Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 24 Dec 2022 16:43:59 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2022/Dec/24/t16718966690h6nn1obmqnkn7t.htm/, Retrieved Tue, 21 May 2024 10:49:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319804, Retrieved Tue, 21 May 2024 10:49:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact38
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [One Sample Tests about the Mean] [one sample T test] [2016-01-10 12:14:24] [9378e2688aa9dcfd1390615d31e9d404]
- RMPD    [Exponential Smoothing] [mogelijke vraag o...] [2022-12-24 15:43:59] [9d78e0215ee362f5c093398655283a14] [Current]
Feedback Forum

Post a new message
Dataseries X:
5160
4220
5840
5140
5480
6720
4840
5220
6260
6020
5340
4940
4300
4420
5340
4960
5380
5840
4680
5580
5820
5180
5220
4400
4580
3940
5100
4320
5220
5980
4220
6180
5720
5440
5420
4480
4880
4520
4920
4340
5340
5700
4100
5520
5220
5640
4600
4440
4240
3600
4280
4280
5180
5320
4500
5720
5780
5680
5180
4560
4400
3820
4400
4960
5400
5460
5240
4880
5260
5160
4200
5000
4340
4120
4520
4160
4600
5620
3960
4220
4900
4820
4060
4200
2900
3700
4280
3760
4320
5020
3460
4480
4740
4160
4000
3780
3280
3280
4180
3480
4820
4920
3160
4400
4160
4040
4020
3560
3180
3140
3780
3440
4100
4440
3280
4220
3900
3820
4200
3160
3040
2900
3260
3500
3380
4380
3400
4120
3860
3860
3820
3140
2780
3120
3620
3240
3300
4340
3360
3700
3880
3560
3800
3440




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319804&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=319804&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319804&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.159177807905577
beta0.0105293553948967
gamma0.363032151825425

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.159177807905577 \tabularnewline
beta & 0.0105293553948967 \tabularnewline
gamma & 0.363032151825425 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319804&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]0.159177807905577[/C][/ROW]
[ROW][C]beta[/C][C]0.0105293553948967[/C][/ROW]
[ROW][C]gamma[/C][C]0.363032151825425[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319804&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319804&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
alpha0.159177807905577
beta0.0105293553948967
gamma0.363032151825425







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1343004496.86431623932-196.864316239317
1444204552.25795682396-132.257956823955
1553405429.3804931561-89.3804931561008
1649605063.17836490758-103.178364907579
1753805481.27365730972-101.273657309722
1858405927.00239822072-87.0023982207213
1946804607.3569873952472.6430126047599
2055805000.74533568096579.254664319044
2158206120.74586996582-300.745869965818
2251805835.99911956001-655.999119560005
2352205036.93778839141183.062211608591
2444004680.90988681936-280.909886819364
2545803952.9651629502627.034837049805
2639404158.74210297804-218.742102978042
2751005034.5575225078465.4424774921563
2843204688.41861427457-368.418614274575
2952205064.06097248046155.939027519536
3059805554.705624734425.294375266001
3142204365.81328518735-145.813285187348
3261804879.178771424361300.82122857564
3357205846.73948070059-126.73948070059
3454405482.86186043632-42.8618604363219
3554205040.15633011036379.843669889637
3644804576.79436192155-96.7943619215494
3748804158.57944310347721.420556896532
3845204124.64576063383395.354239366169
3949205189.42186282135-269.421862821346
4043404661.44870721186-321.448707211856
4153405208.60702651574131.39297348426
4257005781.50444566729-81.5044456672895
4341004340.70397726683-240.703977266831
4455205283.4756251456236.5243748544
4552205647.01561614678-427.015616146777
4656405261.58887905966378.411120940341
4746005016.32060019897-416.320600198968
4844404280.75192156006159.248078439939
4942404153.4954102249986.5045897750124
5036003918.34849828438-318.348498284385
5142804664.78443736304-384.784437363041
5242804100.55918919291179.440810807093
5351804864.50742404339315.492575956612
5453205400.86353511814-80.8635351181374
5545003910.71131839245589.288681607554
5657205131.80345290688588.196547093125
5757805349.90094900137430.09905099863
5856805349.31897185394330.681028146064
5951804856.34309784328323.656902156723
6045604417.97064056421142.029359435785
6144004269.4582916755130.541708324499
6238203921.50496278311-101.504962783114
6344004686.30517829187-286.30517829187
6449604314.27477857988645.72522142012
6554005199.04776633527200.952233664733
