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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 29 Dec 2010 21:45:07 +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/Dec/29/t12936590471x22j3m6ly7gfgg.htm/, Retrieved Fri, 03 May 2024 06:14:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117142, Retrieved Fri, 03 May 2024 06:14:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [Unemployment] [2010-11-30 13:37:23] [b98453cac15ba1066b407e146608df68]
- R  D    [Exponential Smoothing] [Exponential Smoot...] [2010-12-27 15:14:01] [17d39bb3ec485d4ce196f61215d11ba1]
-             [Exponential Smoothing] [Exponential Smoot...] [2010-12-29 21:45:07] [5d543145eb38bc0730d6bf6b0284f470] [Current]
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Dataseries X:
206010
198112
194519
185705
180173
176142
203401
221902
197378
185001
176356
180449
180144
173666
165688
161570
156145
153730
182698
200765
176512
166618
158644
159585
163095
159044
155511
153745
150569
150605
179612
194690
189917
184128
175335
179566
181140
177876
175041
169292
166070
166972
206348
215706
202108
195411
193111
195198
198770
194163
190420
189733
186029
191531
232571
243477
227247
217859
208679
213188
216234
213586
209465
204045
200237
203666
241476
260307
243324
244460
233575
237217
235243
230354
227184
221678
217142
219452
256446
265845
248624
241114
229245
231805
219277
219313
212610
214771
211142
211457
240048
240636
230580
208795
197922
194596
194581
185686
178106
172608
167302
168053
202300
202388
182516
173476
166444
171297
169701
164182
161914
159612
151001
158114
186530
187069
174330
169362
166827
178037
186413
189226
191563
188906
186005
195309
223532
226899
214126
206903
204442
220375
214320
212588
205816
202196
195722
198563
229139
229527
211868
203555
195770




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117142&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117142&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117142&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 time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.786721671208237
beta0.155737227444934
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.786721671208237 \tabularnewline
beta & 0.155737227444934 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117142&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]0.786721671208237[/C][/ROW]
[ROW][C]beta[/C][C]0.155737227444934[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117142&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117142&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
alpha0.786721671208237
beta0.155737227444934
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13180144192256.77590812-12112.7759081197
14173666174646.428106397-980.428106396546
15165688164180.8073711871507.19262881341
16161570159602.1658100821967.83418991757
17156145154188.6069701641956.39302983636
18153730152119.1230186171610.87698138296
19182698179952.3484015222745.65159847814
20200765200442.561219332322.438780667988
21176512176164.427462602347.572537397995
22166618164082.6938745692535.30612543056
23158644157564.6031125531079.39688744652
24159585162699.575040562-3114.57504056211
25163095157033.5205933086061.47940669156
26159044158060.686855116983.313144883898
27155511151876.2857412753634.71425872456
28153745151536.0705339162208.92946608434
29150569148805.6999799931763.30002000669
30150605148982.9099334391622.09006656095
31179612179540.64902107471.3509789262025
32194690199556.1218355-4866.12183550018
33189917172711.69245961517205.3075403846
34184128177934.6383742216193.36162577895
35175335178007.834878522-2672.83487852153
36179566182860.560671384-3294.56067138413
37181140182552.108246818-1412.10824681763
38177876179243.047588606-1367.04758860619
39175041174113.551861834927.448138166044
40169292173346.18218413-4054.18218412981
41166070166832.87427879-762.874278790143
42166972165922.4910065951049.50899340509
43206348196558.7952843899789.20471561147
44215706225216.873886494-9510.87388649434
45202108200907.0069691031200.99303089728
46195411190710.8561367064700.14386329436
47193111187055.8402206386055.1597793616
48195198199049.339913743-3851.339913743
49198770199042.997871197-272.997871196945
50194163197117.93077686-2954.93077686024
51190420191512.249043427-1092.2490434272
52189733188129.6788898931603.32111010668
53186029187498.596717085-1469.59671708496
54191531187061.5533571314469.44664286866
55232571223314.1931842799256.80681572098
56243477248433.712722975-4956.712722975
57227247231545.874832781-4298.87483278071
58217859218649.860480711-790.860480711417
59208679211171.888635607-2492.88863560685
