Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 Aug 2010 19:38:01 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/19/t128224665197029ilybhzuzc5.htm/, Retrieved Fri, 03 May 2024 06:20:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79353, Retrieved Fri, 03 May 2024 06:20:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsGregory Goris
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks A - Sta...] [2010-08-19 19:38:01] [4069dbe0e58b4004934f5f5b0dc60f40] [Current]
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Dataseries X:
159
158
157
155
175
174
159
149
150
150
151
153
146
156
154
151
171
167
144
138
138
132
132
132
125
131
129
131
145
156
126
123
127
116
114
114
109
110
113
114
138
155
126
123
124
124
134
131
126
128
128
124
148
174
146
137
152
159
170
166
165
168
175
180
199
228
206
193
201
214
225
224
215
222
238
248
262
288
261
240
248
260
266
268
256
261
287
295
304
331
299
275
293
309
311
311
289
298
319
325
331
348
320
305
322
337
346
343
321
331
343
345
347
363
322
304
323
340
352
351




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79353&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79353&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79353&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.9999492214626
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.9999492214626 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79353&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]0.9999492214626[/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=79353&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79353&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
alpha0.9999492214626
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2158159-1
3157158.000050778537-1.0000507785374
4155157.000050781116-2.00005078111585
5175155.00010155965319.9998984403466
6174174.998984434409-0.998984434409039
7159174.000050726968-15.0000507269685
8149159.000761680637-10.0007616806368
9150149.0005078240510.999492175948973
10150149.9999492472495.07527508375460e-05
11151149.9999999974231.00000000257717
12153150.9999492214622.00005077853754
13146152.999898440347-6.99989844034673
14156146.0003554446059.99964455539526
15154155.999492232675-1.99949223267495
16151154.000101531291-3.00010153129111
17171151.00015234076819.9998476592322
18167170.998984436988-3.99898443698766
19144167.000203062581-23.0002030625808
20138144.001167916671-6.00116791667142
21138138.000304730530-0.000304730529506969
22132138.000000015474-6.00000001547377
23132132.000304671225-0.000304671225194397
24132132.000000015471-1.54707606725424e-08
25125132.000000000001-7.0000000000008
26131125.0003554497625.9996445502382
27129130.999695346825-1.99969534682481
28131129.0001015416051.99989845839505
29145130.99989844808114.0001015519187
30156144.99928909532011.0007109046803
31126155.99944139999-29.9994413999899
32123126.001523327757-3.0015233277571
33127123.0001524129653.99984758703545
34116126.999796893590-10.9997968935897
35114116.000558553598-2.00055855359795
36114114.000101585437-0.000101585437334961
37109114.000000005158-5.00000000515837
38110109.0002538926870.999746107312731
39113109.9999492343553.0000507656451
40114112.999847661811.00015233819001
41138113.99994921372724.0000507862729
42155137.99878131252417.0012186874764
43126154.999136702981-28.9991367029810
44123126.001472533748-3.00147253374763
45124123.0001524103850.999847589614689
46124123.9999492292025.07707982251304e-05
47134123.99999999742210.0000000025781
48131133.999492214626-2.99949221462586
49126131.000152309828-5.0001523098276
50128126.0002539004211.99974609957893
51128127.9998984558180.000101544182101065
52124127.999999994844-3.99999999484373
53148124.00020311414923.9997968858507
54174147.99878132541626.0012186745838
55146173.998679696145-27.9986796961451
56137146.001421732004-9.00142173200408
57152137.0004570790314.9995429209699
58159151.9992383451497.0007616548512
59170158.99964451156211.0003554884375