6654605601.06714231062-141.067142310623
6752404310.67334601813929.326653981871
6848805590.9090846769-710.9090846769
6952605557.1323680579-297.132368057903
7051605412.39863758242-252.398637582424
7142004825.4423259633-625.442325963305
7250004179.93960604499820.060393955006
7343404136.37086437118203.629135628818
7441203729.865396755390.134603244996
7545204517.983460387892.01653961211377
7641604478.29796612958-318.297966129585
7746005074.19157717654-474.191577176543
7856205263.54827108593356.451728914069
7939604379.12027968193-419.120279681926
8042204941.81754254246-721.817542542456
8149005030.36854744189-130.368547441892
8248204923.87481805953-103.87481805953
8340604244.97936315896-184.979363158963
8442004109.8490551861490.1509448138613
8529003759.73600635395-859.736006353955
8637003236.91805726188463.081942738123
8742803914.32039076524365.679609234764
8837603831.5009030008-71.5009030008014
8943204416.26042400525-96.2604240052515
9050204917.12603686472102.873963135277
9134603752.96977232146-292.969772321464
9244804240.93739274877239.062607251231
9347404662.1737755528377.8262244471725
9441604596.45351154088-436.453511540875
9540003838.85108413752161.14891586248
9637803842.36809866942-62.3680986694239
9732803177.34216349857102.657836501427
9832803212.4266478388567.5733521611542
9941803797.40475832679382.595241673214
10034803584.12242600937-104.122426009367
10148204156.36885910925663.63114089075
10249204840.4880942039179.5119057960901
10331603553.25531314636-393.255313146359
10444004188.96382214466211.036177855344
10541604557.77900420513-397.779004205131
10640404259.83090284176-219.83090284176
10740203719.94803135371300.051968646286
10835603678.40317413672-118.403174136721
10931803055.79260922405124.207390775953
11031403084.595530023255.404469976796
11137803764.7728461718915.2271538281134
11234403344.8067813381495.1932186618624
11341004183.82870348778-83.8287034877821
11444404570.11193287028-130.111932870283
11532803104.29306532398175.70693467602
11642204015.07003101872204.929968981279
11739004197.10995871899-297.109958718989
11838203969.70752296647-149.707522966471
11942003599.99970091731600.000299082687
12031603479.29220361543-319.292203615431
12130402899.24743322709140.752566772905
12229002910.19701716903-10.1970171690255
12332603568.07295670659-308.072956706591
12435003120.91697462879379.083025371212
12533803950.82103522028-570.82103522028
12643804244.9807428829135.019257117101
12734002914.68167448214485.318325517863
12841203884.14799060922235.852009390777
12938603918.40231242493-58.4023124249288
13038603774.9285638044285.0714361955779
13138203672.76857052861147.231429471391
13231403199.95286574596-59.9528657459623
13327802802.62285574678-22.6228557467821
13431202742.22329656331377.776703436687
13536203372.31429296771247.685707032289
13632403225.6890320763214.3109679236786
13733003709.27918470189-409.279184701885
13843404246.5817249206593.4182750793461
13933603018.49257839156341.50742160844
14037003890.58255379036-190.582553790361
14138803768.08706234182111.912937658176
14235603696.7528019381-136.752801938097
14338003579.11994945023220.880050549767
14434403055.77141625543384.228583744572

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4300 & 4496.86431623932 & -196.864316239317 \tabularnewline
14 & 4420 & 4552.25795682396 & -132.257956823955 \tabularnewline
15 & 5340 & 5429.3804931561 & -89.3804931561008 \tabularnewline
16 & 4960 & 5063.17836490758 & -103.178364907579 \tabularnewline
17 & 5380 & 5481.27365730972 & -101.273657309722 \tabularnewline
18 & 5840 & 5927.00239822072 & -87.0023982207213 \tabularnewline
19 & 4680 & 4607.35698739524 & 72.6430126047599 \tabularnewline
20 & 5580 & 5000.74533568096 & 579.254664319044 \tabularnewline
21 & 5820 & 6120.74586996582 & -300.745869965818 \tabularnewline
22 & 5180 & 5835.99911956001 & -655.999119560005 \tabularnewline
23 & 5220 & 5036.93778839141 & 183.062211608591 \tabularnewline
24 & 4400 & 4680.90988681936 & -280.909886819364 \tabularnewline
25 & 4580 & 3952.9651629502 & 627.034837049805 \tabularnewline
26 & 3940 & 4158.74210297804 & -218.742102978042 \tabularnewline
27 & 5100 & 5034.55752250784 & 65.4424774921563 \tabularnewline
28 & 4320 & 4688.41861427457 & -368.418614274575 \tabularnewline
29 & 5220 & 5064.06097248046 & 155.939027519536 \tabularnewline
30 & 5980 & 5554.705624734 & 425.294375266001 \tabularnewline
31 & 4220 & 4365.81328518735 & -145.813285187348 \tabularnewline
