[/C][C]2059525[/C][C]1988925.30622188[/C][C]70599.6937781177[/C][/ROW]
[ROW][C]109[/C][C]1975491[/C][C]2035530.70203704[/C][C]-60039.7020370427[/C][/ROW]
[ROW][C]110[/C][C]1828123[/C][C]1885615.42797153[/C][C]-57492.4279715323[/C][/ROW]
[ROW][C]111[/C][C]1953664[/C][C]1882569.66539788[/C][C]71094.334602119[/C][/ROW]
[ROW][C]112[/C][C]2006549[/C][C]1958490.47534895[/C][C]48058.5246510531[/C][/ROW]
[ROW][C]113[/C][C]2069882[/C][C]2152260.40364543[/C][C]-82378.403645433[/C][/ROW]
[ROW][C]114[/C][C]2164273[/C][C]2269659.29524441[/C][C]-105386.295244413[/C][/ROW]
[ROW][C]115[/C][C]2069882[/C][C]2125257.33846222[/C][C]-55375.3384622186[/C][/ROW]
[ROW][C]116[/C][C]2143570[/C][C]2105439.52032391[/C][C]38130.4796760916[/C][/ROW]
[ROW][C]117[/C][C]2111388[/C][C]2058092.1718037[/C][C]53295.8281962997[/C][/ROW]
[ROW][C]118[/C][C]1996193[/C][C]2049015.25652076[/C][C]-52822.2565207582[/C][/ROW]
[ROW][C]119[/C][C]2237951[/C][C]2211545.4396458[/C][C]26405.5603542044[/C][/ROW]
[ROW][C]120[/C][C]2237951[/C][C]2200821.30773625[/C][C]37129.6922637504[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123457&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123457&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
13462824558671.733707265-95847.7337072651
14399492431689.970568831-32197.9705688309
15347630356235.210612933-8605.21061293338
16347630344263.449170433366.55082957039
17546859536823.21149955910035.7885004407
18567562552061.79788420215500.2021157981
19409838400070.8110596639767.1889403367
20231412295363.638310808-63951.6383108082
21325803259280.34423134466522.6557686558
22325803301299.319296524503.6807035003
23399492326622.51338994272869.4866100576
24442021396682.57124153745338.4287584628
25431664330765.167990704100898.832009296
26325803362870.606236248-37067.6062362481
27378790300680.01020105578109.9897989448
28357986360808.41210223-2822.41210222954
29536412562693.924757464-26281.9247574639
30493873565891.832511297-72018.8325112974
31325803361487.685299066-35684.6852990662
32200263206741.343205456-6478.34320545569
33315447260610.12629066554836.8737093349
34347630287224.42209439660405.5779056037
35378790360796.9775516317993.0224483696
36420195391584.19631737428610.8036826262
37336150339531.504830006-3381.50483000587
38263595257633.3332711015961.66672889888
39294755266896.85048833527858.1495116647
40305101267841.33285363337259.6671463666
41577918490881.00731319287036.9926868076
42577918559305.74117912718612.2588208735
43420195436863.036865369-16668.0368653692
44399492315458.80074851184033.1992514893
45462824463653.298693069-829.298693069024
46431664467813.697670391-36149.6976703912
47515709472246.11284500843462.8871549924
48620447532900.76699806287546.2330019382
49641250519868.621417129121381.378582871
50493873538651.229107855-44778.2291078547
51452367536477.054369802-84110.0543698024
52409838477762.255325897-67924.2553258968
53694135655923.47040402638211.5295959739
54714939673673.89061437341265.1093856266
55661953559540.63860012102412.36139988
56714939560694.126386069154244.873613931
57704481737657.675765578-33176.6757655783
58620447719594.467159476-99147.4671594764
59714939719401.204825352-4462.20482535241
60819676771317.06216605348358.9378339471
61862205750351.693204496111853.306795504
62735641710982.02780603224658.972193968
63651596748602.016135081-97006.0161350807
64714939694651.46255728820287.5374427116
65987746977871.6628639874.3371369997
661071790987816.38738000283973.6126199976
671051088933914.33953725117173.66046275
681092483974316.525497108118166.474502892
6910821371073177.011555588959.98844441678
709773991071659.79062428-94260.7906242833
7111558251119483.2229969736341.7770030291
7211983541229802.47915639-31448.479156395
7312605621189342.9998345971219.0001654108
7410717901102481.27550585-30691.2755058485
759981021069135.57899307-71033.5789930653
7610821371081043.247948621093.75205137627
7712823891355700.6208607-73311.6208606965
7814608141341652.10060816119161.899391844
7914182861328178.5645777390107.4354222682
8014182861356226.2577916762059.7422083342
8114390891383638.4513068955450.5486931051
8213664231381413.88786527-14990.8878652719
8315553071533690.3959042521616.6040957454
8415553071617796.41930744-62489.4193074438
8515231241598429.50454818-75305.5045481764
8613445971381246.6009227-36649.6009226954
8713767801330575.9916140846204.0083859221
8813975831448695.31371395-51112.313713948
8915345031666250.51478704-131747.514787039
9017129291681448.9762766231480.0237233771
9115863551598339.35888899-11984.3588889856
9216496981544149.08517122105548.914828781
9315967121593407.820135433304.17986457003
9415656531526606.3241521139046.6758478915
9518074211722658.9927033284762.0072966805
9617544351816865.52477902-62430.5247790213
9716807461791060.59651405-110314.596514049
9815760091561136.6081288514872.3918711522
9916807461571374.87068301109371.129316992
10017337321697791.7803175935940.2196824111
10117969631948046.28381767-151083.283817667
10218809982010208.39690216-129210.396902159
10317969631804516.53619833-7553.53619832802
10418488261791590.2082237257235.7917762827
10517855851769839.4043333515745.5956666484
10617752391719965.5693678155273.4306321882
10720376991939435.8896952898263.1103047156
10820595251988925.3062218870599.6937781177
10919754912035530.70203704-60039.7020370427
11018281231885615.42797153-57492.4279715323
11119536641882569.6653978871094.334602119
11220065491958490.4753489548058.5246510531
11320698822152260.40364543-82378.403645433
11421642732269659.29524441-105386.295244413
11520698822125257.33846222-55375.3384622186
11621435702105439.5203239138130.4796760916
11721113882058092.171803753295.8281962997
11819961932049015.25652076-52822.2565207582
11922379512211545.439645826405.5603542044
12022379512200821.3077362537129.6922637504