60166169.999441418037-3.99944141803741
61165166.000203085786-1.00020308578561
62168165.0000507888502.99994921115021
63175167.9998476669677.00015233303321
64180174.9996445425035.00035545749705
65199179.99974608926319.0002539107366
66228198.99903519489629.0009648051038
67206227.998527373424-21.9985273734240
68193206.001117053045-13.0011170530450
69201193.0006601777097.99933982229146
70214200.99959380522413.0004061947763
71225213.99933985838811.0006601416122
72224224.999441402568-0.999441402567584
73215224.000050750173-9.00005075017265
74222215.0004570094146.99954299058638
75238221.99964457344416.0003554265555
76248237.99918752535410.0008124746464
77262247.9994921733714.0005078266303
78288261.99928907469026.0007109253103
79261287.998679721928-26.9986797219279
80240261.001370953468-21.001370953468
81248240.0010664189007.9989335810996
82260247.99959382585212.000406174148
83266259.9993906369266.00060936307375
84268265.9996952978332.00030470216694
85256267.999898427453-11.9998984274529
86261256.0006093372914.99939066270889
87287260.99974613825426.0002538617458
88295286.9986797451378.00132025486312
89304294.999593704669.00040629533981
90331303.99954297253227.0004570274677
91299330.998628956283-31.998628956283
92275299.001624843577-24.0016248435772
93293275.00121876740517.9987812325953
94309292.99908604821416.0009139517859
95311308.9991874969922.00081250300752
96311310.9998984016670.000101598332548747
97289310.999999994841-21.9999999948409
98298289.0011171278238.99888287217749
99319297.99954304988921.0004569501105
100325318.9989336275116.00106637248865
101331324.9996952746276.00030472537327
102348330.99969531330217.0003046866979
103320347.999136749393-27.9991367493926
104305320.001421755213-15.0014217552126
105322305.00076175025616.9992382497444
106337321.99913680354515.0008631964553
107346336.9992382781079.00076172189284
108343345.999542954484-2.99954295448424
109321343.000152312404-22.0001523124041
110331321.0011171355579.99888286444303
111343330.99949227135212.0005077286475
112345342.9993906317692.00060936823053
113347344.9998984119822.00010158801763
114363346.99989843776716.0001015622333
115322362.999187538244-40.9991875382444
116304322.002081878778-18.0020818787777
117323304.00091411938818.9990858806121
118340322.99903525420717.0009647457929
119352339.99913671587612.0008632841242
120351351.999390613715-0.999390613714866

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 158 & 159 & -1 \tabularnewline
3 & 157 & 158.000050778537 & -1.0000507785374 \tabularnewline
4 & 155 & 157.000050781116 & -2.00005078111585 \tabularnewline
5 & 175 & 155.000101559653 & 19.9998984403466 \tabularnewline
6 & 174 & 174.998984434409 & -0.998984434409039 \tabularnewline
7 & 159 & 174.000050726968 & -15.0000507269685 \tabularnewline
8 & 149 & 159.000761680637 & -10.0007616806368 \tabularnewline
9 & 150 & 149.000507824051 & 0.999492175948973 \tabularnewline
10 & 150 & 149.999949247249 & 5.07527508375460e-05 \tabularnewline
11 & 151 & 149.999999997423 & 1.00000000257717 \tabularnewline
12 & 153 & 150.999949221462 & 2.00005077853754 \tabularnewline
13 & 146 & 152.999898440347 & -6.99989844034673 \tabularnewline
14 & 156 & 146.000355444605 & 9.99964455539526 \tabularnewline
15 & 154 & 155.999492232675 & -1.99949223267495 \tabularnewline
16 & 151 & 154.000101531291 & -3.00010153129111 \tabularnewline
17 & 171 & 151.000152340768 & 19.9998476592322 \tabularnewline
18 & 167 & 170.998984436988 & -3.99898443698766 \tabularnewline
19 & 144 & 167.000203062581 & -23.0002030625808 \tabularnewline
20 & 138 & 144.001167916671 & -6.00116791667142 \tabularnewline
21 & 138 & 138.000304730530 & -0.000304730529506969 \tabularnewline
22 & 132 & 138.000000015474 & -6.00000001547377 \tabularnewline
23 & 132 & 132.000304671225 & -0.000304671225194397 \tabularnewline
24 & 132 & 132.000000015471 & -1.54707606725424e-08 \tabularnewline
25 & 125 & 132.000000000001 & -7.0000000000008 \tabularnewline
26 & 131 & 125.000355449762 & 5.9996445502382 \tabularnewline