32 & 6180 & 4879.17877142436 & 1300.82122857564 \tabularnewline
33 & 5720 & 5846.73948070059 & -126.73948070059 \tabularnewline
34 & 5440 & 5482.86186043632 & -42.8618604363219 \tabularnewline
35 & 5420 & 5040.15633011036 & 379.843669889637 \tabularnewline
36 & 4480 & 4576.79436192155 & -96.7943619215494 \tabularnewline
37 & 4880 & 4158.57944310347 & 721.420556896532 \tabularnewline
38 & 4520 & 4124.64576063383 & 395.354239366169 \tabularnewline
39 & 4920 & 5189.42186282135 & -269.421862821346 \tabularnewline
40 & 4340 & 4661.44870721186 & -321.448707211856 \tabularnewline
41 & 5340 & 5208.60702651574 & 131.39297348426 \tabularnewline
42 & 5700 & 5781.50444566729 & -81.5044456672895 \tabularnewline
43 & 4100 & 4340.70397726683 & -240.703977266831 \tabularnewline
44 & 5520 & 5283.4756251456 & 236.5243748544 \tabularnewline
45 & 5220 & 5647.01561614678 & -427.015616146777 \tabularnewline
46 & 5640 & 5261.58887905966 & 378.411120940341 \tabularnewline
47 & 4600 & 5016.32060019897 & -416.320600198968 \tabularnewline
48 & 4440 & 4280.75192156006 & 159.248078439939 \tabularnewline
49 & 4240 & 4153.49541022499 & 86.5045897750124 \tabularnewline
50 & 3600 & 3918.34849828438 & -318.348498284385 \tabularnewline
51 & 4280 & 4664.78443736304 & -384.784437363041 \tabularnewline
52 & 4280 & 4100.55918919291 & 179.440810807093 \tabularnewline
53 & 5180 & 4864.50742404339 & 315.492575956612 \tabularnewline
54 & 5320 & 5400.86353511814 & -80.8635351181374 \tabularnewline
55 & 4500 & 3910.71131839245 & 589.288681607554 \tabularnewline
56 & 5720 & 5131.80345290688 & 588.196547093125 \tabularnewline
57 & 5780 & 5349.90094900137 & 430.09905099863 \tabularnewline
58 & 5680 & 5349.31897185394 & 330.681028146064 \tabularnewline
59 & 5180 & 4856.34309784328 & 323.656902156723 \tabularnewline
60 & 4560 & 4417.97064056421 & 142.029359435785 \tabularnewline
61 & 4400 & 4269.4582916755 & 130.541708324499 \tabularnewline
62 & 3820 & 3921.50496278311 & -101.504962783114 \tabularnewline
63 & 4400 & 4686.30517829187 & -286.30517829187 \tabularnewline
64 & 4960 & 4314.27477857988 & 645.72522142012 \tabularnewline
65 & 5400 & 5199.04776633527 & 200.952233664733 \tabularnewline
66 & 5460 & 5601.06714231062 & -141.067142310623 \tabularnewline
67 & 5240 & 4310.67334601813 & 929.326653981871 \tabularnewline
68 & 4880 & 5590.9090846769 & -710.9090846769 \tabularnewline
69 & 5260 & 5557.1323680579 & -297.132368057903 \tabularnewline
70 & 5160 & 5412.39863758242 & -252.398637582424 \tabularnewline
71 & 4200 & 4825.4423259633 & -625.442325963305 \tabularnewline
72 & 5000 & 4179.93960604499 & 820.060393955006 \tabularnewline
73 & 4340 & 4136.37086437118 & 203.629135628818 \tabularnewline
74 & 4120 & 3729.865396755 & 390.134603244996 \tabularnewline
75 & 4520 & 4517.98346038789 & 2.01653961211377 \tabularnewline
76 & 4160 & 4478.29796612958 & -318.297966129585 \tabularnewline
77 & 4600 & 5074.19157717654 & -474.191577176543 \tabularnewline
78 & 5620 & 5263.54827108593 & 356.451728914069 \tabularnewline
79 & 3960 & 4379.12027968193 & -419.120279681926 \tabularnewline
80 & 4220 & 4941.81754254246 & -721.817542542456 \tabularnewline
81 & 4900 & 5030.36854744189 & -130.368547441892 \tabularnewline
82 & 4820 & 4923.87481805953 & -103.87481805953 \tabularnewline
83 & 4060 & 4244.97936315896 & -184.979363158963 \tabularnewline
84 & 4200 & 4109.84905518614 & 90.1509448138613 \tabularnewline
85 & 2900 & 3759.73600635395 & -859.736006353955 \tabularnewline
86 & 3700 & 3236.91805726188 & 463.081942738123 \tabularnewline
87 & 4280 & 3914.32039076524 & 365.679609234764 \tabularnewline
88 & 3760 & 3831.5009030008 & -71.5009030008014 \tabularnewline
89 & 4320 & 4416.26042400525 & -96.2604240052515 \tabularnewline
90 & 5020 & 4917.12603686472 & 102.873963135277 \tabularnewline
91 & 3460 & 3752.96977232146 & -292.969772321464 \tabularnewline
92 & 4480 & 4240.93739274877 & 239.062607251231 \tabularnewline
93 & 4740 & 4662.17377555283 & 77.8262244471725 \tabularnewline
94 & 4160 & 4596.45351154088 & -436.453511540875 \tabularnewline
95 & 4000 & 3838.85108413752 & 161.14891586248 \tabularnewline
96 & 3780 & 3842.36809866942 & -62.3680986694239 \tabularnewline
97 & 3280 & 3177.34216349857 & 102.657836501427 \tabularnewline
98 & 3280 & 3212.42664783885 & 67.5733521611542 \tabularnewline
99 & 4180 & 3797.40475832679 & 382.595241673214 \tabularnewline
100 & 3480 & 3584.12242600937 & -104.122426009367 \tabularnewline
101 & 4820 & 4156.36885910925 & 663.63114089075 \tabularnewline