60213188213488.229628962-300.229628961562
61216234216634.512356744-400.51235674409
62213586213617.211916038-31.211916037777
63209465210647.255498068-1182.25549806794
64204045207696.056936062-3651.05693606203
65200237201559.353700861-1322.35370086058
66203666201806.3581361031859.64186389704
67241476236008.6293294935467.37067050653
68260307253632.974070166674.02592983964
69243324245978.10496673-2654.1049667302
70244460235268.2824712669191.71752873395
71233575236647.931624635-3072.93162463498
72237217240271.63520002-3054.63520001969
73235243242188.152693052-6945.15269305155
74230354234257.517648547-3903.51764854742
75227184227677.911670693-493.911670693051
76221678224508.313359514-2830.31335951379
77217142219381.134929034-2239.13492903442
78219452219340.378779068111.621220931673
79256446252477.5642737663968.4357262344
80265845268537.035194253-2692.03519425297
81248624249733.664875924-1109.66487592363
82241114241164.041968422-50.0419684220105
83229245229923.595156386-678.595156385709
84231805232994.61627415-1189.61627415035
85219277233336.866000631-14059.8660006305
86219313217374.183298221938.81670178048
87212610213750.413699219-1140.41369921915
88214771207127.0340285967643.96597140448
89211142209202.7514305281939.24856947243
90211457212298.996501291-841.996501291404
91240048244740.097239514-4692.09723951353
92240636250736.072567315-10100.0725673146
93230580223704.9450285866875.05497141436
94208795219884.192553616-11089.1925536162
95197922196713.5364857431208.46351425743
96194596198279.950262188-3683.95026218813
97194581190729.0900505363851.90994946379
98185686191278.927945051-5592.92794505064
99178106179159.001172259-1053.00117225942
100172608172574.58126699833.4187330016284
101167302164610.4379122552691.56208774468
102168053164961.7541554043091.2458445956
103202300197414.3760947654885.62390523526
104202388208703.725659619-6315.72565961938
105182516187645.695259936-5129.6952599361
106173476168453.7592840065022.24071599363
107166444160459.7414514645984.25854853578
108171297165203.671089956093.32891004978
109169701168613.714556011087.28544399026
110164182166297.126878907-2115.12687890694
111161914159630.5798763552283.42012364493
112159612158060.5395547471551.46044525341
113151001154201.424991105-3200.42499110513
114158114151624.5621344916489.43786550936
115186530189171.601050891-2641.60105089133
116187069193266.148679687-6197.14867968677
117174330173684.922388921645.077611079323
118169362163039.4116295696322.58837043142
119166827158271.0023488318555.99765116919
120178037167373.95077015410663.0492298462
121186413176183.81580852910229.1841914707
122189226184368.8393573224857.16064267812
123191563188972.4008920422590.59910795817
124188906192372.294027718-3466.29402771773
125186005187821.724755116-1816.72475511601
126195309192839.2157924062469.78420759359
127223532229223.087110724-5691.08711072433
128226899233733.221800341-6834.22180034057
129214126218605.044575766-4479.04457576631
130206903208006.298620989-1103.29862098902
131204442199829.4202577154612.57974228458
132220375207753.52926872612621.4707312738
133214320219725.686840236-5405.68684023627
134212588214263.16287187-1675.16287187024
135205816212242.323659019-6426.32365901885
136202196205149.9623062-2953.96230619974
137195722199310.402816274-3588.40281627362
138198563201587.356456262-3024.35645626215
139229139228974.239624869164.760375131242
140229527235630.868228266-6103.86822826631
141211868219452.446170659-7584.44617065854
142203555204622.969306613-1067.96930661306
143195770195189.669246083580.330753916613

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 180144 & 192256.77590812 & -12112.7759081197 \tabularnewline
14 & 173666 & 174646.428106397 & -980.428106396546 \tabularnewline
15 & 165688 & 164180.807371187 & 1507.19262881341 \tabularnewline
16 & 161570 & 159602.165810082 & 1967.83418991757 \tabularnewline
17 & 156145 & 154188.606970164 & 1956.39302983636 \tabularnewline
18 & 153730 & 152119.123018617 & 1610.87698138296 \tabularnewline
19 & 182698 & 179952.348401522 & 2745.65159847814 \tabularnewline
20 & 200765 & 200442.561219332 & 322.438780667988 \tabularnewline
21 & 176512 & 176164.427462602 & 347.572537397995 \tabularnewline
22 & 166618 & 164082.693874569 & 2535.30612543056 \tabularnewline
23 & 158644 & 157564.603112553 & 1079.39688744652 \tabularnewline
24 & 159585 & 162699.575040562 & -3114.57504056211 \tabularnewline
25 & 163095 & 157033.520593308 & 6061.47940669156 \tabularnewline
26 & 159044 & 158060.686855116 & 983.313144883898 \tabularnewline
27 & 155511 & 151876.285741275 & 3634.71425872456 \tabularnewline
28 & 153745 & 151536.070533916 & 2208.92946608434 \tabularnewline