27 & 129 & 130.999695346825 & -1.99969534682481 \tabularnewline
28 & 131 & 129.000101541605 & 1.99989845839505 \tabularnewline
29 & 145 & 130.999898448081 & 14.0001015519187 \tabularnewline
30 & 156 & 144.999289095320 & 11.0007109046803 \tabularnewline
31 & 126 & 155.99944139999 & -29.9994413999899 \tabularnewline
32 & 123 & 126.001523327757 & -3.0015233277571 \tabularnewline
33 & 127 & 123.000152412965 & 3.99984758703545 \tabularnewline
34 & 116 & 126.999796893590 & -10.9997968935897 \tabularnewline
35 & 114 & 116.000558553598 & -2.00055855359795 \tabularnewline
36 & 114 & 114.000101585437 & -0.000101585437334961 \tabularnewline
37 & 109 & 114.000000005158 & -5.00000000515837 \tabularnewline
38 & 110 & 109.000253892687 & 0.999746107312731 \tabularnewline
39 & 113 & 109.999949234355 & 3.0000507656451 \tabularnewline
40 & 114 & 112.99984766181 & 1.00015233819001 \tabularnewline
41 & 138 & 113.999949213727 & 24.0000507862729 \tabularnewline
42 & 155 & 137.998781312524 & 17.0012186874764 \tabularnewline
43 & 126 & 154.999136702981 & -28.9991367029810 \tabularnewline
44 & 123 & 126.001472533748 & -3.00147253374763 \tabularnewline
45 & 124 & 123.000152410385 & 0.999847589614689 \tabularnewline
46 & 124 & 123.999949229202 & 5.07707982251304e-05 \tabularnewline
47 & 134 & 123.999999997422 & 10.0000000025781 \tabularnewline
48 & 131 & 133.999492214626 & -2.99949221462586 \tabularnewline
49 & 126 & 131.000152309828 & -5.0001523098276 \tabularnewline
50 & 128 & 126.000253900421 & 1.99974609957893 \tabularnewline
51 & 128 & 127.999898455818 & 0.000101544182101065 \tabularnewline
52 & 124 & 127.999999994844 & -3.99999999484373 \tabularnewline
53 & 148 & 124.000203114149 & 23.9997968858507 \tabularnewline
54 & 174 & 147.998781325416 & 26.0012186745838 \tabularnewline
55 & 146 & 173.998679696145 & -27.9986796961451 \tabularnewline
56 & 137 & 146.001421732004 & -9.00142173200408 \tabularnewline
57 & 152 & 137.00045707903 & 14.9995429209699 \tabularnewline
58 & 159 & 151.999238345149 & 7.0007616548512 \tabularnewline
59 & 170 & 158.999644511562 & 11.0003554884375 \tabularnewline
60 & 166 & 169.999441418037 & -3.99944141803741 \tabularnewline
61 & 165 & 166.000203085786 & -1.00020308578561 \tabularnewline
62 & 168 & 165.000050788850 & 2.99994921115021 \tabularnewline
63 & 175 & 167.999847666967 & 7.00015233303321 \tabularnewline
64 & 180 & 174.999644542503 & 5.00035545749705 \tabularnewline
65 & 199 & 179.999746089263 & 19.0002539107366 \tabularnewline
66 & 228 & 198.999035194896 & 29.0009648051038 \tabularnewline
67 & 206 & 227.998527373424 & -21.9985273734240 \tabularnewline
68 & 193 & 206.001117053045 & -13.0011170530450 \tabularnewline
69 & 201 & 193.000660177709 & 7.99933982229146 \tabularnewline
70 & 214 & 200.999593805224 & 13.0004061947763 \tabularnewline
71 & 225 & 213.999339858388 & 11.0006601416122 \tabularnewline
72 & 224 & 224.999441402568 & -0.999441402567584 \tabularnewline
73 & 215 & 224.000050750173 & -9.00005075017265 \tabularnewline
74 & 222 & 215.000457009414 & 6.99954299058638 \tabularnewline
75 & 238 & 221.999644573444 & 16.0003554265555 \tabularnewline
76 & 248 & 237.999187525354 & 10.0008124746464 \tabularnewline
77 & 262 & 247.99949217337 & 14.0005078266303 \tabularnewline
78 & 288 & 261.999289074690 & 26.0007109253103 \tabularnewline
79 & 261 & 287.998679721928 & -26.9986797219279 \tabularnewline
80 & 240 & 261.001370953468 & -21.001370953468 \tabularnewline
81 & 248 & 240.001066418900 & 7.9989335810996 \tabularnewline
82 & 260 & 247.999593825852 & 12.000406174148 \tabularnewline
83 & 266 & 259.999390636926 & 6.00060936307375 \tabularnewline
84 & 268 & 265.999695297833 & 2.00030470216694 \tabularnewline
85 & 256 & 267.999898427453 & -11.9998984274529 \tabularnewline
86 & 261 & 256.000609337291 & 4.99939066270889 \tabularnewline
87 & 287 & 260.999746138254 & 26.0002538617458 \tabularnewline
88 & 295 & 286.998679745137 & 8.00132025486312 \tabularnewline
