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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 computationMon, 12 Dec 2016 22:25:46 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/12/t1481577971vyzw0vo9sow17bt.htm/, Retrieved Fri, 01 Nov 2024 03:44:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298996, Retrieved Fri, 01 Nov 2024 03:44:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2016-12-12 21:25:46] [130d73899007e5ff8a4f636b9bcfb397] [Current]
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Dataseries X:
5483.5
5386.2
5781.8
5137.4
5001.7
5123.8
5340
5696.4
5544.7
5747.6
5487.4
5590.1
5571.9
5363.1
6014.1
5480.4
5907.5
5772.2
5620
6614.7
6294.7
5938.3
5722.6
5595.6
5569.5
5753.7
5838.8
5401.1
6013.9
5461.1
5176.3
5916.5
5519.5
5873.9
5663.8
5339
5671.2
5741
5881.3
5531.2
5811.2
5391.4
5461.2
6091.3
5951
6511.7
6371.4
5601.2
6001.2
5920.7
5455.2
5703.8
5863
5762.9
5997.8
6542.7
6594.5
6915.1
6584.6
6412.2
5930.1
6022.3
6268.6
6179.9
6608.6
6424
6230.8
6628.2
6576.2
6947
6672.8
6249.9
5964.2
5840.1
6115.2
5800.5
6566.6
6377.3
6355.2
6999.3
6603.7
6998.3
6966.2
6383.3
5960
5682.1
5640.2
5694.1
6392.4
5835.3
6075.6
7387.1
6632.6
7048.1
6792.1
6094
6408.3
6492.1
6596.8
6078.2
6297.3
5960.8
6125.1
7253.4
6505.8
7419.5
7308.2
6373.1
6667.4
6518.6
6324.8
6764.1
6985
6091.5
6526
7116.9
6770.3
7221.9
7344.5
6565.6
6577.3
6597.8
6560.6
6729.2
6703.2
6716.1




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=298996&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=298996&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298996&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
alpha0.414503629096572
beta0.0114803432407423
gamma0.494320833032801

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.414503629096572 \tabularnewline
beta & 0.0114803432407423 \tabularnewline
gamma & 0.494320833032801 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298996&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]0.414503629096572[/C][/ROW]
[ROW][C]beta[/C][C]0.0114803432407423[/C][/ROW]
[ROW][C]gamma[/C][C]0.494320833032801[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298996&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298996&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
alpha0.414503629096572
beta0.0114803432407423
gamma0.494320833032801







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
135571.95331.57395833334240.326041666662
145363.15214.41257810429148.687421895715
156014.15900.19087458009113.909125419912
165480.45417.7121605885462.687839411461
175907.55896.5503467664110.9496532335943
185772.25799.31163917831-27.1116391783062
1956205776.59237311998-156.59237311998
206614.76108.04103893122506.65896106878
216294.76202.724966026591.9750339734956
225938.36465.30441018384-527.004410183842
235722.65977.64430206072-255.04430206072
245595.65951.67398070258-356.073980702575
255569.55856.86295849915-287.362958499152
265753.75491.24138695676262.458613043244
275838.86211.44515433677-372.645154336774
285401.15507.48050610318-106.380506103176
296013.95895.47769108665118.422308913349
305461.15826.49506335481-365.395063354807
315176.35619.19570005068-442.895700050683
325916.56015.6827279802-99.1827279801955
335519.55728.09290645764-208.592906457643
345873.95674.3775504336199.522449566398
355663.85557.47289284099106.327107159012
3653395644.66755732667-305.667557326669
375671.25583.4921440270587.7078559729516
3857415527.11006259969213.88993740031
395881.36037.7773828605-156.477382860504
405531.25495.9159704959235.2840295040778
415811.26003.80865039872-192.608650398719
425391.45660.50648788771-269.106487887709
435461.25465.77864863857-4.57864863857412
446091.36140.60396888805-49.3039688880472
4559515839.43642711301111.563572886993
466511.76035.48177805054476.218221949457
476371.46006.54903007638364.850969923616
485601.26083.14563136194-481.945631361937
496001.26063.39899688618-62.1989968861781
505920.75981.33139776131-60.6313977613136
515455.26269.64085168474-814.440851684744
525703.85506.04541758636197.754582413643
5358636011.59252578497-148.592525784969