29 & 150569 & 148805.699979993 & 1763.30002000669 \tabularnewline
30 & 150605 & 148982.909933439 & 1622.09006656095 \tabularnewline
31 & 179612 & 179540.649021074 & 71.3509789262025 \tabularnewline
32 & 194690 & 199556.1218355 & -4866.12183550018 \tabularnewline
33 & 189917 & 172711.692459615 & 17205.3075403846 \tabularnewline
34 & 184128 & 177934.638374221 & 6193.36162577895 \tabularnewline
35 & 175335 & 178007.834878522 & -2672.83487852153 \tabularnewline
36 & 179566 & 182860.560671384 & -3294.56067138413 \tabularnewline
37 & 181140 & 182552.108246818 & -1412.10824681763 \tabularnewline
38 & 177876 & 179243.047588606 & -1367.04758860619 \tabularnewline
39 & 175041 & 174113.551861834 & 927.448138166044 \tabularnewline
40 & 169292 & 173346.18218413 & -4054.18218412981 \tabularnewline
41 & 166070 & 166832.87427879 & -762.874278790143 \tabularnewline
42 & 166972 & 165922.491006595 & 1049.50899340509 \tabularnewline
43 & 206348 & 196558.795284389 & 9789.20471561147 \tabularnewline
44 & 215706 & 225216.873886494 & -9510.87388649434 \tabularnewline
45 & 202108 & 200907.006969103 & 1200.99303089728 \tabularnewline
46 & 195411 & 190710.856136706 & 4700.14386329436 \tabularnewline
47 & 193111 & 187055.840220638 & 6055.1597793616 \tabularnewline
48 & 195198 & 199049.339913743 & -3851.339913743 \tabularnewline
49 & 198770 & 199042.997871197 & -272.997871196945 \tabularnewline
50 & 194163 & 197117.93077686 & -2954.93077686024 \tabularnewline
51 & 190420 & 191512.249043427 & -1092.2490434272 \tabularnewline
52 & 189733 & 188129.678889893 & 1603.32111010668 \tabularnewline
53 & 186029 & 187498.596717085 & -1469.59671708496 \tabularnewline
54 & 191531 & 187061.553357131 & 4469.44664286866 \tabularnewline
55 & 232571 & 223314.193184279 & 9256.80681572098 \tabularnewline
56 & 243477 & 248433.712722975 & -4956.712722975 \tabularnewline
57 & 227247 & 231545.874832781 & -4298.87483278071 \tabularnewline
58 & 217859 & 218649.860480711 & -790.860480711417 \tabularnewline
59 & 208679 & 211171.888635607 & -2492.88863560685 \tabularnewline
60 & 213188 & 213488.229628962 & -300.229628961562 \tabularnewline
61 & 216234 & 216634.512356744 & -400.51235674409 \tabularnewline
62 & 213586 & 213617.211916038 & -31.211916037777 \tabularnewline
63 & 209465 & 210647.255498068 & -1182.25549806794 \tabularnewline
64 & 204045 & 207696.056936062 & -3651.05693606203 \tabularnewline
65 & 200237 & 201559.353700861 & -1322.35370086058 \tabularnewline
66 & 203666 & 201806.358136103 & 1859.64186389704 \tabularnewline
67 & 241476 & 236008.629329493 & 5467.37067050653 \tabularnewline
68 & 260307 & 253632.97407016 & 6674.02592983964 \tabularnewline
69 & 243324 & 245978.10496673 & -2654.1049667302 \tabularnewline
70 & 244460 & 235268.282471266 & 9191.71752873395 \tabularnewline
71 & 233575 & 236647.931624635 & -3072.93162463498 \tabularnewline
72 & 237217 & 240271.63520002 & -3054.63520001969 \tabularnewline
73 & 235243 & 242188.152693052 & -6945.15269305155 \tabularnewline
74 & 230354 & 234257.517648547 & -3903.51764854742 \tabularnewline
75 & 227184 & 227677.911670693 & -493.911670693051 \tabularnewline
76 & 221678 & 224508.313359514 & -2830.31335951379 \tabularnewline
77 & 217142 & 219381.134929034 & -2239.13492903442 \tabularnewline
78 & 219452 & 219340.378779068 & 111.621220931673 \tabularnewline
79 & 256446 & 252477.564273766 & 3968.4357262344 \tabularnewline
80 & 265845 & 268537.035194253 & -2692.03519425297 \tabularnewline
81 & 248624 & 249733.664875924 & -1109.66487592363 \tabularnewline
82 & 241114 & 241164.041968422 & -50.0419684220105 \tabularnewline
83 & 229245 & 229923.595156386 & -678.595156385709 \tabularnewline
84 & 231805 & 232994.61627415 & -1189.61627415035 \tabularnewline
85 & 219277 & 233336.866000631 & -14059.8660006305 \tabularnewline
86 & 219313 & 217374.18329822 & 1938.81670178048 \tabularnewline
87 & 212610 & 213750.413699219 & -1140.41369921915 \tabularnewline
88 & 214771 & 207127.034028596 & 7643.96597140448 \tabularnewline
89 & 211142 & 209202.751430528 & 1939.24856947243 \tabularnewline
90 & 211457 & 212298.996501291 & -841.996501291404 \tabularnewline
91 & 240048 & 244740.097239514 & -4692.09723951353 \tabularnewline
92 & 240636 & 250736.072567315 & -10100.0725673146 \tabularnewline
93 & 230580 & 223704.945028586 & 6875.05497141436 \tabularnewline
94 & 208795 & 219884.192553616 & -11089.1925536162 \tabularnewline
95 & 197922 & 196713.536485743 & 1208.46351425743 \tabularnewline
96 & 194596 & 198279.950262188 & -3683.95026218813 \tabularnewline
97 & 194581 & 190729.090050536 & 3851.90994946379 \tabularnewline