102 & 4920 & 4840.48809420391 & 79.5119057960901 \tabularnewline
103 & 3160 & 3553.25531314636 & -393.255313146359 \tabularnewline
104 & 4400 & 4188.96382214466 & 211.036177855344 \tabularnewline
105 & 4160 & 4557.77900420513 & -397.779004205131 \tabularnewline
106 & 4040 & 4259.83090284176 & -219.83090284176 \tabularnewline
107 & 4020 & 3719.94803135371 & 300.051968646286 \tabularnewline
108 & 3560 & 3678.40317413672 & -118.403174136721 \tabularnewline
109 & 3180 & 3055.79260922405 & 124.207390775953 \tabularnewline
110 & 3140 & 3084.5955300232 & 55.404469976796 \tabularnewline
111 & 3780 & 3764.77284617189 & 15.2271538281134 \tabularnewline
112 & 3440 & 3344.80678133814 & 95.1932186618624 \tabularnewline
113 & 4100 & 4183.82870348778 & -83.8287034877821 \tabularnewline
114 & 4440 & 4570.11193287028 & -130.111932870283 \tabularnewline
115 & 3280 & 3104.29306532398 & 175.70693467602 \tabularnewline
116 & 4220 & 4015.07003101872 & 204.929968981279 \tabularnewline
117 & 3900 & 4197.10995871899 & -297.109958718989 \tabularnewline
118 & 3820 & 3969.70752296647 & -149.707522966471 \tabularnewline
119 & 4200 & 3599.99970091731 & 600.000299082687 \tabularnewline
120 & 3160 & 3479.29220361543 & -319.292203615431 \tabularnewline
121 & 3040 & 2899.24743322709 & 140.752566772905 \tabularnewline
122 & 2900 & 2910.19701716903 & -10.1970171690255 \tabularnewline
123 & 3260 & 3568.07295670659 & -308.072956706591 \tabularnewline
124 & 3500 & 3120.91697462879 & 379.083025371212 \tabularnewline
125 & 3380 & 3950.82103522028 & -570.82103522028 \tabularnewline
126 & 4380 & 4244.9807428829 & 135.019257117101 \tabularnewline
127 & 3400 & 2914.68167448214 & 485.318325517863 \tabularnewline
128 & 4120 & 3884.14799060922 & 235.852009390777 \tabularnewline
129 & 3860 & 3918.40231242493 & -58.4023124249288 \tabularnewline
130 & 3860 & 3774.92856380442 & 85.0714361955779 \tabularnewline
131 & 3820 & 3672.76857052861 & 147.231429471391 \tabularnewline
132 & 3140 & 3199.95286574596 & -59.9528657459623 \tabularnewline
133 & 2780 & 2802.62285574678 & -22.6228557467821 \tabularnewline
134 & 3120 & 2742.22329656331 & 377.776703436687 \tabularnewline
135 & 3620 & 3372.31429296771 & 247.685707032289 \tabularnewline
136 & 3240 & 3225.68903207632 & 14.3109679236786 \tabularnewline
137 & 3300 & 3709.27918470189 & -409.279184701885 \tabularnewline
138 & 4340 & 4246.58172492065 & 93.4182750793461 \tabularnewline
139 & 3360 & 3018.49257839156 & 341.50742160844 \tabularnewline
140 & 3700 & 3890.58255379036 & -190.582553790361 \tabularnewline
141 & 3880 & 3768.08706234182 & 111.912937658176 \tabularnewline
142 & 3560 & 3696.7528019381 & -136.752801938097 \tabularnewline
143 & 3800 & 3579.11994945023 & 220.880050549767 \tabularnewline
144 & 3440 & 3055.77141625543 & 384.228583744572 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319804&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]4300[/C][C]4496.86431623932[/C][C]-196.864316239317[/C][/ROW]
[ROW][C]14[/C][C]4420[/C][C]4552.25795682396[/C][C]-132.257956823955[/C][/ROW]
[ROW][C]15[/C][C]5340[/C][C]5429.3804931561[/C][C]-89.3804931561008[/C][/ROW]
[ROW][C]16[/C][C]4960[/C][C]5063.17836490758[/C][C]-103.178364907579[/C][/ROW]
[ROW][C]17[/C][C]5380[/C][C]5481.27365730972[/C][C]-101.273657309722[/C][/ROW]
[ROW][C]18[/C][C]5840[/C][C]5927.00239822072[/C][C]-87.0023982207213[/C][/ROW]
[ROW][C]19[/C][C]4680[/C][C]4607.35698739524[/C][C]72.6430126047599[/C][/ROW]
[ROW][C]20[/C][C]5580[/C][C]5000.74533568096[/C][C]579.254664319044[/C][/ROW]
[ROW][C]21[/C][C]5820[/C][C]6120.74586996582[/C][C]-300.745869965818[/C][/ROW]
[ROW][C]22[/C][C]5180[/C][C]5835.99911956001[/C][C]-655.999119560005[/C][/ROW]
[ROW][C]23[/C][C]5220[/C][C]5036.93778839141[/C][C]183.062211608591[/C][/ROW]
[ROW][C]24[/C][C]4400[/C][C]4680.90988681936[/C][C]-280.909886819364[/C][/ROW]
[ROW][C]25[/C][C]4580[/C][C]3952.9651629502[/C][C]627.034837049805[/C][/ROW]
[ROW][C]26[/C][C]3940[/C][C]4158.74210297804[/C][C]-218.742102978042[/C][/ROW]
[ROW][C]27[/C][C]5100[/C][C]5034.55752250784[/C][C]65.4424774921563[/C][/ROW]
[ROW][C]28[/C][C]4320[/C][C]4688.41861427457[/C][C]-368.418614274575[/C][/ROW]
[ROW][C]29[/C][C]5220[/C][C]5064.06097248046[/C][C]155.939027519536[/C][/ROW]
[ROW][C]30[/C][C]5980[/C][C]5554.705624734[/C][C]425.294375266001[/C][/ROW]
[ROW][C]31[/C][C]4220[/C][C]4365.81328518735[/C][C]-145.813285187348[/C][/ROW]
[ROW][C]32[/C][C]6180[/C][C]4879.17877142436[/C][C]1300.82122857564[/C][/ROW]