89 & 304 & 294.99959370466 & 9.00040629533981 \tabularnewline
90 & 331 & 303.999542972532 & 27.0004570274677 \tabularnewline
91 & 299 & 330.998628956283 & -31.998628956283 \tabularnewline
92 & 275 & 299.001624843577 & -24.0016248435772 \tabularnewline
93 & 293 & 275.001218767405 & 17.9987812325953 \tabularnewline
94 & 309 & 292.999086048214 & 16.0009139517859 \tabularnewline
95 & 311 & 308.999187496992 & 2.00081250300752 \tabularnewline
96 & 311 & 310.999898401667 & 0.000101598332548747 \tabularnewline
97 & 289 & 310.999999994841 & -21.9999999948409 \tabularnewline
98 & 298 & 289.001117127823 & 8.99888287217749 \tabularnewline
99 & 319 & 297.999543049889 & 21.0004569501105 \tabularnewline
100 & 325 & 318.998933627511 & 6.00106637248865 \tabularnewline
101 & 331 & 324.999695274627 & 6.00030472537327 \tabularnewline
102 & 348 & 330.999695313302 & 17.0003046866979 \tabularnewline
103 & 320 & 347.999136749393 & -27.9991367493926 \tabularnewline
104 & 305 & 320.001421755213 & -15.0014217552126 \tabularnewline
105 & 322 & 305.000761750256 & 16.9992382497444 \tabularnewline
106 & 337 & 321.999136803545 & 15.0008631964553 \tabularnewline
107 & 346 & 336.999238278107 & 9.00076172189284 \tabularnewline
108 & 343 & 345.999542954484 & -2.99954295448424 \tabularnewline
109 & 321 & 343.000152312404 & -22.0001523124041 \tabularnewline
110 & 331 & 321.001117135557 & 9.99888286444303 \tabularnewline
111 & 343 & 330.999492271352 & 12.0005077286475 \tabularnewline
112 & 345 & 342.999390631769 & 2.00060936823053 \tabularnewline
113 & 347 & 344.999898411982 & 2.00010158801763 \tabularnewline
114 & 363 & 346.999898437767 & 16.0001015622333 \tabularnewline
115 & 322 & 362.999187538244 & -40.9991875382444 \tabularnewline
116 & 304 & 322.002081878778 & -18.0020818787777 \tabularnewline
117 & 323 & 304.000914119388 & 18.9990858806121 \tabularnewline
118 & 340 & 322.999035254207 & 17.0009647457929 \tabularnewline
119 & 352 & 339.999136715876 & 12.0008632841242 \tabularnewline
120 & 351 & 351.999390613715 & -0.999390613714866 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79353&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]158[/C][C]159[/C][C]-1[/C][/ROW]
[ROW][C]3[/C][C]157[/C][C]158.000050778537[/C][C]-1.0000507785374[/C][/ROW]
[ROW][C]4[/C][C]155[/C][C]157.000050781116[/C][C]-2.00005078111585[/C][/ROW]
[ROW][C]5[/C][C]175[/C][C]155.000101559653[/C][C]19.9998984403466[/C][/ROW]
[ROW][C]6[/C][C]174[/C][C]174.998984434409[/C][C]-0.998984434409039[/C][/ROW]
[ROW][C]7[/C][C]159[/C][C]174.000050726968[/C][C]-15.0000507269685[/C][/ROW]
[ROW][C]8[/C][C]149[/C][C]159.000761680637[/C][C]-10.0007616806368[/C][/ROW]
[ROW][C]9[/C][C]150[/C][C]149.000507824051[/C][C]0.999492175948973[/C][/ROW]
[ROW][C]10[/C][C]150[/C][C]149.999949247249[/C][C]5.07527508375460e-05[/C][/ROW]
[ROW][C]11[/C][C]151[/C][C]149.999999997423[/C][C]1.00000000257717[/C][/ROW]
[ROW][C]12[/C][C]153[/C][C]150.999949221462[/C][C]2.00005077853754[/C][/ROW]
[ROW][C]13[/C][C]146[/C][C]152.999898440347[/C][C]-6.99989844034673[/C][/ROW]
[ROW][C]14[/C][C]156[/C][C]146.000355444605[/C][C]9.99964455539526[/C][/ROW]
[ROW][C]15[/C][C]154[/C][C]155.999492232675[/C][C]-1.99949223267495[/C][/ROW]
[ROW][C]16[/C][C]151[/C][C]154.000101531291[/C][C]-3.00010153129111[/C][/ROW]
[ROW][C]17[/C][C]171[/C][C]151.000152340768[/C][C]19.9998476592322[/C][/ROW]
[ROW][C]18[/C][C]167[/C][C]170.998984436988[/C][C]-3.99898443698766[/C][/ROW]
[ROW][C]19[/C][C]144[/C][C]167.000203062581[/C][C]-23.0002030625808[/C][/ROW]
[ROW][C]20[/C][C]138[/C][C]144.001167916671[/C][C]-6.00116791667142[/C][/ROW]
[ROW][C]21[/C][C]138[/C][C]138.000304730530[/C][C]-0.000304730529506969[/C][/ROW]
[ROW][C]22[/C][C]132[/C][C]138.000000015474[/C][C]-6.00000001547377[/C][/ROW]
[ROW][C]23[/C][C]132[/C][C]132.000304671225[/C][C]-0.000304671225194397[/C][/ROW]
[ROW][C]24[/C][C]132[/C][C]132.000000015471[/C][C]-1.54707606725424e-08[/C][/ROW]
[ROW][C]25[/C][C]125[/C][C]132.000000000001[/C][C]-7.0000000000008[/C][/ROW]