98 & 185686 & 191278.927945051 & -5592.92794505064 \tabularnewline
99 & 178106 & 179159.001172259 & -1053.00117225942 \tabularnewline
100 & 172608 & 172574.581266998 & 33.4187330016284 \tabularnewline
101 & 167302 & 164610.437912255 & 2691.56208774468 \tabularnewline
102 & 168053 & 164961.754155404 & 3091.2458445956 \tabularnewline
103 & 202300 & 197414.376094765 & 4885.62390523526 \tabularnewline
104 & 202388 & 208703.725659619 & -6315.72565961938 \tabularnewline
105 & 182516 & 187645.695259936 & -5129.6952599361 \tabularnewline
106 & 173476 & 168453.759284006 & 5022.24071599363 \tabularnewline
107 & 166444 & 160459.741451464 & 5984.25854853578 \tabularnewline
108 & 171297 & 165203.67108995 & 6093.32891004978 \tabularnewline
109 & 169701 & 168613.71455601 & 1087.28544399026 \tabularnewline
110 & 164182 & 166297.126878907 & -2115.12687890694 \tabularnewline
111 & 161914 & 159630.579876355 & 2283.42012364493 \tabularnewline
112 & 159612 & 158060.539554747 & 1551.46044525341 \tabularnewline
113 & 151001 & 154201.424991105 & -3200.42499110513 \tabularnewline
114 & 158114 & 151624.562134491 & 6489.43786550936 \tabularnewline
115 & 186530 & 189171.601050891 & -2641.60105089133 \tabularnewline
116 & 187069 & 193266.148679687 & -6197.14867968677 \tabularnewline
117 & 174330 & 173684.922388921 & 645.077611079323 \tabularnewline
118 & 169362 & 163039.411629569 & 6322.58837043142 \tabularnewline
119 & 166827 & 158271.002348831 & 8555.99765116919 \tabularnewline
120 & 178037 & 167373.950770154 & 10663.0492298462 \tabularnewline
121 & 186413 & 176183.815808529 & 10229.1841914707 \tabularnewline
122 & 189226 & 184368.839357322 & 4857.16064267812 \tabularnewline
123 & 191563 & 188972.400892042 & 2590.59910795817 \tabularnewline
124 & 188906 & 192372.294027718 & -3466.29402771773 \tabularnewline
125 & 186005 & 187821.724755116 & -1816.72475511601 \tabularnewline
126 & 195309 & 192839.215792406 & 2469.78420759359 \tabularnewline
127 & 223532 & 229223.087110724 & -5691.08711072433 \tabularnewline
128 & 226899 & 233733.221800341 & -6834.22180034057 \tabularnewline
129 & 214126 & 218605.044575766 & -4479.04457576631 \tabularnewline
130 & 206903 & 208006.298620989 & -1103.29862098902 \tabularnewline
131 & 204442 & 199829.420257715 & 4612.57974228458 \tabularnewline
132 & 220375 & 207753.529268726 & 12621.4707312738 \tabularnewline
133 & 214320 & 219725.686840236 & -5405.68684023627 \tabularnewline
134 & 212588 & 214263.16287187 & -1675.16287187024 \tabularnewline
135 & 205816 & 212242.323659019 & -6426.32365901885 \tabularnewline
136 & 202196 & 205149.9623062 & -2953.96230619974 \tabularnewline
137 & 195722 & 199310.402816274 & -3588.40281627362 \tabularnewline
138 & 198563 & 201587.356456262 & -3024.35645626215 \tabularnewline
139 & 229139 & 228974.239624869 & 164.760375131242 \tabularnewline
140 & 229527 & 235630.868228266 & -6103.86822826631 \tabularnewline
141 & 211868 & 219452.446170659 & -7584.44617065854 \tabularnewline
142 & 203555 & 204622.969306613 & -1067.96930661306 \tabularnewline
143 & 195770 & 195189.669246083 & 580.330753916613 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117142&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]180144[/C][C]192256.77590812[/C][C]-12112.7759081197[/C][/ROW]
[ROW][C]14[/C][C]173666[/C][C]174646.428106397[/C][C]-980.428106396546[/C][/ROW]
[ROW][C]15[/C][C]165688[/C][C]164180.807371187[/C][C]1507.19262881341[/C][/ROW]
[ROW][C]16[/C][C]161570[/C][C]159602.165810082[/C][C]1967.83418991757[/C][/ROW]
[ROW][C]17[/C][C]156145[/C][C]154188.606970164[/C][C]1956.39302983636[/C][/ROW]
[ROW][C]18[/C][C]153730[/C][C]152119.123018617[/C][C]1610.87698138296[/C][/ROW]
[ROW][C]19[/C][C]182698[/C][C]179952.348401522[/C][C]2745.65159847814[/C][/ROW]
[ROW][C]20[/C][C]200765[/C][C]200442.561219332[/C][C]322.438780667988[/C][/ROW]
[ROW][C]21[/C][C]176512[/C][C]176164.427462602[/C][C]347.572537397995[/C][/ROW]
[ROW][C]22[/C][C]166618[/C][C]164082.693874569[/C][C]2535.30612543056[/C][/ROW]
[ROW][C]23[/C][C]158644[/C][C]157564.603112553[/C][C]1079.39688744652[/C][/ROW]
[ROW][C]24[/C][C]159585[/C][C]162699.575040562[/C][C]-3114.57504056211[/C][/ROW]
[ROW][C]25[/C][C]163095[/C][C]157033.520593308[/C][C]6061.47940669156[/C][/ROW]
[ROW][C]26[/C][C]159044[/C][C]158060.686855116[/C][C]983.313144883898[/C][/ROW]
[ROW][C]27[/C][C]155511[/C][C]151876.285741275[/C][C]3634.71425872456[/C][/ROW]
[ROW][C]28[/C][C]153745[/C][C]151536.070533916[/C][C]2208.92946608434[/C][/ROW]
[ROW][C]29[/C][C]150569[/C][C]148805.699979993[/C][C]1763.30002000669[/C][/ROW]
[ROW][C]30[/C][C]150605[/C][C]148982.909933439[/C][C]1622.09006656095[/C][/ROW]