[ROW][C]33[/C][C]5720[/C][C]5846.73948070059[/C][C]-126.73948070059[/C][/ROW]
[ROW][C]34[/C][C]5440[/C][C]5482.86186043632[/C][C]-42.8618604363219[/C][/ROW]
[ROW][C]35[/C][C]5420[/C][C]5040.15633011036[/C][C]379.843669889637[/C][/ROW]
[ROW][C]36[/C][C]4480[/C][C]4576.79436192155[/C][C]-96.7943619215494[/C][/ROW]
[ROW][C]37[/C][C]4880[/C][C]4158.57944310347[/C][C]721.420556896532[/C][/ROW]
[ROW][C]38[/C][C]4520[/C][C]4124.64576063383[/C][C]395.354239366169[/C][/ROW]
[ROW][C]39[/C][C]4920[/C][C]5189.42186282135[/C][C]-269.421862821346[/C][/ROW]
[ROW][C]40[/C][C]4340[/C][C]4661.44870721186[/C][C]-321.448707211856[/C][/ROW]
[ROW][C]41[/C][C]5340[/C][C]5208.60702651574[/C][C]131.39297348426[/C][/ROW]
[ROW][C]42[/C][C]5700[/C][C]5781.50444566729[/C][C]-81.5044456672895[/C][/ROW]
[ROW][C]43[/C][C]4100[/C][C]4340.70397726683[/C][C]-240.703977266831[/C][/ROW]
[ROW][C]44[/C][C]5520[/C][C]5283.4756251456[/C][C]236.5243748544[/C][/ROW]
[ROW][C]45[/C][C]5220[/C][C]5647.01561614678[/C][C]-427.015616146777[/C][/ROW]
[ROW][C]46[/C][C]5640[/C][C]5261.58887905966[/C][C]378.411120940341[/C][/ROW]
[ROW][C]47[/C][C]4600[/C][C]5016.32060019897[/C][C]-416.320600198968[/C][/ROW]
[ROW][C]48[/C][C]4440[/C][C]4280.75192156006[/C][C]159.248078439939[/C][/ROW]
[ROW][C]49[/C][C]4240[/C][C]4153.49541022499[/C][C]86.5045897750124[/C][/ROW]
[ROW][C]50[/C][C]3600[/C][C]3918.34849828438[/C][C]-318.348498284385[/C][/ROW]
[ROW][C]51[/C][C]4280[/C][C]4664.78443736304[/C][C]-384.784437363041[/C][/ROW]
[ROW][C]52[/C][C]4280[/C][C]4100.55918919291[/C][C]179.440810807093[/C][/ROW]
[ROW][C]53[/C][C]5180[/C][C]4864.50742404339[/C][C]315.492575956612[/C][/ROW]
[ROW][C]54[/C][C]5320[/C][C]5400.86353511814[/C][C]-80.8635351181374[/C][/ROW]
[ROW][C]55[/C][C]4500[/C][C]3910.71131839245[/C][C]589.288681607554[/C][/ROW]
[ROW][C]56[/C][C]5720[/C][C]5131.80345290688[/C][C]588.196547093125[/C][/ROW]
[ROW][C]57[/C][C]5780[/C][C]5349.90094900137[/C][C]430.09905099863[/C][/ROW]
[ROW][C]58[/C][C]5680[/C][C]5349.31897185394[/C][C]330.681028146064[/C][/ROW]
[ROW][C]59[/C][C]5180[/C][C]4856.34309784328[/C][C]323.656902156723[/C][/ROW]
[ROW][C]60[/C][C]4560[/C][C]4417.97064056421[/C][C]142.029359435785[/C][/ROW]
[ROW][C]61[/C][C]4400[/C][C]4269.4582916755[/C][C]130.541708324499[/C][/ROW]
[ROW][C]62[/C][C]3820[/C][C]3921.50496278311[/C][C]-101.504962783114[/C][/ROW]
[ROW][C]63[/C][C]4400[/C][C]4686.30517829187[/C][C]-286.30517829187[/C][/ROW]
[ROW][C]64[/C][C]4960[/C][C]4314.27477857988[/C][C]645.72522142012[/C][/ROW]
[ROW][C]65[/C][C]5400[/C][C]5199.04776633527[/C][C]200.952233664733[/C][/ROW]
[ROW][C]66[/C][C]5460[/C][C]5601.06714231062[/C][C]-141.067142310623[/C][/ROW]
[ROW][C]67[/C][C]5240[/C][C]4310.67334601813[/C][C]929.326653981871[/C][/ROW]
[ROW][C]68[/C][C]4880[/C][C]5590.9090846769[/C][C]-710.9090846769[/C][/ROW]
[ROW][C]69[/C][C]5260[/C][C]5557.1323680579[/C][C]-297.132368057903[/C][/ROW]
[ROW][C]70[/C][C]5160[/C][C]5412.39863758242[/C][C]-252.398637582424[/C][/ROW]
[ROW][C]71[/C][C]4200[/C][C]4825.4423259633[/C][C]-625.442325963305[/C][/ROW]
[ROW][C]72[/C][C]5000[/C][C]4179.93960604499[/C][C]820.060393955006[/C][/ROW]
[ROW][C]73[/C][C]4340[/C][C]4136.37086437118[/C][C]203.629135628818[/C][/ROW]
[ROW][C]74[/C][C]4120[/C][C]3729.865396755[/C][C]390.134603244996[/C][/ROW]
[ROW][C]75[/C][C]4520[/C][C]4517.98346038789[/C][C]2.01653961211377[/C][/ROW]
[ROW][C]76[/C][C]4160[/C][C]4478.29796612958[/C][C]-318.297966129585[/C][/ROW]
[ROW][C]77[/C][C]4600[/C][C]5074.19157717654[/C][C]-474.191577176543[/C][/ROW]
[ROW][C]78[/C][C]5620[/C][C]5263.54827108593[/C][C]356.451728914069[/C][/ROW]
[ROW][C]79[/C][C]3960[/C][C]4379.12027968193[/C][C]-419.120279681926[/C][/ROW]
[ROW][C]80[/C][C]4220[/C][C]4941.81754254246[/C][C]-721.817542542456[/C][/ROW]
[ROW][C]81[/C][C]4900[/C][C]5030.36854744189[/C][C]-130.368547441892[/C][/ROW]
[ROW][C]82[/C][C]4820[/C][C]4923.87481805953[/C][C]-103.87481805953[/C][/ROW]
[ROW][C]83[/C][C]4060[/C][C]4244.97936315896[/C][C]-184.979363158963[/C][/ROW]
[ROW][C]84[/C][C]4200[/C][C]4109.84905518614[/C][C]90.1509448138613[/C][/ROW]
[ROW][C]85[/C][C]2900[/C][C]3759.73600635395[/C][C]-859.736006353955[/C][/ROW]
[ROW][C]86[/C][C]3700[/C][C]3236.91805726188[/C][C]463.081942738123[/C][/ROW]
[ROW][C]87[/C][C]4280[/C][C]3914.32039076524[/C][C]365.679609234764[/C][/ROW]
[ROW][C]88[/C][C]3760[/C][C]3831.5009030008[/C][C]-71.5009030008014[/C][/ROW]
[ROW][C]89[/C][C]4320[/C][C]4416.26042400525[/C][C]-96.2604240052515[/C][/ROW]