[ROW][C]26[/C][C]131[/C][C]125.000355449762[/C][C]5.9996445502382[/C][/ROW]
[ROW][C]27[/C][C]129[/C][C]130.999695346825[/C][C]-1.99969534682481[/C][/ROW]
[ROW][C]28[/C][C]131[/C][C]129.000101541605[/C][C]1.99989845839505[/C][/ROW]
[ROW][C]29[/C][C]145[/C][C]130.999898448081[/C][C]14.0001015519187[/C][/ROW]
[ROW][C]30[/C][C]156[/C][C]144.999289095320[/C][C]11.0007109046803[/C][/ROW]
[ROW][C]31[/C][C]126[/C][C]155.99944139999[/C][C]-29.9994413999899[/C][/ROW]
[ROW][C]32[/C][C]123[/C][C]126.001523327757[/C][C]-3.0015233277571[/C][/ROW]
[ROW][C]33[/C][C]127[/C][C]123.000152412965[/C][C]3.99984758703545[/C][/ROW]
[ROW][C]34[/C][C]116[/C][C]126.999796893590[/C][C]-10.9997968935897[/C][/ROW]
[ROW][C]35[/C][C]114[/C][C]116.000558553598[/C][C]-2.00055855359795[/C][/ROW]
[ROW][C]36[/C][C]114[/C][C]114.000101585437[/C][C]-0.000101585437334961[/C][/ROW]
[ROW][C]37[/C][C]109[/C][C]114.000000005158[/C][C]-5.00000000515837[/C][/ROW]
[ROW][C]38[/C][C]110[/C][C]109.000253892687[/C][C]0.999746107312731[/C][/ROW]
[ROW][C]39[/C][C]113[/C][C]109.999949234355[/C][C]3.0000507656451[/C][/ROW]
[ROW][C]40[/C][C]114[/C][C]112.99984766181[/C][C]1.00015233819001[/C][/ROW]
[ROW][C]41[/C][C]138[/C][C]113.999949213727[/C][C]24.0000507862729[/C][/ROW]
[ROW][C]42[/C][C]155[/C][C]137.998781312524[/C][C]17.0012186874764[/C][/ROW]
[ROW][C]43[/C][C]126[/C][C]154.999136702981[/C][C]-28.9991367029810[/C][/ROW]
[ROW][C]44[/C][C]123[/C][C]126.001472533748[/C][C]-3.00147253374763[/C][/ROW]
[ROW][C]45[/C][C]124[/C][C]123.000152410385[/C][C]0.999847589614689[/C][/ROW]
[ROW][C]46[/C][C]124[/C][C]123.999949229202[/C][C]5.07707982251304e-05[/C][/ROW]
[ROW][C]47[/C][C]134[/C][C]123.999999997422[/C][C]10.0000000025781[/C][/ROW]
[ROW][C]48[/C][C]131[/C][C]133.999492214626[/C][C]-2.99949221462586[/C][/ROW]
[ROW][C]49[/C][C]126[/C][C]131.000152309828[/C][C]-5.0001523098276[/C][/ROW]
[ROW][C]50[/C][C]128[/C][C]126.000253900421[/C][C]1.99974609957893[/C][/ROW]
[ROW][C]51[/C][C]128[/C][C]127.999898455818[/C][C]0.000101544182101065[/C][/ROW]
[ROW][C]52[/C][C]124[/C][C]127.999999994844[/C][C]-3.99999999484373[/C][/ROW]
[ROW][C]53[/C][C]148[/C][C]124.000203114149[/C][C]23.9997968858507[/C][/ROW]
[ROW][C]54[/C][C]174[/C][C]147.998781325416[/C][C]26.0012186745838[/C][/ROW]
[ROW][C]55[/C][C]146[/C][C]173.998679696145[/C][C]-27.9986796961451[/C][/ROW]
[ROW][C]56[/C][C]137[/C][C]146.001421732004[/C][C]-9.00142173200408[/C][/ROW]
[ROW][C]57[/C][C]152[/C][C]137.00045707903[/C][C]14.9995429209699[/C][/ROW]
[ROW][C]58[/C][C]159[/C][C]151.999238345149[/C][C]7.0007616548512[/C][/ROW]
[ROW][C]59[/C][C]170[/C][C]158.999644511562[/C][C]11.0003554884375[/C][/ROW]
[ROW][C]60[/C][C]166[/C][C]169.999441418037[/C][C]-3.99944141803741[/C][/ROW]
[ROW][C]61[/C][C]165[/C][C]166.000203085786[/C][C]-1.00020308578561[/C][/ROW]
[ROW][C]62[/C][C]168[/C][C]165.000050788850[/C][C]2.99994921115021[/C][/ROW]
[ROW][C]63[/C][C]175[/C][C]167.999847666967[/C][C]7.00015233303321[/C][/ROW]
[ROW][C]64[/C][C]180[/C][C]174.999644542503[/C][C]5.00035545749705[/C][/ROW]
[ROW][C]65[/C][C]199[/C][C]179.999746089263[/C][C]19.0002539107366[/C][/ROW]
[ROW][C]66[/C][C]228[/C][C]198.999035194896[/C][C]29.0009648051038[/C][/ROW]
[ROW][C]67[/C][C]206[/C][C]227.998527373424[/C][C]-21.9985273734240[/C][/ROW]
[ROW][C]68[/C][C]193[/C][C]206.001117053045[/C][C]-13.0011170530450[/C][/ROW]
[ROW][C]69[/C][C]201[/C][C]193.000660177709[/C][C]7.99933982229146[/C][/ROW]
[ROW][C]70[/C][C]214[/C][C]200.999593805224[/C][C]13.0004061947763[/C][/ROW]
[ROW][C]71[/C][C]225[/C][C]213.999339858388[/C][C]11.0006601416122[/C][/ROW]
[ROW][C]72[/C][C]224[/C][C]224.999441402568[/C][C]-0.999441402567584[/C][/ROW]
[ROW][C]73[/C][C]215[/C][C]224.000050750173[/C][C]-9.00005075017265[/C][/ROW]
[ROW][C]74[/C][C]222[/C][C]215.000457009414[/C][C]6.99954299058638[/C][/ROW]
[ROW][C]75[/C][C]238[/C][C]221.999644573444[/C][C]16.0003554265555[/C][/ROW]
[ROW][C]76[/C][C]248[/C][C]237.999187525354[/C][C]10.0008124746464[/C][/ROW]