[ROW][C]31[/C][C]179612[/C][C]179540.649021074[/C][C]71.3509789262025[/C][/ROW]
[ROW][C]32[/C][C]194690[/C][C]199556.1218355[/C][C]-4866.12183550018[/C][/ROW]
[ROW][C]33[/C][C]189917[/C][C]172711.692459615[/C][C]17205.3075403846[/C][/ROW]
[ROW][C]34[/C][C]184128[/C][C]177934.638374221[/C][C]6193.36162577895[/C][/ROW]
[ROW][C]35[/C][C]175335[/C][C]178007.834878522[/C][C]-2672.83487852153[/C][/ROW]
[ROW][C]36[/C][C]179566[/C][C]182860.560671384[/C][C]-3294.56067138413[/C][/ROW]
[ROW][C]37[/C][C]181140[/C][C]182552.108246818[/C][C]-1412.10824681763[/C][/ROW]
[ROW][C]38[/C][C]177876[/C][C]179243.047588606[/C][C]-1367.04758860619[/C][/ROW]
[ROW][C]39[/C][C]175041[/C][C]174113.551861834[/C][C]927.448138166044[/C][/ROW]
[ROW][C]40[/C][C]169292[/C][C]173346.18218413[/C][C]-4054.18218412981[/C][/ROW]
[ROW][C]41[/C][C]166070[/C][C]166832.87427879[/C][C]-762.874278790143[/C][/ROW]
[ROW][C]42[/C][C]166972[/C][C]165922.491006595[/C][C]1049.50899340509[/C][/ROW]
[ROW][C]43[/C][C]206348[/C][C]196558.795284389[/C][C]9789.20471561147[/C][/ROW]
[ROW][C]44[/C][C]215706[/C][C]225216.873886494[/C][C]-9510.87388649434[/C][/ROW]
[ROW][C]45[/C][C]202108[/C][C]200907.006969103[/C][C]1200.99303089728[/C][/ROW]
[ROW][C]46[/C][C]195411[/C][C]190710.856136706[/C][C]4700.14386329436[/C][/ROW]
[ROW][C]47[/C][C]193111[/C][C]187055.840220638[/C][C]6055.1597793616[/C][/ROW]
[ROW][C]48[/C][C]195198[/C][C]199049.339913743[/C][C]-3851.339913743[/C][/ROW]
[ROW][C]49[/C][C]198770[/C][C]199042.997871197[/C][C]-272.997871196945[/C][/ROW]
[ROW][C]50[/C][C]194163[/C][C]197117.93077686[/C][C]-2954.93077686024[/C][/ROW]
[ROW][C]51[/C][C]190420[/C][C]191512.249043427[/C][C]-1092.2490434272[/C][/ROW]
[ROW][C]52[/C][C]189733[/C][C]188129.678889893[/C][C]1603.32111010668[/C][/ROW]
[ROW][C]53[/C][C]186029[/C][C]187498.596717085[/C][C]-1469.59671708496[/C][/ROW]
[ROW][C]54[/C][C]191531[/C][C]187061.553357131[/C][C]4469.44664286866[/C][/ROW]
[ROW][C]55[/C][C]232571[/C][C]223314.193184279[/C][C]9256.80681572098[/C][/ROW]
[ROW][C]56[/C][C]243477[/C][C]248433.712722975[/C][C]-4956.712722975[/C][/ROW]
[ROW][C]57[/C][C]227247[/C][C]231545.874832781[/C][C]-4298.87483278071[/C][/ROW]
[ROW][C]58[/C][C]217859[/C][C]218649.860480711[/C][C]-790.860480711417[/C][/ROW]
[ROW][C]59[/C][C]208679[/C][C]211171.888635607[/C][C]-2492.88863560685[/C][/ROW]
[ROW][C]60[/C][C]213188[/C][C]213488.229628962[/C][C]-300.229628961562[/C][/ROW]
[ROW][C]61[/C][C]216234[/C][C]216634.512356744[/C][C]-400.51235674409[/C][/ROW]
[ROW][C]62[/C][C]213586[/C][C]213617.211916038[/C][C]-31.211916037777[/C][/ROW]
[ROW][C]63[/C][C]209465[/C][C]210647.255498068[/C][C]-1182.25549806794[/C][/ROW]
[ROW][C]64[/C][C]204045[/C][C]207696.056936062[/C][C]-3651.05693606203[/C][/ROW]
[ROW][C]65[/C][C]200237[/C][C]201559.353700861[/C][C]-1322.35370086058[/C][/ROW]
[ROW][C]66[/C][C]203666[/C][C]201806.358136103[/C][C]1859.64186389704[/C][/ROW]
[ROW][C]67[/C][C]241476[/C][C]236008.629329493[/C][C]5467.37067050653[/C][/ROW]
[ROW][C]68[/C][C]260307[/C][C]253632.97407016[/C][C]6674.02592983964[/C][/ROW]
[ROW][C]69[/C][C]243324[/C][C]245978.10496673[/C][C]-2654.1049667302[/C][/ROW]
[ROW][C]70[/C][C]244460[/C][C]235268.282471266[/C][C]9191.71752873395[/C][/ROW]
[ROW][C]71[/C][C]233575[/C][C]236647.931624635[/C][C]-3072.93162463498[/C][/ROW]
[ROW][C]72[/C][C]237217[/C][C]240271.63520002[/C][C]-3054.63520001969[/C][/ROW]
[ROW][C]73[/C][C]235243[/C][C]242188.152693052[/C][C]-6945.15269305155[/C][/ROW]
[ROW][C]74[/C][C]230354[/C][C]234257.517648547[/C][C]-3903.51764854742[/C][/ROW]
[ROW][C]75[/C][C]227184[/C][C]227677.911670693[/C][C]-493.911670693051[/C][/ROW]
[ROW][C]76[/C][C]221678[/C][C]224508.313359514[/C][C]-2830.31335951379[/C][/ROW]
[ROW][C]77[/C][C]217142[/C][C]219381.134929034[/C][C]-2239.13492903442[/C][/ROW]
[ROW][C]78[/C][C]219452[/C][C]219340.378779068[/C][C]111.621220931673[/C][/ROW]
[ROW][C]79[/C][C]256446[/C][C]252477.564273766[/C][C]3968.4357262344[/C][/ROW]
[ROW][C]80[/C][C]265845[/C][C]268537.035194253[/C][C]-2692.03519425297[/C][/ROW]
[ROW][C]81[/C][C]248624[/C][C]249733.664875924[/C][C]-1109.66487592363[/C][/ROW]
[ROW][C]82[/C][C]241114[/C][C]241164.041968422[/C][C]-50.0419684220105[/C][/ROW]
[ROW][C]83[/C][C]229245[/C][C]229923.595156386[/C][C]-678.595156385709[/C][/ROW]
[ROW][C]84[/C][C]231805[/C][C]232994.61627415[/C][C]-1189.61627415035[/C][/ROW]
[ROW][C]85[/C][C]219277[/C][C]233336.866000631[/C][C]-14059.8660006305[/C][/ROW]
[ROW][C]86[/C][C]219313[/C][C]217374.18329822[/C][C]1938.81670178048[/C][/ROW]
[ROW][C]87[/C][C]212610[/C][C]213750.413699219[/C][C]-1140.41369921915[/C][/ROW]