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1212175476.57393622046785.663042542304167.48482986
1222062941.56424181906719.270046112219163.85843748
1232141258.349839661959439.929761762323076.76991756
1242159516.039936231953218.694011132365813.38586134
1252271814.616332962041712.415705412501916.81696051
1262433059.550021792179558.331810042686560.76823354
1272376480.611194742099811.538111272653149.68427821
1282428779.663711332129054.132277592728505.19514506
1292363977.211541212041221.315276752686733.10780566
1302283678.282959561937855.574764892629500.99115423
1312510375.336360182141402.476459032879348.19626132
1322487391.379443862095149.244460142879633.51442759

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 2175476.5739362 & 2046785.66304254 & 2304167.48482986 \tabularnewline
122 & 2062941.5642418 & 1906719.27004611 & 2219163.85843748 \tabularnewline
123 & 2141258.34983966 & 1959439.92976176 & 2323076.76991756 \tabularnewline
124 & 2159516.03993623 & 1953218.69401113 & 2365813.38586134 \tabularnewline
125 & 2271814.61633296 & 2041712.41570541 & 2501916.81696051 \tabularnewline
126 & 2433059.55002179 & 2179558.33181004 & 2686560.76823354 \tabularnewline
127 & 2376480.61119474 & 2099811.53811127 & 2653149.68427821 \tabularnewline
128 & 2428779.66371133 & 2129054.13227759 & 2728505.19514506 \tabularnewline
129 & 2363977.21154121 & 2041221.31527675 & 2686733.10780566 \tabularnewline
130 & 2283678.28295956 & 1937855.57476489 & 2629500.99115423 \tabularnewline
131 & 2510375.33636018 & 2141402.47645903 & 2879348.19626132 \tabularnewline
132 & 2487391.37944386 & 2095149.24446014 & 2879633.51442759 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123457&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]121[/C][C]2175476.5739362[/C][C]2046785.66304254[/C][C]2304167.48482986[/C][/ROW]
[ROW][C]122[/C][C]2062941.5642418[/C][C]1906719.27004611[/C][C]2219163.85843748[/C][/ROW]
[ROW][C]123[/C][C]2141258.34983966[/C][C]1959439.92976176[/C][C]2323076.76991756[/C][/ROW]
[ROW][C]124[/C][C]2159516.03993623[/C][C]1953218.69401113[/C][C]2365813.38586134[/C][/ROW]
[ROW][C]125[/C][C]2271814.61633296[/C][C]2041712.41570541[/C][C]2501916.81696051[/C][/ROW]
[ROW][C]126[/C][C]2433059.55002179[/C][C]2179558.33181004[/C][C]2686560.76823354[/C][/ROW]
[ROW][C]127[/C][C]2376480.61119474[/C][C]2099811.53811127[/C][C]2653149.68427821[/C][/ROW]
[ROW][C]128[/C][C]2428779.66371133[/C][C]2129054.13227759[/C][C]2728505.19514506[/C][/ROW]
[ROW][C]129[/C][C]2363977.21154121[/C][C]2041221.31527675[/C][C]2686733.10780566[/C][/ROW]
[ROW][C]130[/C][C]2283678.28295956[/C][C]1937855.57476489[/C][C]2629500.99115423[/C][/ROW]
[ROW][C]131[/C][C]2510375.33636018[/C][C]2141402.47645903[/C][C]2879348.19626132[/C][/ROW]
[ROW][C]132[/C][C]2487391.37944386[/C][C]2095149.24446014[/C][C]2879633.51442759[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123457&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123457&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
1212175476.57393622046785.663042542304167.48482986
1222062941.56424181906719.270046112219163.85843748
1232141258.349839661959439.929761762323076.76991756
1242159516.039936231953218.694011132365813.38586134
1252271814.616332962041712.415705412501916.81696051
1262433059.550021792179558.331810042686560.76823354
1272376480.611194742099811.538111272653149.68427821
1282428779.663711332129054.132277592728505.19514506
1292363977.211541212041221.315276752686733.10780566
1302283678.282959561937855.574764892629500.99115423
1312510375.336360182141402.476459032879348.19626132
1322487391.379443862095149.244460142879633.51442759



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')