545762.95660.87161584448102.028384155517
555997.85694.78372861608303.016271383923
566542.76483.8702010619458.8297989380617
576594.56274.30432409987320.195675900132
586915.16663.58175731227251.518242687727
596584.66509.4223914222975.1776085777101
606412.26219.63201162004192.567988379955
615930.16602.93398005891-672.833980058906
626022.36267.27977610453-244.979776104529
636268.66259.199188177029.40081182297672
646179.96132.1550402523847.744959747617
656608.66476.6811686116131.918831388401
6664246317.50294787865106.497052121349
676230.86414.19337719262-183.393377192616
686628.26931.42894955276-303.228949552762
696576.26646.1516680265-69.9516680265015
7069476850.6961569199796.3038430800316
716672.86577.2855822780795.5144177219281
726249.96326.11990952044-76.2199095204369
735964.26342.48151609004-378.281516090035
745840.16249.09339573764-408.993395737642
756115.26242.21383945723-127.013839457228
765800.56064.63552076982-264.135520769822
776566.66297.67630580031268.923694199687
786377.36182.00979498712195.290205012883
796355.26226.10721616111129.092783838885
806999.36834.17615044784165.12384955216
816603.76808.76724270108-205.067242701084
826998.37002.99966202115-4.69966202114665
836966.26684.58929908903281.610700910973
846383.36458.8379126146-75.5379126145972
8559606386.04243712042-426.042437120424
865682.16261.72505881268-579.62505881268
875640.26262.67401104497-622.474011044969
885694.15834.62632667975-140.526326679745
896392.46268.35825851252124.041741487477
905835.36065.81204298925-230.512042989253
916075.65906.71320579555168.886794204454
927387.16534.35386688844852.746133111558
936632.66682.74594834739-50.1459483473909
947048.16995.84291239652.2570876040027
956792.16780.8352942626211.2647057373788
9660946335.30013476076-241.30013476076
976408.36087.20538884414321.094611155861
986492.16226.53789836116265.562101638839
996596.86567.849687278428.9503127216021
1006078.26554.83758220601-476.637582206006
1016297.36929.75390571015-632.453905710151
1025960.86311.35319520217-350.553195202167
1036125.16217.852598035-92.752598035001
1047253.46933.48289317443319.917106825566
1056505.86595.67753587104-89.87753587104
1067419.56917.73425339827501.765746601731
1077308.26875.1153583551433.084641644899
1086373.16531.26518954016-158.16518954016
1096667.46480.7329783791186.667021620899
1106518.66547.9654761107-29.3654761107045
1116324.86696.83745230364-372.037452303643
1126764.16367.66715798037396.432842019632
11369857059.9136229735-74.9136229734977
1146091.56757.39320158903-665.893201589028
11565266609.48512672738-83.4851267273771
1167116.97450.12571239303-333.225712393035
1176770.36721.6109590116448.6890409883645
1187221.97271.62330982216-49.7233098221559
1197344.56977.19204302314367.307956976862
1206565.66431.30259885385134.297401146152
1216577.36599.53804069723-22.2380406972325
1226597.86514.3981981253383.4018018746665
1236560.66608.11642118593-47.5164211859283
1246729.26634.6995420575394.5004579424703
1256703.27062.7638668415-359.563866841499
1266716.16467.24568484558248.854315154418

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5571.9 & 5331.57395833334 & 240.326041666662 \tabularnewline
14 & 5363.1 & 5214.41257810429 & 148.687421895715 \tabularnewline
15 & 6014.1 & 5900.19087458009 & 113.909125419912 \tabularnewline
16 & 5480.4 & 5417.71216058854 & 62.687839411461 \tabularnewline
17 & 5907.5 & 5896.55034676641 & 10.9496532335943 \tabularnewline
18 & 5772.2 & 5799.31163917831 & -27.1116391783062 \tabularnewline
19 & 5620 & 5776.59237311998 & -156.59237311998 \tabularnewline
20 & 6614.7 & 6108.04103893122 & 506.65896106878 \tabularnewline
21 & 6294.7 & 6202.7249660265 & 91.9750339734956 \tabularnewline
22 & 5938.3 & 6465.30441018384 & -527.004410183842 \tabularnewline
23 & 5722.6 & 5977.64430206072 & -255.04430206072 \tabularnewline
24 & 5595.6 & 5951.67398070258 & -356.073980702575 \tabularnewline
25 & 5569.5 & 5856.86295849915 & -287.362958499152 \tabularnewline
26 & 5753.7 & 5491.24138695676 & 262.458613043244 \tabularnewline
27 & 5838.8 & 6211.44515433677 & -372.645154336774 \tabularnewline