[ROW][C]77[/C][C]262[/C][C]247.99949217337[/C][C]14.0005078266303[/C][/ROW]
[ROW][C]78[/C][C]288[/C][C]261.999289074690[/C][C]26.0007109253103[/C][/ROW]
[ROW][C]79[/C][C]261[/C][C]287.998679721928[/C][C]-26.9986797219279[/C][/ROW]
[ROW][C]80[/C][C]240[/C][C]261.001370953468[/C][C]-21.001370953468[/C][/ROW]
[ROW][C]81[/C][C]248[/C][C]240.001066418900[/C][C]7.9989335810996[/C][/ROW]
[ROW][C]82[/C][C]260[/C][C]247.999593825852[/C][C]12.000406174148[/C][/ROW]
[ROW][C]83[/C][C]266[/C][C]259.999390636926[/C][C]6.00060936307375[/C][/ROW]
[ROW][C]84[/C][C]268[/C][C]265.999695297833[/C][C]2.00030470216694[/C][/ROW]
[ROW][C]85[/C][C]256[/C][C]267.999898427453[/C][C]-11.9998984274529[/C][/ROW]
[ROW][C]86[/C][C]261[/C][C]256.000609337291[/C][C]4.99939066270889[/C][/ROW]
[ROW][C]87[/C][C]287[/C][C]260.999746138254[/C][C]26.0002538617458[/C][/ROW]
[ROW][C]88[/C][C]295[/C][C]286.998679745137[/C][C]8.00132025486312[/C][/ROW]
[ROW][C]89[/C][C]304[/C][C]294.99959370466[/C][C]9.00040629533981[/C][/ROW]
[ROW][C]90[/C][C]331[/C][C]303.999542972532[/C][C]27.0004570274677[/C][/ROW]
[ROW][C]91[/C][C]299[/C][C]330.998628956283[/C][C]-31.998628956283[/C][/ROW]
[ROW][C]92[/C][C]275[/C][C]299.001624843577[/C][C]-24.0016248435772[/C][/ROW]
[ROW][C]93[/C][C]293[/C][C]275.001218767405[/C][C]17.9987812325953[/C][/ROW]
[ROW][C]94[/C][C]309[/C][C]292.999086048214[/C][C]16.0009139517859[/C][/ROW]
[ROW][C]95[/C][C]311[/C][C]308.999187496992[/C][C]2.00081250300752[/C][/ROW]
[ROW][C]96[/C][C]311[/C][C]310.999898401667[/C][C]0.000101598332548747[/C][/ROW]
[ROW][C]97[/C][C]289[/C][C]310.999999994841[/C][C]-21.9999999948409[/C][/ROW]
[ROW][C]98[/C][C]298[/C][C]289.001117127823[/C][C]8.99888287217749[/C][/ROW]
[ROW][C]99[/C][C]319[/C][C]297.999543049889[/C][C]21.0004569501105[/C][/ROW]
[ROW][C]100[/C][C]325[/C][C]318.998933627511[/C][C]6.00106637248865[/C][/ROW]
[ROW][C]101[/C][C]331[/C][C]324.999695274627[/C][C]6.00030472537327[/C][/ROW]
[ROW][C]102[/C][C]348[/C][C]330.999695313302[/C][C]17.0003046866979[/C][/ROW]
[ROW][C]103[/C][C]320[/C][C]347.999136749393[/C][C]-27.9991367493926[/C][/ROW]
[ROW][C]104[/C][C]305[/C][C]320.001421755213[/C][C]-15.0014217552126[/C][/ROW]
[ROW][C]105[/C][C]322[/C][C]305.000761750256[/C][C]16.9992382497444[/C][/ROW]
[ROW][C]106[/C][C]337[/C][C]321.999136803545[/C][C]15.0008631964553[/C][/ROW]
[ROW][C]107[/C][C]346[/C][C]336.999238278107[/C][C]9.00076172189284[/C][/ROW]
[ROW][C]108[/C][C]343[/C][C]345.999542954484[/C][C]-2.99954295448424[/C][/ROW]
[ROW][C]109[/C][C]321[/C][C]343.000152312404[/C][C]-22.0001523124041[/C][/ROW]
[ROW][C]110[/C][C]331[/C][C]321.001117135557[/C][C]9.99888286444303[/C][/ROW]
[ROW][C]111[/C][C]343[/C][C]330.999492271352[/C][C]12.0005077286475[/C][/ROW]
[ROW][C]112[/C][C]345[/C][C]342.999390631769[/C][C]2.00060936823053[/C][/ROW]
[ROW][C]113[/C][C]347[/C][C]344.999898411982[/C][C]2.00010158801763[/C][/ROW]
[ROW][C]114[/C][C]363[/C][C]346.999898437767[/C][C]16.0001015622333[/C][/ROW]
[ROW][C]115[/C][C]322[/C][C]362.999187538244[/C][C]-40.9991875382444[/C][/ROW]
[ROW][C]116[/C][C]304[/C][C]322.002081878778[/C][C]-18.0020818787777[/C][/ROW]
[ROW][C]117[/C][C]323[/C][C]304.000914119388[/C][C]18.9990858806121[/C][/ROW]
[ROW][C]118[/C][C]340[/C][C]322.999035254207[/C][C]17.0009647457929[/C][/ROW]
[ROW][C]119[/C][C]352[/C][C]339.999136715876[/C][C]12.0008632841242[/C][/ROW]
[ROW][C]120[/C][C]351[/C][C]351.999390613715[/C][C]-0.999390613714866[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79353&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79353&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
2158159-1
3157158.000050778537-1.0000507785374
4155157.000050781116-2.00005078111585
5175155.00010155965319.9998984403466
6174174.998984434409-0.998984434409039
7159174.000050726968-15.0000507269685
8149159.000761680637-10.0007616806368
9150149.0005078240510.999492175948973
10150149.9999492472495.07527508375460e-05
11151149.9999999974231.00000000257717