[ROW][C]90[/C][C]5020[/C][C]4917.12603686472[/C][C]102.873963135277[/C][/ROW]
[ROW][C]91[/C][C]3460[/C][C]3752.96977232146[/C][C]-292.969772321464[/C][/ROW]
[ROW][C]92[/C][C]4480[/C][C]4240.93739274877[/C][C]239.062607251231[/C][/ROW]
[ROW][C]93[/C][C]4740[/C][C]4662.17377555283[/C][C]77.8262244471725[/C][/ROW]
[ROW][C]94[/C][C]4160[/C][C]4596.45351154088[/C][C]-436.453511540875[/C][/ROW]
[ROW][C]95[/C][C]4000[/C][C]3838.85108413752[/C][C]161.14891586248[/C][/ROW]
[ROW][C]96[/C][C]3780[/C][C]3842.36809866942[/C][C]-62.3680986694239[/C][/ROW]
[ROW][C]97[/C][C]3280[/C][C]3177.34216349857[/C][C]102.657836501427[/C][/ROW]
[ROW][C]98[/C][C]3280[/C][C]3212.42664783885[/C][C]67.5733521611542[/C][/ROW]
[ROW][C]99[/C][C]4180[/C][C]3797.40475832679[/C][C]382.595241673214[/C][/ROW]
[ROW][C]100[/C][C]3480[/C][C]3584.12242600937[/C][C]-104.122426009367[/C][/ROW]
[ROW][C]101[/C][C]4820[/C][C]4156.36885910925[/C][C]663.63114089075[/C][/ROW]
[ROW][C]102[/C][C]4920[/C][C]4840.48809420391[/C][C]79.5119057960901[/C][/ROW]
[ROW][C]103[/C][C]3160[/C][C]3553.25531314636[/C][C]-393.255313146359[/C][/ROW]
[ROW][C]104[/C][C]4400[/C][C]4188.96382214466[/C][C]211.036177855344[/C][/ROW]
[ROW][C]105[/C][C]4160[/C][C]4557.77900420513[/C][C]-397.779004205131[/C][/ROW]
[ROW][C]106[/C][C]4040[/C][C]4259.83090284176[/C][C]-219.83090284176[/C][/ROW]
[ROW][C]107[/C][C]4020[/C][C]3719.94803135371[/C][C]300.051968646286[/C][/ROW]
[ROW][C]108[/C][C]3560[/C][C]3678.40317413672[/C][C]-118.403174136721[/C][/ROW]
[ROW][C]109[/C][C]3180[/C][C]3055.79260922405[/C][C]124.207390775953[/C][/ROW]
[ROW][C]110[/C][C]3140[/C][C]3084.5955300232[/C][C]55.404469976796[/C][/ROW]
[ROW][C]111[/C][C]3780[/C][C]3764.77284617189[/C][C]15.2271538281134[/C][/ROW]
[ROW][C]112[/C][C]3440[/C][C]3344.80678133814[/C][C]95.1932186618624[/C][/ROW]
[ROW][C]113[/C][C]4100[/C][C]4183.82870348778[/C][C]-83.8287034877821[/C][/ROW]
[ROW][C]114[/C][C]4440[/C][C]4570.11193287028[/C][C]-130.111932870283[/C][/ROW]
[ROW][C]115[/C][C]3280[/C][C]3104.29306532398[/C][C]175.70693467602[/C][/ROW]
[ROW][C]116[/C][C]4220[/C][C]4015.07003101872[/C][C]204.929968981279[/C][/ROW]
[ROW][C]117[/C][C]3900[/C][C]4197.10995871899[/C][C]-297.109958718989[/C][/ROW]
[ROW][C]118[/C][C]3820[/C][C]3969.70752296647[/C][C]-149.707522966471[/C][/ROW]
[ROW][C]119[/C][C]4200[/C][C]3599.99970091731[/C][C]600.000299082687[/C][/ROW]
[ROW][C]120[/C][C]3160[/C][C]3479.29220361543[/C][C]-319.292203615431[/C][/ROW]
[ROW][C]121[/C][C]3040[/C][C]2899.24743322709[/C][C]140.752566772905[/C][/ROW]
[ROW][C]122[/C][C]2900[/C][C]2910.19701716903[/C][C]-10.1970171690255[/C][/ROW]
[ROW][C]123[/C][C]3260[/C][C]3568.07295670659[/C][C]-308.072956706591[/C][/ROW]
[ROW][C]124[/C][C]3500[/C][C]3120.91697462879[/C][C]379.083025371212[/C][/ROW]
[ROW][C]125[/C][C]3380[/C][C]3950.82103522028[/C][C]-570.82103522028[/C][/ROW]
[ROW][C]126[/C][C]4380[/C][C]4244.9807428829[/C][C]135.019257117101[/C][/ROW]
[ROW][C]127[/C][C]3400[/C][C]2914.68167448214[/C][C]485.318325517863[/C][/ROW]
[ROW][C]128[/C][C]4120[/C][C]3884.14799060922[/C][C]235.852009390777[/C][/ROW]
[ROW][C]129[/C][C]3860[/C][C]3918.40231242493[/C][C]-58.4023124249288[/C][/ROW]
[ROW][C]130[/C][C]3860[/C][C]3774.92856380442[/C][C]85.0714361955779[/C][/ROW]
[ROW][C]131[/C][C]3820[/C][C]3672.76857052861[/C][C]147.231429471391[/C][/ROW]
[ROW][C]132[/C][C]3140[/C][C]3199.95286574596[/C][C]-59.9528657459623[/C][/ROW]
[ROW][C]133[/C][C]2780[/C][C]2802.62285574678[/C][C]-22.6228557467821[/C][/ROW]
[ROW][C]134[/C][C]3120[/C][C]2742.22329656331[/C][C]377.776703436687[/C][/ROW]
[ROW][C]135[/C][C]3620[/C][C]3372.31429296771[/C][C]247.685707032289[/C][/ROW]
[ROW][C]136[/C][C]3240[/C][C]3225.68903207632[/C][C]14.3109679236786[/C][/ROW]
[ROW][C]137[/C][C]3300[/C][C]3709.27918470189[/C][C]-409.279184701885[/C][/ROW]
[ROW][C]138[/C][C]4340[/C][C]4246.58172492065[/C][C]93.4182750793461[/C][/ROW]
[ROW][C]139[/C][C]3360[/C][C]3018.49257839156[/C][C]341.50742160844[/C][/ROW]
[ROW][C]140[/C][C]3700[/C][C]3890.58255379036[/C][C]-190.582553790361[/C][/ROW]
[ROW][C]141[/C][C]3880[/C][C]3768.08706234182[/C][C]111.912937658176[/C][/ROW]
[ROW][C]142[/C][C]3560[/C][C]3696.7528019381[/C][C]-136.752801938097[/C][/ROW]
[ROW][C]143[/C][C]3800[/C][C]3579.11994945023[/C][C]220.880050549767[/C][/ROW]
[ROW][C]144[/C][C]3440[/C][C]3055.77141625543[/C][C]384.228583744572[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319804&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319804&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