28 & 5401.1 & 5507.48050610318 & -106.380506103176 \tabularnewline
29 & 6013.9 & 5895.47769108665 & 118.422308913349 \tabularnewline
30 & 5461.1 & 5826.49506335481 & -365.395063354807 \tabularnewline
31 & 5176.3 & 5619.19570005068 & -442.895700050683 \tabularnewline
32 & 5916.5 & 6015.6827279802 & -99.1827279801955 \tabularnewline
33 & 5519.5 & 5728.09290645764 & -208.592906457643 \tabularnewline
34 & 5873.9 & 5674.3775504336 & 199.522449566398 \tabularnewline
35 & 5663.8 & 5557.47289284099 & 106.327107159012 \tabularnewline
36 & 5339 & 5644.66755732667 & -305.667557326669 \tabularnewline
37 & 5671.2 & 5583.49214402705 & 87.7078559729516 \tabularnewline
38 & 5741 & 5527.11006259969 & 213.88993740031 \tabularnewline
39 & 5881.3 & 6037.7773828605 & -156.477382860504 \tabularnewline
40 & 5531.2 & 5495.91597049592 & 35.2840295040778 \tabularnewline
41 & 5811.2 & 6003.80865039872 & -192.608650398719 \tabularnewline
42 & 5391.4 & 5660.50648788771 & -269.106487887709 \tabularnewline
43 & 5461.2 & 5465.77864863857 & -4.57864863857412 \tabularnewline
44 & 6091.3 & 6140.60396888805 & -49.3039688880472 \tabularnewline
45 & 5951 & 5839.43642711301 & 111.563572886993 \tabularnewline
46 & 6511.7 & 6035.48177805054 & 476.218221949457 \tabularnewline
47 & 6371.4 & 6006.54903007638 & 364.850969923616 \tabularnewline
48 & 5601.2 & 6083.14563136194 & -481.945631361937 \tabularnewline
49 & 6001.2 & 6063.39899688618 & -62.1989968861781 \tabularnewline
50 & 5920.7 & 5981.33139776131 & -60.6313977613136 \tabularnewline
51 & 5455.2 & 6269.64085168474 & -814.440851684744 \tabularnewline
52 & 5703.8 & 5506.04541758636 & 197.754582413643 \tabularnewline
53 & 5863 & 6011.59252578497 & -148.592525784969 \tabularnewline
54 & 5762.9 & 5660.87161584448 & 102.028384155517 \tabularnewline
55 & 5997.8 & 5694.78372861608 & 303.016271383923 \tabularnewline
56 & 6542.7 & 6483.87020106194 & 58.8297989380617 \tabularnewline
57 & 6594.5 & 6274.30432409987 & 320.195675900132 \tabularnewline
58 & 6915.1 & 6663.58175731227 & 251.518242687727 \tabularnewline
59 & 6584.6 & 6509.42239142229 & 75.1776085777101 \tabularnewline
60 & 6412.2 & 6219.63201162004 & 192.567988379955 \tabularnewline
61 & 5930.1 & 6602.93398005891 & -672.833980058906 \tabularnewline
62 & 6022.3 & 6267.27977610453 & -244.979776104529 \tabularnewline
63 & 6268.6 & 6259.19918817702 & 9.40081182297672 \tabularnewline
64 & 6179.9 & 6132.15504025238 & 47.744959747617 \tabularnewline
65 & 6608.6 & 6476.6811686116 & 131.918831388401 \tabularnewline
66 & 6424 & 6317.50294787865 & 106.497052121349 \tabularnewline
67 & 6230.8 & 6414.19337719262 & -183.393377192616 \tabularnewline
68 & 6628.2 & 6931.42894955276 & -303.228949552762 \tabularnewline
69 & 6576.2 & 6646.1516680265 & -69.9516680265015 \tabularnewline
70 & 6947 & 6850.69615691997 & 96.3038430800316 \tabularnewline
71 & 6672.8 & 6577.28558227807 & 95.5144177219281 \tabularnewline
72 & 6249.9 & 6326.11990952044 & -76.2199095204369 \tabularnewline
73 & 5964.2 & 6342.48151609004 & -378.281516090035 \tabularnewline
74 & 5840.1 & 6249.09339573764 & -408.993395737642 \tabularnewline
75 & 6115.2 & 6242.21383945723 & -127.013839457228 \tabularnewline
76 & 5800.5 & 6064.63552076982 & -264.135520769822 \tabularnewline
77 & 6566.6 & 6297.67630580031 & 268.923694199687 \tabularnewline
78 & 6377.3 & 6182.00979498712 & 195.290205012883 \tabularnewline
79 & 6355.2 & 6226.10721616111 & 129.092783838885 \tabularnewline
80 & 6999.3 & 6834.17615044784 & 165.12384955216 \tabularnewline
81 & 6603.7 & 6808.76724270108 & -205.067242701084 \tabularnewline
82 & 6998.3 & 7002.99966202115 & -4.69966202114665 \tabularnewline
83 & 6966.2 & 6684.58929908903 & 281.610700910973 \tabularnewline
84 & 6383.3 & 6458.8379126146 & -75.5379126145972 \tabularnewline
85 & 5960 & 6386.04243712042 & -426.042437120424 \tabularnewline
86 & 5682.1 & 6261.72505881268 & -579.62505881268 \tabularnewline
87 & 5640.2 & 6262.67401104497 & -622.474011044969 \tabularnewline
88 & 5694.1 & 5834.62632667975 & -140.526326679745 \tabularnewline
89 & 6392.4 & 6268.35825851252 & 124.041741487477 \tabularnewline