[ROW][C]88[/C][C]214771[/C][C]207127.034028596[/C][C]7643.96597140448[/C][/ROW]
[ROW][C]89[/C][C]211142[/C][C]209202.751430528[/C][C]1939.24856947243[/C][/ROW]
[ROW][C]90[/C][C]211457[/C][C]212298.996501291[/C][C]-841.996501291404[/C][/ROW]
[ROW][C]91[/C][C]240048[/C][C]244740.097239514[/C][C]-4692.09723951353[/C][/ROW]
[ROW][C]92[/C][C]240636[/C][C]250736.072567315[/C][C]-10100.0725673146[/C][/ROW]
[ROW][C]93[/C][C]230580[/C][C]223704.945028586[/C][C]6875.05497141436[/C][/ROW]
[ROW][C]94[/C][C]208795[/C][C]219884.192553616[/C][C]-11089.1925536162[/C][/ROW]
[ROW][C]95[/C][C]197922[/C][C]196713.536485743[/C][C]1208.46351425743[/C][/ROW]
[ROW][C]96[/C][C]194596[/C][C]198279.950262188[/C][C]-3683.95026218813[/C][/ROW]
[ROW][C]97[/C][C]194581[/C][C]190729.090050536[/C][C]3851.90994946379[/C][/ROW]
[ROW][C]98[/C][C]185686[/C][C]191278.927945051[/C][C]-5592.92794505064[/C][/ROW]
[ROW][C]99[/C][C]178106[/C][C]179159.001172259[/C][C]-1053.00117225942[/C][/ROW]
[ROW][C]100[/C][C]172608[/C][C]172574.581266998[/C][C]33.4187330016284[/C][/ROW]
[ROW][C]101[/C][C]167302[/C][C]164610.437912255[/C][C]2691.56208774468[/C][/ROW]
[ROW][C]102[/C][C]168053[/C][C]164961.754155404[/C][C]3091.2458445956[/C][/ROW]
[ROW][C]103[/C][C]202300[/C][C]197414.376094765[/C][C]4885.62390523526[/C][/ROW]
[ROW][C]104[/C][C]202388[/C][C]208703.725659619[/C][C]-6315.72565961938[/C][/ROW]
[ROW][C]105[/C][C]182516[/C][C]187645.695259936[/C][C]-5129.6952599361[/C][/ROW]
[ROW][C]106[/C][C]173476[/C][C]168453.759284006[/C][C]5022.24071599363[/C][/ROW]
[ROW][C]107[/C][C]166444[/C][C]160459.741451464[/C][C]5984.25854853578[/C][/ROW]
[ROW][C]108[/C][C]171297[/C][C]165203.67108995[/C][C]6093.32891004978[/C][/ROW]
[ROW][C]109[/C][C]169701[/C][C]168613.71455601[/C][C]1087.28544399026[/C][/ROW]
[ROW][C]110[/C][C]164182[/C][C]166297.126878907[/C][C]-2115.12687890694[/C][/ROW]
[ROW][C]111[/C][C]161914[/C][C]159630.579876355[/C][C]2283.42012364493[/C][/ROW]
[ROW][C]112[/C][C]159612[/C][C]158060.539554747[/C][C]1551.46044525341[/C][/ROW]
[ROW][C]113[/C][C]151001[/C][C]154201.424991105[/C][C]-3200.42499110513[/C][/ROW]
[ROW][C]114[/C][C]158114[/C][C]151624.562134491[/C][C]6489.43786550936[/C][/ROW]
[ROW][C]115[/C][C]186530[/C][C]189171.601050891[/C][C]-2641.60105089133[/C][/ROW]
[ROW][C]116[/C][C]187069[/C][C]193266.148679687[/C][C]-6197.14867968677[/C][/ROW]
[ROW][C]117[/C][C]174330[/C][C]173684.922388921[/C][C]645.077611079323[/C][/ROW]
[ROW][C]118[/C][C]169362[/C][C]163039.411629569[/C][C]6322.58837043142[/C][/ROW]
[ROW][C]119[/C][C]166827[/C][C]158271.002348831[/C][C]8555.99765116919[/C][/ROW]
[ROW][C]120[/C][C]178037[/C][C]167373.950770154[/C][C]10663.0492298462[/C][/ROW]
[ROW][C]121[/C][C]186413[/C][C]176183.815808529[/C][C]10229.1841914707[/C][/ROW]
[ROW][C]122[/C][C]189226[/C][C]184368.839357322[/C][C]4857.16064267812[/C][/ROW]
[ROW][C]123[/C][C]191563[/C][C]188972.400892042[/C][C]2590.59910795817[/C][/ROW]
[ROW][C]124[/C][C]188906[/C][C]192372.294027718[/C][C]-3466.29402771773[/C][/ROW]
[ROW][C]125[/C][C]186005[/C][C]187821.724755116[/C][C]-1816.72475511601[/C][/ROW]
[ROW][C]126[/C][C]195309[/C][C]192839.215792406[/C][C]2469.78420759359[/C][/ROW]
[ROW][C]127[/C][C]223532[/C][C]229223.087110724[/C][C]-5691.08711072433[/C][/ROW]
[ROW][C]128[/C][C]226899[/C][C]233733.221800341[/C][C]-6834.22180034057[/C][/ROW]
[ROW][C]129[/C][C]214126[/C][C]218605.044575766[/C][C]-4479.04457576631[/C][/ROW]
[ROW][C]130[/C][C]206903[/C][C]208006.298620989[/C][C]-1103.29862098902[/C][/ROW]
[ROW][C]131[/C][C]204442[/C][C]199829.420257715[/C][C]4612.57974228458[/C][/ROW]
[ROW][C]132[/C][C]220375[/C][C]207753.529268726[/C][C]12621.4707312738[/C][/ROW]
[ROW][C]133[/C][C]214320[/C][C]219725.686840236[/C][C]-5405.68684023627[/C][/ROW]
[ROW][C]134[/C][C]212588[/C][C]214263.16287187[/C][C]-1675.16287187024[/C][/ROW]
[ROW][C]135[/C][C]205816[/C][C]212242.323659019[/C][C]-6426.32365901885[/C][/ROW]
[ROW][C]136[/C][C]202196[/C][C]205149.9623062[/C][C]-2953.96230619974[/C][/ROW]
[ROW][C]137[/C][C]195722[/C][C]199310.402816274[/C][C]-3588.40281627362[/C][/ROW]
[ROW][C]138[/C][C]198563[/C][C]201587.356456262[/C][C]-3024.35645626215[/C][/ROW]
[ROW][C]139[/C][C]229139[/C][C]228974.239624869[/C][C]164.760375131242[/C][/ROW]
[ROW][C]140[/C][C]229527[/C][C]235630.868228266[/C][C]-6103.86822826631[/C][/ROW]
[ROW][C]141[/C][C]211868[/C][C]219452.446170659[/C][C]-7584.44617065854[/C][/ROW]
[ROW][C]142[/C][C]203555[/C][C]204622.969306613[/C][C]-1067.96930661306[/C][/ROW]
[ROW][C]143[/C][C]195770[/C][C]195189.669246083[/C][C]580.330753916613[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117142&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117142&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