12153150.9999492214622.00005077853754
13146152.999898440347-6.99989844034673
14156146.0003554446059.99964455539526
15154155.999492232675-1.99949223267495
16151154.000101531291-3.00010153129111
17171151.00015234076819.9998476592322
18167170.998984436988-3.99898443698766
19144167.000203062581-23.0002030625808
20138144.001167916671-6.00116791667142
21138138.000304730530-0.000304730529506969
22132138.000000015474-6.00000001547377
23132132.000304671225-0.000304671225194397
24132132.000000015471-1.54707606725424e-08
25125132.000000000001-7.0000000000008
26131125.0003554497625.9996445502382
27129130.999695346825-1.99969534682481
28131129.0001015416051.99989845839505
29145130.99989844808114.0001015519187
30156144.99928909532011.0007109046803
31126155.99944139999-29.9994413999899
32123126.001523327757-3.0015233277571
33127123.0001524129653.99984758703545
34116126.999796893590-10.9997968935897
35114116.000558553598-2.00055855359795
36114114.000101585437-0.000101585437334961
37109114.000000005158-5.00000000515837
38110109.0002538926870.999746107312731
39113109.9999492343553.0000507656451
40114112.999847661811.00015233819001
41138113.99994921372724.0000507862729
42155137.99878131252417.0012186874764
43126154.999136702981-28.9991367029810
44123126.001472533748-3.00147253374763
45124123.0001524103850.999847589614689
46124123.9999492292025.07707982251304e-05
47134123.99999999742210.0000000025781
48131133.999492214626-2.99949221462586
49126131.000152309828-5.0001523098276
50128126.0002539004211.99974609957893
51128127.9998984558180.000101544182101065
52124127.999999994844-3.99999999484373
53148124.00020311414923.9997968858507
54174147.99878132541626.0012186745838
55146173.998679696145-27.9986796961451
56137146.001421732004-9.00142173200408
57152137.0004570790314.9995429209699
58159151.9992383451497.0007616548512
59170158.99964451156211.0003554884375
60166169.999441418037-3.99944141803741
61165166.000203085786-1.00020308578561
62168165.0000507888502.99994921115021
63175167.9998476669677.00015233303321
64180174.9996445425035.00035545749705
65199179.99974608926319.0002539107366
66228198.99903519489629.0009648051038
67206227.998527373424-21.9985273734240
68193206.001117053045-13.0011170530450
69201193.0006601777097.99933982229146
70214200.99959380522413.0004061947763
71225213.99933985838811.0006601416122
72224224.999441402568-0.999441402567584
73215224.000050750173-9.00005075017265
74222215.0004570094146.99954299058638
75238221.99964457344416.0003554265555
76248237.99918752535410.0008124746464
77262247.9994921733714.0005078266303
78288261.99928907469026.0007109253103
79261287.998679721928-26.9986797219279
80240261.001370953468-21.001370953468
81248240.0010664189007.9989335810996
82260247.99959382585212.000406174148
83266259.9993906369266.00060936307375
84268265.9996952978332.00030470216694
85256267.999898427453-11.9998984274529
86261256.0006093372914.99939066270889
87287260.99974613825426.0002538617458
88295286.9986797451378.00132025486312
89304294.999593704669.00040629533981
90331303.99954297253227.0004570274677
91299330.998628956283-31.998628956283
92275299.001624843577-24.0016248435772
93293275.00121876740517.9987812325953
94309292.99908604821416.0009139517859
95311308.9991874969922.00081250300752
96311310.9998984016670.000101598332548747
97289310.999999994841-21.9999999948409
98298289.0011171278238.99888287217749
99319297.99954304988921.0004569501105
100325318.9989336275116.00106637248865
101331324.9996952746276.00030472537327
102348330.99969531330217.0003046866979
103320347.999136749393-27.9991367493926
104305320.001421755213-15.0014217552126
105322305.00076175025616.9992382497444
106337321.99913680354515.0008631964553
107346336.9992382781079.00076172189284
108343345.999542954484-2.99954295448424
109321343.000152312404-22.0001523124041
110331321.0011171355579.99888286444303
111343330.99949227135212.0005077286475
112345342.9993906317692.00060936823053
113347344.9998984119822.00010158801763