90 & 5835.3 & 6065.81204298925 & -230.512042989253 \tabularnewline
91 & 6075.6 & 5906.71320579555 & 168.886794204454 \tabularnewline
92 & 7387.1 & 6534.35386688844 & 852.746133111558 \tabularnewline
93 & 6632.6 & 6682.74594834739 & -50.1459483473909 \tabularnewline
94 & 7048.1 & 6995.842912396 & 52.2570876040027 \tabularnewline
95 & 6792.1 & 6780.83529426262 & 11.2647057373788 \tabularnewline
96 & 6094 & 6335.30013476076 & -241.30013476076 \tabularnewline
97 & 6408.3 & 6087.20538884414 & 321.094611155861 \tabularnewline
98 & 6492.1 & 6226.53789836116 & 265.562101638839 \tabularnewline
99 & 6596.8 & 6567.8496872784 & 28.9503127216021 \tabularnewline
100 & 6078.2 & 6554.83758220601 & -476.637582206006 \tabularnewline
101 & 6297.3 & 6929.75390571015 & -632.453905710151 \tabularnewline
102 & 5960.8 & 6311.35319520217 & -350.553195202167 \tabularnewline
103 & 6125.1 & 6217.852598035 & -92.752598035001 \tabularnewline
104 & 7253.4 & 6933.48289317443 & 319.917106825566 \tabularnewline
105 & 6505.8 & 6595.67753587104 & -89.87753587104 \tabularnewline
106 & 7419.5 & 6917.73425339827 & 501.765746601731 \tabularnewline
107 & 7308.2 & 6875.1153583551 & 433.084641644899 \tabularnewline
108 & 6373.1 & 6531.26518954016 & -158.16518954016 \tabularnewline
109 & 6667.4 & 6480.7329783791 & 186.667021620899 \tabularnewline
110 & 6518.6 & 6547.9654761107 & -29.3654761107045 \tabularnewline
111 & 6324.8 & 6696.83745230364 & -372.037452303643 \tabularnewline
112 & 6764.1 & 6367.66715798037 & 396.432842019632 \tabularnewline
113 & 6985 & 7059.9136229735 & -74.9136229734977 \tabularnewline
114 & 6091.5 & 6757.39320158903 & -665.893201589028 \tabularnewline
115 & 6526 & 6609.48512672738 & -83.4851267273771 \tabularnewline
116 & 7116.9 & 7450.12571239303 & -333.225712393035 \tabularnewline
117 & 6770.3 & 6721.61095901164 & 48.6890409883645 \tabularnewline
118 & 7221.9 & 7271.62330982216 & -49.7233098221559 \tabularnewline
119 & 7344.5 & 6977.19204302314 & 367.307956976862 \tabularnewline
120 & 6565.6 & 6431.30259885385 & 134.297401146152 \tabularnewline
121 & 6577.3 & 6599.53804069723 & -22.2380406972325 \tabularnewline
122 & 6597.8 & 6514.39819812533 & 83.4018018746665 \tabularnewline
123 & 6560.6 & 6608.11642118593 & -47.5164211859283 \tabularnewline
124 & 6729.2 & 6634.69954205753 & 94.5004579424703 \tabularnewline
125 & 6703.2 & 7062.7638668415 & -359.563866841499 \tabularnewline
126 & 6716.1 & 6467.24568484558 & 248.854315154418 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298996&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]5571.9[/C][C]5331.57395833334[/C][C]240.326041666662[/C][/ROW]
[ROW][C]14[/C][C]5363.1[/C][C]5214.41257810429[/C][C]148.687421895715[/C][/ROW]
[ROW][C]15[/C][C]6014.1[/C][C]5900.19087458009[/C][C]113.909125419912[/C][/ROW]
[ROW][C]16[/C][C]5480.4[/C][C]5417.71216058854[/C][C]62.687839411461[/C][/ROW]
[ROW][C]17[/C][C]5907.5[/C][C]5896.55034676641[/C][C]10.9496532335943[/C][/ROW]
[ROW][C]18[/C][C]5772.2[/C][C]5799.31163917831[/C][C]-27.1116391783062[/C][/ROW]
[ROW][C]19[/C][C]5620[/C][C]5776.59237311998[/C][C]-156.59237311998[/C][/ROW]
[ROW][C]20[/C][C]6614.7[/C][C]6108.04103893122[/C][C]506.65896106878[/C][/ROW]
[ROW][C]21[/C][C]6294.7[/C][C]6202.7249660265[/C][C]91.9750339734956[/C][/ROW]
[ROW][C]22[/C][C]5938.3[/C][C]6465.30441018384[/C][C]-527.004410183842[/C][/ROW]
[ROW][C]23[/C][C]5722.6[/C][C]5977.64430206072[/C][C]-255.04430206072[/C][/ROW]
[ROW][C]24[/C][C]5595.6[/C][C]5951.67398070258[/C][C]-356.073980702575[/C][/ROW]
[ROW][C]25[/C][C]5569.5[/C][C]5856.86295849915[/C][C]-287.362958499152[/C][/ROW]
[ROW][C]26[/C][C]5753.7[/C][C]5491.24138695676[/C][C]262.458613043244[/C][/ROW]
[ROW][C]27[/C][C]5838.8[/C][C]6211.44515433677[/C][C]-372.645154336774[/C][/ROW]
[ROW][C]28[/C][C]5401.1[/C][C]5507.48050610318[/C][C]-106.380506103176[/C][/ROW]
[ROW][C]29[/C][C]6013.9[/C][C]5895.47769108665[/C][C]118.422308913349[/C][/ROW]
[ROW][C]30[/C][C]5461.1[/C][C]5826.49506335481[/C][C]-365.395063354807[/C][/ROW]
[ROW][C]31[/C][C]5176.3[/C][C]5619.19570005068[/C][C]-442.895700050683[/C][/ROW]