13180144192256.77590812-12112.7759081197
14173666174646.428106397-980.428106396546
15165688164180.8073711871507.19262881341
16161570159602.1658100821967.83418991757
17156145154188.6069701641956.39302983636
18153730152119.1230186171610.87698138296
19182698179952.3484015222745.65159847814
20200765200442.561219332322.438780667988
21176512176164.427462602347.572537397995
22166618164082.6938745692535.30612543056
23158644157564.6031125531079.39688744652
24159585162699.575040562-3114.57504056211
25163095157033.5205933086061.47940669156
26159044158060.686855116983.313144883898
27155511151876.2857412753634.71425872456
28153745151536.0705339162208.92946608434
29150569148805.6999799931763.30002000669
30150605148982.9099334391622.09006656095
31179612179540.64902107471.3509789262025
32194690199556.1218355-4866.12183550018
33189917172711.69245961517205.3075403846
34184128177934.6383742216193.36162577895
35175335178007.834878522-2672.83487852153
36179566182860.560671384-3294.56067138413
37181140182552.108246818-1412.10824681763
38177876179243.047588606-1367.04758860619
39175041174113.551861834927.448138166044
40169292173346.18218413-4054.18218412981
41166070166832.87427879-762.874278790143
42166972165922.4910065951049.50899340509
43206348196558.7952843899789.20471561147
44215706225216.873886494-9510.87388649434
45202108200907.0069691031200.99303089728
46195411190710.8561367064700.14386329436
47193111187055.8402206386055.1597793616
48195198199049.339913743-3851.339913743
49198770199042.997871197-272.997871196945
50194163197117.93077686-2954.93077686024
51190420191512.249043427-1092.2490434272
52189733188129.6788898931603.32111010668
53186029187498.596717085-1469.59671708496
54191531187061.5533571314469.44664286866
55232571223314.1931842799256.80681572098
56243477248433.712722975-4956.712722975
57227247231545.874832781-4298.87483278071
58217859218649.860480711-790.860480711417
59208679211171.888635607-2492.88863560685
60213188213488.229628962-300.229628961562
61216234216634.512356744-400.51235674409
62213586213617.211916038-31.211916037777
63209465210647.255498068-1182.25549806794
64204045207696.056936062-3651.05693606203
65200237201559.353700861-1322.35370086058
66203666201806.3581361031859.64186389704
67241476236008.6293294935467.37067050653
68260307253632.974070166674.02592983964
69243324245978.10496673-2654.1049667302
70244460235268.2824712669191.71752873395
71233575236647.931624635-3072.93162463498
72237217240271.63520002-3054.63520001969
73235243242188.152693052-6945.15269305155
74230354234257.517648547-3903.51764854742
75227184227677.911670693-493.911670693051
76221678224508.313359514-2830.31335951379
77217142219381.134929034-2239.13492903442
78219452219340.378779068111.621220931673
79256446252477.5642737663968.4357262344
80265845268537.035194253-2692.03519425297
81248624249733.664875924-1109.66487592363
82241114241164.041968422-50.0419684220105
83229245229923.595156386-678.595156385709
84231805232994.61627415-1189.61627415035
85219277233336.866000631-14059.8660006305
86219313217374.183298221938.81670178048
87212610213750.413699219-1140.41369921915
88214771207127.0340285967643.96597140448
89211142209202.7514305281939.24856947243
90211457212298.996501291-841.996501291404
91240048244740.097239514-4692.09723951353
92240636250736.072567315-10100.0725673146
93230580223704.9450285866875.05497141436
94208795219884.192553616-11089.1925536162
95197922196713.5364857431208.46351425743
96194596198279.950262188-3683.95026218813
97194581190729.0900505363851.90994946379
98185686191278.927945051-5592.92794505064
99178106179159.001172259-1053.00117225942
100172608172574.58126699833.4187330016284
101167302164610.4379122552691.56208774468
102168053164961.7541554043091.2458445956
103202300197414.3760947654885.62390523526
104202388208703.725659619-6315.72565961938
105182516187645.695259936-5129.6952599361
106173476168453.7592840065022.24071599363
107166444160459.7414514645984.25854853578
108171297165203.671089956093.32891004978
109169701168613.714556011087.28544399026
110164182166297.126878907-2115.12687890694
111161914159630.5798763552283.42012364493
112159612158060.5395547471551.46044525341
113151001154201.424991105-3200.42499110513
114158114151624.5621344916489.43786550936
115186530189171.601050891-2641.60105089133
116187069193266.148679687-6197.14867968677
117174330173684.922388921645.077611079323
118169362163039.4116295696322.58837043142
119166827158271.0023488318555.99765116919
120178037167373.95077015410663.0492298462
121186413176183.81580852910229.1841914707