1343004496.86431623932-196.864316239317
1444204552.25795682396-132.257956823955
1553405429.3804931561-89.3804931561008
1649605063.17836490758-103.178364907579
1753805481.27365730972-101.273657309722
1858405927.00239822072-87.0023982207213
1946804607.3569873952472.6430126047599
2055805000.74533568096579.254664319044
2158206120.74586996582-300.745869965818
2251805835.99911956001-655.999119560005
2352205036.93778839141183.062211608591
2444004680.90988681936-280.909886819364
2545803952.9651629502627.034837049805
2639404158.74210297804-218.742102978042
2751005034.5575225078465.4424774921563
2843204688.41861427457-368.418614274575
2952205064.06097248046155.939027519536
3059805554.705624734425.294375266001
3142204365.81328518735-145.813285187348
3261804879.178771424361300.82122857564
3357205846.73948070059-126.73948070059
3454405482.86186043632-42.8618604363219
3554205040.15633011036379.843669889637
3644804576.79436192155-96.7943619215494
3748804158.57944310347721.420556896532
3845204124.64576063383395.354239366169
3949205189.42186282135-269.421862821346
4043404661.44870721186-321.448707211856
4153405208.60702651574131.39297348426
4257005781.50444566729-81.5044456672895
4341004340.70397726683-240.703977266831
4455205283.4756251456236.5243748544
4552205647.01561614678-427.015616146777
4656405261.58887905966378.411120940341
4746005016.32060019897-416.320600198968
4844404280.75192156006159.248078439939
4942404153.4954102249986.5045897750124
5036003918.34849828438-318.348498284385
5142804664.78443736304-384.784437363041
5242804100.55918919291179.440810807093
5351804864.50742404339315.492575956612
5453205400.86353511814-80.8635351181374
5545003910.71131839245589.288681607554
5657205131.80345290688588.196547093125
5757805349.90094900137430.09905099863
5856805349.31897185394330.681028146064
5951804856.34309784328323.656902156723
6045604417.97064056421142.029359435785
6144004269.4582916755130.541708324499
6238203921.50496278311-101.504962783114
6344004686.30517829187-286.30517829187
6449604314.27477857988645.72522142012
6554005199.04776633527200.952233664733
6654605601.06714231062-141.067142310623
6752404310.67334601813929.326653981871
6848805590.9090846769-710.9090846769
6952605557.1323680579-297.132368057903
7051605412.39863758242-252.398637582424
7142004825.4423259633-625.442325963305
7250004179.93960604499820.060393955006
7343404136.37086437118203.629135628818
7441203729.865396755390.134603244996
7545204517.983460387892.01653961211377
7641604478.29796612958-318.297966129585
7746005074.19157717654-474.191577176543
7856205263.54827108593356.451728914069
7939604379.12027968193-419.120279681926
8042204941.81754254246-721.817542542456
8149005030.36854744189-130.368547441892
8248204923.87481805953-103.87481805953
8340604244.97936315896-184.979363158963
8442004109.8490551861490.1509448138613
8529003759.73600635395-859.736006353955
8637003236.91805726188463.081942738123
8742803914.32039076524365.679609234764
8837603831.5009030008-71.5009030008014
8943204416.26042400525-96.2604240052515
9050204917.12603686472102.873963135277
9134603752.96977232146-292.969772321464
9244804240.93739274877239.062607251231
9347404662.1737755528377.8262244471725
9441604596.45351154088-436.453511540875
9540003838.85108413752161.14891586248
9637803842.36809866942-62.3680986694239
9732803177.34216349857102.657836501427
9832803212.4266478388567.5733521611542
9941803797.40475832679382.595241673214
10034803584.12242600937-104.122426009367
10148204156.36885910925663.63114089075
10249204840.4880942039179.5119057960901
10331603553.25531314636-393.255313146359
10444004188.96382214466211.036177855344
10541604557.77900420513-397.779004205131
10640404259.83090284176-219.83090284176
10740203719.94803135371300.051968646286
10835603678.40317413672-118.403174136721
10931803055.79260922405124.207390775953
11031403084.595530023255.404469976796
11137803764.7728461718915.2271538281134
11234403344.8067813381495.1932186618624
11341004183.82870348778-83.8287034877821
11444404570.11193287028-130.111932870283
11532803104.29306532398175.70693467602
11642204015.07003101872204.929968981279
11739004197.10995871899-297.109958718989
11838203969.70752296647-149.707522966471
11942003599.99970091731600.000299082687
12031603479.29220361543-319.292203615431
12130402899.24743322709140.752566772905
12229002910.19701716903-10.1970171690255
12332603568.07295670659-308.072956706591
12435003120.91697462879379.083025371212