[ROW][C]32[/C][C]5916.5[/C][C]6015.6827279802[/C][C]-99.1827279801955[/C][/ROW]
[ROW][C]33[/C][C]5519.5[/C][C]5728.09290645764[/C][C]-208.592906457643[/C][/ROW]
[ROW][C]34[/C][C]5873.9[/C][C]5674.3775504336[/C][C]199.522449566398[/C][/ROW]
[ROW][C]35[/C][C]5663.8[/C][C]5557.47289284099[/C][C]106.327107159012[/C][/ROW]
[ROW][C]36[/C][C]5339[/C][C]5644.66755732667[/C][C]-305.667557326669[/C][/ROW]
[ROW][C]37[/C][C]5671.2[/C][C]5583.49214402705[/C][C]87.7078559729516[/C][/ROW]
[ROW][C]38[/C][C]5741[/C][C]5527.11006259969[/C][C]213.88993740031[/C][/ROW]
[ROW][C]39[/C][C]5881.3[/C][C]6037.7773828605[/C][C]-156.477382860504[/C][/ROW]
[ROW][C]40[/C][C]5531.2[/C][C]5495.91597049592[/C][C]35.2840295040778[/C][/ROW]
[ROW][C]41[/C][C]5811.2[/C][C]6003.80865039872[/C][C]-192.608650398719[/C][/ROW]
[ROW][C]42[/C][C]5391.4[/C][C]5660.50648788771[/C][C]-269.106487887709[/C][/ROW]
[ROW][C]43[/C][C]5461.2[/C][C]5465.77864863857[/C][C]-4.57864863857412[/C][/ROW]
[ROW][C]44[/C][C]6091.3[/C][C]6140.60396888805[/C][C]-49.3039688880472[/C][/ROW]
[ROW][C]45[/C][C]5951[/C][C]5839.43642711301[/C][C]111.563572886993[/C][/ROW]
[ROW][C]46[/C][C]6511.7[/C][C]6035.48177805054[/C][C]476.218221949457[/C][/ROW]
[ROW][C]47[/C][C]6371.4[/C][C]6006.54903007638[/C][C]364.850969923616[/C][/ROW]
[ROW][C]48[/C][C]5601.2[/C][C]6083.14563136194[/C][C]-481.945631361937[/C][/ROW]
[ROW][C]49[/C][C]6001.2[/C][C]6063.39899688618[/C][C]-62.1989968861781[/C][/ROW]
[ROW][C]50[/C][C]5920.7[/C][C]5981.33139776131[/C][C]-60.6313977613136[/C][/ROW]
[ROW][C]51[/C][C]5455.2[/C][C]6269.64085168474[/C][C]-814.440851684744[/C][/ROW]
[ROW][C]52[/C][C]5703.8[/C][C]5506.04541758636[/C][C]197.754582413643[/C][/ROW]
[ROW][C]53[/C][C]5863[/C][C]6011.59252578497[/C][C]-148.592525784969[/C][/ROW]
[ROW][C]54[/C][C]5762.9[/C][C]5660.87161584448[/C][C]102.028384155517[/C][/ROW]
[ROW][C]55[/C][C]5997.8[/C][C]5694.78372861608[/C][C]303.016271383923[/C][/ROW]
[ROW][C]56[/C][C]6542.7[/C][C]6483.87020106194[/C][C]58.8297989380617[/C][/ROW]
[ROW][C]57[/C][C]6594.5[/C][C]6274.30432409987[/C][C]320.195675900132[/C][/ROW]
[ROW][C]58[/C][C]6915.1[/C][C]6663.58175731227[/C][C]251.518242687727[/C][/ROW]
[ROW][C]59[/C][C]6584.6[/C][C]6509.42239142229[/C][C]75.1776085777101[/C][/ROW]
[ROW][C]60[/C][C]6412.2[/C][C]6219.63201162004[/C][C]192.567988379955[/C][/ROW]
[ROW][C]61[/C][C]5930.1[/C][C]6602.93398005891[/C][C]-672.833980058906[/C][/ROW]
[ROW][C]62[/C][C]6022.3[/C][C]6267.27977610453[/C][C]-244.979776104529[/C][/ROW]
[ROW][C]63[/C][C]6268.6[/C][C]6259.19918817702[/C][C]9.40081182297672[/C][/ROW]
[ROW][C]64[/C][C]6179.9[/C][C]6132.15504025238[/C][C]47.744959747617[/C][/ROW]
[ROW][C]65[/C][C]6608.6[/C][C]6476.6811686116[/C][C]131.918831388401[/C][/ROW]
[ROW][C]66[/C][C]6424[/C][C]6317.50294787865[/C][C]106.497052121349[/C][/ROW]
[ROW][C]67[/C][C]6230.8[/C][C]6414.19337719262[/C][C]-183.393377192616[/C][/ROW]
[ROW][C]68[/C][C]6628.2[/C][C]6931.42894955276[/C][C]-303.228949552762[/C][/ROW]
[ROW][C]69[/C][C]6576.2[/C][C]6646.1516680265[/C][C]-69.9516680265015[/C][/ROW]
[ROW][C]70[/C][C]6947[/C][C]6850.69615691997[/C][C]96.3038430800316[/C][/ROW]
[ROW][C]71[/C][C]6672.8[/C][C]6577.28558227807[/C][C]95.5144177219281[/C][/ROW]
[ROW][C]72[/C][C]6249.9[/C][C]6326.11990952044[/C][C]-76.2199095204369[/C][/ROW]
[ROW][C]73[/C][C]5964.2[/C][C]6342.48151609004[/C][C]-378.281516090035[/C][/ROW]
[ROW][C]74[/C][C]5840.1[/C][C]6249.09339573764[/C][C]-408.993395737642[/C][/ROW]
[ROW][C]75[/C][C]6115.2[/C][C]6242.21383945723[/C][C]-127.013839457228[/C][/ROW]
[ROW][C]76[/C][C]5800.5[/C][C]6064.63552076982[/C][C]-264.135520769822[/C][/ROW]
[ROW][C]77[/C][C]6566.6[/C][C]6297.67630580031[/C][C]268.923694199687[/C][/ROW]
[ROW][C]78[/C][C]6377.3[/C][C]6182.00979498712[/C][C]195.290205012883[/C][/ROW]
[ROW][C]79[/C][C]6355.2[/C][C]6226.10721616111[/C][C]129.092783838885[/C][/ROW]
[ROW][C]80[/C][C]6999.3[/C][C]6834.17615044784[/C][C]165.12384955216[/C][/ROW]
[ROW][C]81[/C][C]6603.7[/C][C]6808.76724270108[/C][C]-205.067242701084[/C][/ROW]
[ROW][C]82[/C][C]6998.3[/C][C]7002.99966202115[/C][C]-4.69966202114665[/C][/ROW]