122189226184368.8393573224857.16064267812
123191563188972.4008920422590.59910795817
124188906192372.294027718-3466.29402771773
125186005187821.724755116-1816.72475511601
126195309192839.2157924062469.78420759359
127223532229223.087110724-5691.08711072433
128226899233733.221800341-6834.22180034057
129214126218605.044575766-4479.04457576631
130206903208006.298620989-1103.29862098902
131204442199829.4202577154612.57974228458
132220375207753.52926872612621.4707312738
133214320219725.686840236-5405.68684023627
134212588214263.16287187-1675.16287187024
135205816212242.323659019-6426.32365901885
136202196205149.9623062-2953.96230619974
137195722199310.402816274-3588.40281627362
138198563201587.356456262-3024.35645626215
139229139228974.239624869164.760375131242
140229527235630.868228266-6103.86822826631
141211868219452.446170659-7584.44617065854
142203555204622.969306613-1067.96930661306
143195770195189.669246083580.330753916613







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
144198652.31584729188946.127403192208358.504291388
145192306.353232713179187.823603671205424.882861755
146188010.82132942171506.694169197204514.948489644
147182618.374637975162670.69897198202566.05030397
148178433.511095258154949.581220176201917.440970341
149172255.700582945145126.928102198199384.473063691
150175388.800333859144499.251040227206278.34962749
151204118.502515161169349.186596989238887.818433332
152207571.683921239168802.856144804246340.511697675
153194890.525319255152002.965606995237778.085031515
154187357.973538446140233.710876374234482.236200517
155179187.517956523127710.236010429230664.799902617

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
144 & 198652.31584729 & 188946.127403192 & 208358.504291388 \tabularnewline
145 & 192306.353232713 & 179187.823603671 & 205424.882861755 \tabularnewline
146 & 188010.82132942 & 171506.694169197 & 204514.948489644 \tabularnewline
147 & 182618.374637975 & 162670.69897198 & 202566.05030397 \tabularnewline
148 & 178433.511095258 & 154949.581220176 & 201917.440970341 \tabularnewline
149 & 172255.700582945 & 145126.928102198 & 199384.473063691 \tabularnewline
150 & 175388.800333859 & 144499.251040227 & 206278.34962749 \tabularnewline
151 & 204118.502515161 & 169349.186596989 & 238887.818433332 \tabularnewline
152 & 207571.683921239 & 168802.856144804 & 246340.511697675 \tabularnewline
153 & 194890.525319255 & 152002.965606995 & 237778.085031515 \tabularnewline
154 & 187357.973538446 & 140233.710876374 & 234482.236200517 \tabularnewline
155 & 179187.517956523 & 127710.236010429 & 230664.799902617 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117142&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]144[/C][C]198652.31584729[/C][C]188946.127403192[/C][C]208358.504291388[/C][/ROW]
[ROW][C]145[/C][C]192306.353232713[/C][C]179187.823603671[/C][C]205424.882861755[/C][/ROW]
[ROW][C]146[/C][C]188010.82132942[/C][C]171506.694169197[/C][C]204514.948489644[/C][/ROW]
[ROW][C]147[/C][C]182618.374637975[/C][C]162670.69897198[/C][C]202566.05030397[/C][/ROW]
[ROW][C]148[/C][C]178433.511095258[/C][C]154949.581220176[/C][C]201917.440970341[/C][/ROW]
[ROW][C]149[/C][C]172255.700582945[/C][C]145126.928102198[/C][C]199384.473063691[/C][/ROW]
[ROW][C]150[/C][C]175388.800333859[/C][C]144499.251040227[/C][C]206278.34962749[/C][/ROW]
[ROW][C]151[/C][C]204118.502515161[/C][C]169349.186596989[/C][C]238887.818433332[/C][/ROW]
[ROW][C]152[/C][C]207571.683921239[/C][C]168802.856144804[/C][C]246340.511697675[/C][/ROW]
[ROW][C]153[/C][C]194890.525319255[/C][C]152002.965606995[/C][C]237778.085031515[/C][/ROW]
[ROW][C]154[/C][C]187357.973538446[/C][C]140233.710876374[/C][C]234482.236200517[/C][/ROW]
[ROW][C]155[/C][C]179187.517956523[/C][C]127710.236010429[/C][C]230664.799902617[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117142&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117142&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
144198652.31584729188946.127403192208358.504291388
145192306.353232713179187.823603671205424.882861755
146188010.82132942171506.694169197204514.948489644
147182618.374637975162670.69897198202566.05030397
148178433.511095258154949.581220176201917.440970341
149172255.700582945145126.928102198199384.473063691
150175388.800333859144499.251040227206278.34962749
151204118.502515161169349.186596989238887.818433332
152207571.683921239168802.856144804246340.511697675
153194890.525319255152002.965606995237778.085031515
154187357.973538446140233.710876374234482.236200517
155179187.517956523127710.236010429230664.799902617



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')