114363346.99989843776716.0001015622333
115322362.999187538244-40.9991875382444
116304322.002081878778-18.0020818787777
117323304.00091411938818.9990858806121
118340322.99903525420717.0009647457929
119352339.99913671587612.0008632841242
120351351.999390613715-0.999390613714866







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121351.000050747594323.490412931058378.509688564129
122351.000050747594312.096535595816389.903565899372
123351.000050747594303.353573338111398.646528157076
124351.000050747594295.982870449981406.017231045206
125351.000050747594289.489129389938412.510972105249
126351.000050747594283.618326484739418.381775010448
127351.000050747594278.219558285650423.780543209537
128351.000050747594273.194502093461428.805599401727
129351.000050747594268.474862351939433.525239143249
130351.000050747594264.010913275688437.989188219499
131351.000050747594259.76511579133442.234985703857
132351.000050747594255.708305696717446.291795798471

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 351.000050747594 & 323.490412931058 & 378.509688564129 \tabularnewline
122 & 351.000050747594 & 312.096535595816 & 389.903565899372 \tabularnewline
123 & 351.000050747594 & 303.353573338111 & 398.646528157076 \tabularnewline
124 & 351.000050747594 & 295.982870449981 & 406.017231045206 \tabularnewline
125 & 351.000050747594 & 289.489129389938 & 412.510972105249 \tabularnewline
126 & 351.000050747594 & 283.618326484739 & 418.381775010448 \tabularnewline
127 & 351.000050747594 & 278.219558285650 & 423.780543209537 \tabularnewline
128 & 351.000050747594 & 273.194502093461 & 428.805599401727 \tabularnewline
129 & 351.000050747594 & 268.474862351939 & 433.525239143249 \tabularnewline
130 & 351.000050747594 & 264.010913275688 & 437.989188219499 \tabularnewline
131 & 351.000050747594 & 259.76511579133 & 442.234985703857 \tabularnewline
132 & 351.000050747594 & 255.708305696717 & 446.291795798471 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79353&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]351.000050747594[/C][C]323.490412931058[/C][C]378.509688564129[/C][/ROW]
[ROW][C]122[/C][C]351.000050747594[/C][C]312.096535595816[/C][C]389.903565899372[/C][/ROW]
[ROW][C]123[/C][C]351.000050747594[/C][C]303.353573338111[/C][C]398.646528157076[/C][/ROW]
[ROW][C]124[/C][C]351.000050747594[/C][C]295.982870449981[/C][C]406.017231045206[/C][/ROW]
[ROW][C]125[/C][C]351.000050747594[/C][C]289.489129389938[/C][C]412.510972105249[/C][/ROW]
[ROW][C]126[/C][C]351.000050747594[/C][C]283.618326484739[/C][C]418.381775010448[/C][/ROW]
[ROW][C]127[/C][C]351.000050747594[/C][C]278.219558285650[/C][C]423.780543209537[/C][/ROW]
[ROW][C]128[/C][C]351.000050747594[/C][C]273.194502093461[/C][C]428.805599401727[/C][/ROW]
[ROW][C]129[/C][C]351.000050747594[/C][C]268.474862351939[/C][C]433.525239143249[/C][/ROW]
[ROW][C]130[/C][C]351.000050747594[/C][C]264.010913275688[/C][C]437.989188219499[/C][/ROW]
[ROW][C]131[/C][C]351.000050747594[/C][C]259.76511579133[/C][C]442.234985703857[/C][/ROW]
[ROW][C]132[/C][C]351.000050747594[/C][C]255.708305696717[/C][C]446.291795798471[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79353&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79353&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
121351.000050747594323.490412931058378.509688564129
122351.000050747594312.096535595816389.903565899372
123351.000050747594303.353573338111398.646528157076
124351.000050747594295.982870449981406.017231045206
125351.000050747594289.489129389938412.510972105249
126351.000050747594283.618326484739418.381775010448
127351.000050747594278.219558285650423.780543209537
128351.000050747594273.194502093461428.805599401727
129351.000050747594268.474862351939433.525239143249
130351.000050747594264.010913275688437.989188219499
131351.000050747594259.76511579133442.234985703857
132351.000050747594255.708305696717446.291795798471



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