[ROW][C]83[/C][C]6966.2[/C][C]6684.58929908903[/C][C]281.610700910973[/C][/ROW]
[ROW][C]84[/C][C]6383.3[/C][C]6458.8379126146[/C][C]-75.5379126145972[/C][/ROW]
[ROW][C]85[/C][C]5960[/C][C]6386.04243712042[/C][C]-426.042437120424[/C][/ROW]
[ROW][C]86[/C][C]5682.1[/C][C]6261.72505881268[/C][C]-579.62505881268[/C][/ROW]
[ROW][C]87[/C][C]5640.2[/C][C]6262.67401104497[/C][C]-622.474011044969[/C][/ROW]
[ROW][C]88[/C][C]5694.1[/C][C]5834.62632667975[/C][C]-140.526326679745[/C][/ROW]
[ROW][C]89[/C][C]6392.4[/C][C]6268.35825851252[/C][C]124.041741487477[/C][/ROW]
[ROW][C]90[/C][C]5835.3[/C][C]6065.81204298925[/C][C]-230.512042989253[/C][/ROW]
[ROW][C]91[/C][C]6075.6[/C][C]5906.71320579555[/C][C]168.886794204454[/C][/ROW]
[ROW][C]92[/C][C]7387.1[/C][C]6534.35386688844[/C][C]852.746133111558[/C][/ROW]
[ROW][C]93[/C][C]6632.6[/C][C]6682.74594834739[/C][C]-50.1459483473909[/C][/ROW]
[ROW][C]94[/C][C]7048.1[/C][C]6995.842912396[/C][C]52.2570876040027[/C][/ROW]
[ROW][C]95[/C][C]6792.1[/C][C]6780.83529426262[/C][C]11.2647057373788[/C][/ROW]
[ROW][C]96[/C][C]6094[/C][C]6335.30013476076[/C][C]-241.30013476076[/C][/ROW]
[ROW][C]97[/C][C]6408.3[/C][C]6087.20538884414[/C][C]321.094611155861[/C][/ROW]
[ROW][C]98[/C][C]6492.1[/C][C]6226.53789836116[/C][C]265.562101638839[/C][/ROW]
[ROW][C]99[/C][C]6596.8[/C][C]6567.8496872784[/C][C]28.9503127216021[/C][/ROW]
[ROW][C]100[/C][C]6078.2[/C][C]6554.83758220601[/C][C]-476.637582206006[/C][/ROW]
[ROW][C]101[/C][C]6297.3[/C][C]6929.75390571015[/C][C]-632.453905710151[/C][/ROW]
[ROW][C]102[/C][C]5960.8[/C][C]6311.35319520217[/C][C]-350.553195202167[/C][/ROW]
[ROW][C]103[/C][C]6125.1[/C][C]6217.852598035[/C][C]-92.752598035001[/C][/ROW]
[ROW][C]104[/C][C]7253.4[/C][C]6933.48289317443[/C][C]319.917106825566[/C][/ROW]
[ROW][C]105[/C][C]6505.8[/C][C]6595.67753587104[/C][C]-89.87753587104[/C][/ROW]
[ROW][C]106[/C][C]7419.5[/C][C]6917.73425339827[/C][C]501.765746601731[/C][/ROW]
[ROW][C]107[/C][C]7308.2[/C][C]6875.1153583551[/C][C]433.084641644899[/C][/ROW]
[ROW][C]108[/C][C]6373.1[/C][C]6531.26518954016[/C][C]-158.16518954016[/C][/ROW]
[ROW][C]109[/C][C]6667.4[/C][C]6480.7329783791[/C][C]186.667021620899[/C][/ROW]
[ROW][C]110[/C][C]6518.6[/C][C]6547.9654761107[/C][C]-29.3654761107045[/C][/ROW]
[ROW][C]111[/C][C]6324.8[/C][C]6696.83745230364[/C][C]-372.037452303643[/C][/ROW]
[ROW][C]112[/C][C]6764.1[/C][C]6367.66715798037[/C][C]396.432842019632[/C][/ROW]
[ROW][C]113[/C][C]6985[/C][C]7059.9136229735[/C][C]-74.9136229734977[/C][/ROW]
[ROW][C]114[/C][C]6091.5[/C][C]6757.39320158903[/C][C]-665.893201589028[/C][/ROW]
[ROW][C]115[/C][C]6526[/C][C]6609.48512672738[/C][C]-83.4851267273771[/C][/ROW]
[ROW][C]116[/C][C]7116.9[/C][C]7450.12571239303[/C][C]-333.225712393035[/C][/ROW]
[ROW][C]117[/C][C]6770.3[/C][C]6721.61095901164[/C][C]48.6890409883645[/C][/ROW]
[ROW][C]118[/C][C]7221.9[/C][C]7271.62330982216[/C][C]-49.7233098221559[/C][/ROW]
[ROW][C]119[/C][C]7344.5[/C][C]6977.19204302314[/C][C]367.307956976862[/C][/ROW]
[ROW][C]120[/C][C]6565.6[/C][C]6431.30259885385[/C][C]134.297401146152[/C][/ROW]
[ROW][C]121[/C][C]6577.3[/C][C]6599.53804069723[/C][C]-22.2380406972325[/C][/ROW]
[ROW][C]122[/C][C]6597.8[/C][C]6514.39819812533[/C][C]83.4018018746665[/C][/ROW]
[ROW][C]123[/C][C]6560.6[/C][C]6608.11642118593[/C][C]-47.5164211859283[/C][/ROW]
[ROW][C]124[/C][C]6729.2[/C][C]6634.69954205753[/C][C]94.5004579424703[/C][/ROW]
[ROW][C]125[/C][C]6703.2[/C][C]7062.7638668415[/C][C]-359.563866841499[/C][/ROW]
[ROW][C]126[/C][C]6716.1[/C][C]6467.24568484558[/C][C]248.854315154418[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298996&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298996&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
135571.95331.57395833334240.326041666662
145363.15214.41257810429148.687421895715
156014.15900.19087458009113.909125419912
165480.45417.7121605885462.687839411461
175907.55896.5503467664110.9496532335943
185772.25799.31163917831-27.1116391783062
1956205776.59237311998-156.59237311998
206614.76108.04103893122506.65896106878
216294.76202.724966026591.9750339734956