12533803950.82103522028-570.82103522028
12643804244.9807428829135.019257117101
12734002914.68167448214485.318325517863
12841203884.14799060922235.852009390777
12938603918.40231242493-58.4023124249288
13038603774.9285638044285.0714361955779
13138203672.76857052861147.231429471391
13231403199.95286574596-59.9528657459623
13327802802.62285574678-22.6228557467821
13431202742.22329656331377.776703436687
13536203372.31429296771247.685707032289
13632403225.6890320763214.3109679236786
13733003709.27918470189-409.279184701885
13843404246.5817249206593.4182750793461
13933603018.49257839156341.50742160844
14037003890.58255379036-190.582553790361
14138803768.08706234182111.912937658176
14235603696.7528019381-136.752801938097
14338003579.11994945023220.880050549767
14434403055.77141625543384.228583744572







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1452742.27053580992053.081407761123431.45966385868
1462809.460592464212111.41237730873507.50880761971
1473340.843462411662633.865097049154047.82182777416
1483084.275646998882368.296863795223800.25443020254
1493436.984941697162711.936249571024162.03363382331
1504194.263859951053460.07652588074928.45119402141
1513028.258199770712284.864230724093771.65216881732
1523684.222836883062931.554962172664436.89071159345
1533685.371796492012923.363450554464447.38014242955
1543521.104367514882749.689673113954292.51906191581
1553535.419527554632754.533279404954316.30577570431
1563027.417177474072236.994826282093817.83952866605

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
145 & 2742.2705358099 & 2053.08140776112 & 3431.45966385868 \tabularnewline
146 & 2809.46059246421 & 2111.4123773087 & 3507.50880761971 \tabularnewline
147 & 3340.84346241166 & 2633.86509704915 & 4047.82182777416 \tabularnewline
148 & 3084.27564699888 & 2368.29686379522 & 3800.25443020254 \tabularnewline
149 & 3436.98494169716 & 2711.93624957102 & 4162.03363382331 \tabularnewline
150 & 4194.26385995105 & 3460.0765258807 & 4928.45119402141 \tabularnewline
151 & 3028.25819977071 & 2284.86423072409 & 3771.65216881732 \tabularnewline
152 & 3684.22283688306 & 2931.55496217266 & 4436.89071159345 \tabularnewline
153 & 3685.37179649201 & 2923.36345055446 & 4447.38014242955 \tabularnewline
154 & 3521.10436751488 & 2749.68967311395 & 4292.51906191581 \tabularnewline
155 & 3535.41952755463 & 2754.53327940495 & 4316.30577570431 \tabularnewline
156 & 3027.41717747407 & 2236.99482628209 & 3817.83952866605 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319804&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]145[/C][C]2742.2705358099[/C][C]2053.08140776112[/C][C]3431.45966385868[/C][/ROW]
[ROW][C]146[/C][C]2809.46059246421[/C][C]2111.4123773087[/C][C]3507.50880761971[/C][/ROW]
[ROW][C]147[/C][C]3340.84346241166[/C][C]2633.86509704915[/C][C]4047.82182777416[/C][/ROW]
[ROW][C]148[/C][C]3084.27564699888[/C][C]2368.29686379522[/C][C]3800.25443020254[/C][/ROW]
[ROW][C]149[/C][C]3436.98494169716[/C][C]2711.93624957102[/C][C]4162.03363382331[/C][/ROW]
[ROW][C]150[/C][C]4194.26385995105[/C][C]3460.0765258807[/C][C]4928.45119402141[/C][/ROW]
[ROW][C]151[/C][C]3028.25819977071[/C][C]2284.86423072409[/C][C]3771.65216881732[/C][/ROW]
[ROW][C]152[/C][C]3684.22283688306[/C][C]2931.55496217266[/C][C]4436.89071159345[/C][/ROW]
[ROW][C]153[/C][C]3685.37179649201[/C][C]2923.36345055446[/C][C]4447.38014242955[/C][/ROW]
[ROW][C]154[/C][C]3521.10436751488[/C][C]2749.68967311395[/C][C]4292.51906191581[/C][/ROW]
[ROW][C]155[/C][C]3535.41952755463[/C][C]2754.53327940495[/C][C]4316.30577570431[/C][/ROW]
[ROW][C]156[/C][C]3027.41717747407[/C][C]2236.99482628209[/C][C]3817.83952866605[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319804&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319804&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
1452742.27053580992053.081407761123431.45966385868
1462809.460592464212111.41237730873507.50880761971
1473340.843462411662633.865097049154047.82182777416
1483084.275646998882368.296863795223800.25443020254
1493436.984941697162711.936249571024162.03363382331
1504194.263859951053460.07652588074928.45119402141
1513028.258199770712284.864230724093771.65216881732
1523684.222836883062931.554962172664436.89071159345
1533685.371796492012923.363450554464447.38014242955
1543521.104367514882749.689673113954292.51906191581
1553535.419527554632754.533279404954316.30577570431
1563027.417177474072236.994826282093817.83952866605



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