225938.36465.30441018384-527.004410183842
235722.65977.64430206072-255.04430206072
245595.65951.67398070258-356.073980702575
255569.55856.86295849915-287.362958499152
265753.75491.24138695676262.458613043244
275838.86211.44515433677-372.645154336774
285401.15507.48050610318-106.380506103176
296013.95895.47769108665118.422308913349
305461.15826.49506335481-365.395063354807
315176.35619.19570005068-442.895700050683
325916.56015.6827279802-99.1827279801955
335519.55728.09290645764-208.592906457643
345873.95674.3775504336199.522449566398
355663.85557.47289284099106.327107159012
3653395644.66755732667-305.667557326669
375671.25583.4921440270587.7078559729516
3857415527.11006259969213.88993740031
395881.36037.7773828605-156.477382860504
405531.25495.9159704959235.2840295040778
415811.26003.80865039872-192.608650398719
425391.45660.50648788771-269.106487887709
435461.25465.77864863857-4.57864863857412
446091.36140.60396888805-49.3039688880472
4559515839.43642711301111.563572886993
466511.76035.48177805054476.218221949457
476371.46006.54903007638364.850969923616
485601.26083.14563136194-481.945631361937
496001.26063.39899688618-62.1989968861781
505920.75981.33139776131-60.6313977613136
515455.26269.64085168474-814.440851684744
525703.85506.04541758636197.754582413643
5358636011.59252578497-148.592525784969
545762.95660.87161584448102.028384155517
555997.85694.78372861608303.016271383923
566542.76483.8702010619458.8297989380617
576594.56274.30432409987320.195675900132
586915.16663.58175731227251.518242687727
596584.66509.4223914222975.1776085777101
606412.26219.63201162004192.567988379955
615930.16602.93398005891-672.833980058906
626022.36267.27977610453-244.979776104529
636268.66259.199188177029.40081182297672
646179.96132.1550402523847.744959747617
656608.66476.6811686116131.918831388401
6664246317.50294787865106.497052121349
676230.86414.19337719262-183.393377192616
686628.26931.42894955276-303.228949552762
696576.26646.1516680265-69.9516680265015
7069476850.6961569199796.3038430800316
716672.86577.2855822780795.5144177219281
726249.96326.11990952044-76.2199095204369
735964.26342.48151609004-378.281516090035
745840.16249.09339573764-408.993395737642
756115.26242.21383945723-127.013839457228
765800.56064.63552076982-264.135520769822
776566.66297.67630580031268.923694199687
786377.36182.00979498712195.290205012883
796355.26226.10721616111129.092783838885
806999.36834.17615044784165.12384955216
816603.76808.76724270108-205.067242701084
826998.37002.99966202115-4.69966202114665
836966.26684.58929908903281.610700910973
846383.36458.8379126146-75.5379126145972
8559606386.04243712042-426.042437120424
865682.16261.72505881268-579.62505881268
875640.26262.67401104497-622.474011044969
885694.15834.62632667975-140.526326679745
896392.46268.35825851252124.041741487477
905835.36065.81204298925-230.512042989253
916075.65906.71320579555168.886794204454
927387.16534.35386688844852.746133111558
936632.66682.74594834739-50.1459483473909
947048.16995.84291239652.2570876040027
956792.16780.8352942626211.2647057373788
9660946335.30013476076-241.30013476076
976408.36087.20538884414321.094611155861
986492.16226.53789836116265.562101638839
996596.86567.849687278428.9503127216021
1006078.26554.83758220601-476.637582206006
1016297.36929.75390571015-632.453905710151
1025960.86311.35319520217-350.553195202167
1036125.16217.852598035-92.752598035001
1047253.46933.48289317443319.917106825566
1056505.86595.67753587104-89.87753587104
1067419.56917.73425339827501.765746601731
1077308.26875.1153583551433.084641644899
1086373.16531.26518954016-158.16518954016
1096667.46480.7329783791186.667021620899
1106518.66547.9654761107-29.3654761107045
1116324.86696.83745230364-372.037452303643
1126764.16367.66715798037396.432842019632
11369857059.9136229735-74.9136229734977
1146091.56757.39320158903-665.893201589028
11565266609.48512672738-83.4851267273771
1167116.97450.12571239303-333.225712393035
1176770.36721.6109590116448.6890409883645
1187221.97271.62330982216-49.7233098221559
1197344.56977.19204302314367.307956976862
1206565.66431.30259885385134.297401146152
1216577.36599.53804069723-22.2380406972325
1226597.86514.3981981253383.4018018746665
1236560.66608.11642118593-47.5164211859283
1246729.26634.6995420575394.5004579424703
1256703.27062.7638668415-359.563866841499
1266716.16467.24568484558248.854315154418







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1276867.452969563986303.388786704487431.51715242348
1287671.201906861017059.567771334558282.83604238747
1297193.715203895656536.980095858687850.45031193262
1307697.201122711016997.346229752928397.05601566909
1317546.453581874156805.104586731278287.80257701702
1326781.501912944826000.016279049177562.98754684047
1336848.753438554266028.280604752797669.22627235572
1346803.499582839315945.023976131047661.97518954758
1356824.453457397825928.826138387787720.08077640786
1366911.758132835875979.720653766957843.79561190478
1377168.708164012726200.910932946088136.50539507936
1386899.504967014825896.521637930297902.48829609935

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
127 & 6867.45296956398 & 6303.38878670448 & 7431.51715242348 \tabularnewline
128 & 7671.20190686101 & 7059.56777133455 & 8282.83604238747 \tabularnewline
129 & 7193.71520389565 & 6536.98009585868 & 7850.45031193262 \tabularnewline
130 & 7697.20112271101 & 6997.34622975292 & 8397.05601566909 \tabularnewline
131 & 7546.45358187415 & 6805.10458673127 & 8287.80257701702 \tabularnewline
132 & 6781.50191294482 & 6000.01627904917 & 7562.98754684047 \tabularnewline
133 & 6848.75343855426 & 6028.28060475279 & 7669.22627235572 \tabularnewline
134 & 6803.49958283931 & 5945.02397613104 & 7661.97518954758 \tabularnewline
135 & 6824.45345739782 & 5928.82613838778 & 7720.08077640786 \tabularnewline
136 & 6911.75813283587 & 5979.72065376695 & 7843.79561190478 \tabularnewline
137 & 7168.70816401272 & 6200.91093294608 & 8136.50539507936 \tabularnewline
138 & 6899.50496701482 & 5896.52163793029 & 7902.48829609935 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298996&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]127[/C][C]6867.45296956398[/C][C]6303.38878670448[/C][C]7431.51715242348[/C][/ROW]
[ROW][C]128[/C][C]7671.20190686101[/C][C]7059.56777133455[/C][C]8282.83604238747[/C][/ROW]
[ROW][C]129[/C][C]7193.71520389565[/C][C]6536.98009585868[/C][C]7850.45031193262[/C][/ROW]
[ROW][C]130[/C][C]7697.20112271101[/C][C]6997.34622975292[/C][C]8397.05601566909[/C][/ROW]
[ROW][C]131[/C][C]7546.45358187415[/C][C]6805.10458673127[/C][C]8287.80257701702[/C][/ROW]
[ROW][C]132[/C][C]6781.50191294482[/C][C]6000.01627904917[/C][C]7562.98754684047[/C][/ROW]
[ROW][C]133[/C][C]6848.75343855426[/C][C]6028.28060475279[/C][C]7669.22627235572[/C][/ROW]
[ROW][C]134[/C][C]6803.49958283931[/C][C]5945.02397613104[/C][C]7661.97518954758[/C][/ROW]
[ROW][C]135[/C][C]6824.45345739782[/C][C]5928.82613838778[/C][C]7720.08077640786[/C][/ROW]
[ROW][C]136[/C][C]6911.75813283587[/C][C]5979.72065376695[/C][C]7843.79561190478[/C][/ROW]
[ROW][C]137[/C][C]7168.70816401272[/C][C]6200.91093294608[/C][C]8136.50539507936[/C][/ROW]
[ROW][C]138[/C][C]6899.50496701482[/C][C]5896.52163793029[/C][C]7902.48829609935[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298996&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298996&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
1276867.452969563986303.388786704487431.51715242348
1287671.201906861017059.567771334558282.83604238747
1297193.715203895656536.980095858687850.45031193262
1307697.201122711016997.346229752928397.05601566909
1317546.453581874156805.104586731278287.80257701702
1326781.501912944826000.016279049177562.98754684047
1336848.753438554266028.280604752797669.22627235572
1346803.499582839315945.023976131047661.97518954758
1356824.453457397825928.826138387787720.08077640786
1366911.758132835875979.720653766957843.79561190478
1377168.708164012726200.910932946088136.50539507936
1386899.504967014825896.521637930297902.48829609935



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
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 <- 'Single'
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')