Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 29 Jul 2012 07:39:43 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Jul/29/t1343562108ofwg5odiwpxj53j.htm/, Retrieved Wed, 01 May 2024 19:40:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=168946, Retrieved Wed, 01 May 2024 19:40:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsBart Mortelmans
Estimated Impact179
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Tijdreeks 2 - Stap 1] [2012-07-29 10:04:17] [f85cc8f00ef4b762f0a6fdfddc793773]
- RMP   [Harrell-Davis Quantiles] [Tijdreeks 2 - Stap 5] [2012-07-29 10:30:29] [226376a35b8869827dc57271384c00a4]
- RMP     [Mean versus Median] [Tijdreeks 2 - Stap 8] [2012-07-29 10:41:52] [226376a35b8869827dc57271384c00a4]
- RM        [(Partial) Autocorrelation Function] [Tijdreeks 2 - Sta...] [2012-07-29 11:08:12] [226376a35b8869827dc57271384c00a4]
- RM            [Exponential Smoothing] [Tijdreeks 2 - Sta...] [2012-07-29 11:39:43] [480fcaba71e70207c3e0ad7177944aa6] [Current]
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Dataseries X:
940
950
920
930
930
900
940
840
890
850
830
940
960
900
940
920
930
970
930
780
810
870
720
880
920
920
950
950
890
960
780
780
760
860
740
1020
890
1040
920
900
950
990
840
740
840
960
790
1010
900
970
920
980
890
1000
880
740
860
940
760
1010
870
980
920
950
880
980
910
730
880
820
690
990
800
960
910
950
940
1010
890
660
860
840
740
980
820
1080
930
970
930
1010
880
740
860
810
750
890
790
1000
890
970
900
990
910
730
850
840
830
950




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168946&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168946&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168946&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 time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0453111528314821
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0453111528314821 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168946&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]0.0453111528314821[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168946&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168946&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
alpha0.0453111528314821
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
295094010
3920940.453111528315-20.4531115283148
4930939.526357465976-9.52635746597605
5930939.094707226908-9.09470722690787
6900938.682615557792-38.6826155577919
7940936.9298616523313.07013834766872
8840937.068973160216-97.0689731602163
9890932.670666082159-42.6706660821587
10850930.737209009889-80.7372090098889
11830927.078912993255-97.0789129932546
12940922.68015552990317.319844470097
13960923.46493764970536.5350623502949
14900925.120383443567-25.1203834435671
15940923.9821499101716.0178500898298
16920924.707937163622-4.7079371636222
17930924.494615103285.50538489671965
18970924.74407043973245.2559295602682
19930926.7946687805683.20533121943208
20780926.939906033327-146.939906033327
21810920.281889494007-110.281889494007
22870915.2848899446-45.2848899445997
23720913.232979375363-193.232979375363
24880904.477370314803-24.4773703148035
25920903.36827244755716.6317275524434
26920904.12187519653715.878124803463
27950904.84133133618445.158668663816
28950906.88752267367643.1124773263235
29890908.840998722753-18.8409987227533
30960907.98729135012952.0127086498711
31780910.344047140943-130.344047140943
32780904.438008100265-124.438008100265
33760898.799578497189-138.799578497189
34860892.510409582958-32.5104095829575
35740891.03732544573-151.03732544573
361020884.1936501092135.8063498908
37890890.347192384588-0.34719238458797
381040890.331460697388149.668539302612
39920897.11311475579322.8868852442066
40900898.150145910931.84985408906982
41950898.23396493227651.766035067724
42990900.57954365870989.4204563412906
43840904.631287622251-64.6312876222505
44740901.702769471103-161.702769471103
45840894.375830570324-54.3758305703242
46960891.91199900101368.0880009989866
47790894.997144820269-104.997144820269
481010890.239603144448119.760396855552
49900895.6660847895294.33391521047088
50970895.86245948398974.1375405160105
51920899.22171691286120.7782830871394
52980900.16320487339879.8367951266022
53890903.780702098955-13.780702098955
541000903.15628260002496.8437173999758
55880907.544383079903-27.5443830799034
56740906.296315328521-166.296315328521
57860898.761237569358-38.7612375693581
58940897.00492120991542.9950787900846
59760898.953077795975-138.953077795975
601010892.656953651556117.343046348444
61870897.973902358362-27.9739023583624
62980896.7063725933183.2936274066903
63920900.48050287462319.5194971253773
64950901.36495379206448.6350462079356
65880903.568663803758-23.5686638037583
66980902.50074047611277.4992595238875
67910906.0123212687263.98767873127395
68730906.193007589162-176.193007589162
69880898.209499294451-18.2094992944507
70820897.384405888935-77.384405888935
71690893.878029246928-203.878029246928
72990884.640080704739105.359919295261
73800889.414060110239-89.4140601102392
74960885.36260596730174.6373940326991
75910888.7445123352621.2554876647399
76950889.70762298534560.2923770146552
77940892.43954009482947.5604599051709
781010894.594559362328115.405440637672
79890899.823712920646-9.82371292064602
80660899.378589163126-239.378589163126
81860888.532069324971-28.532069324971
82840887.239248371189-47.2392483711888
83740885.098783568597-145.098783568597
84980878.524190410659101.475809589341
85820883.12217632766-63.1221763276595
861080880.262037749021199.737962250979
87930889.31239508282440.6876049171759
88970891.15599736757378.8440026324269
89930894.72851002069735.2714899793032
901010896.326701893743113.673298106257
91880901.477370077094-21.4773700770944
92740900.504205679113-160.504205679113
93860893.231575085491-33.2315750854909
94810891.725814107961-81.7258141079614
95750888.022723254638-138.022723254638
96890881.768754547038.23124545297003
97790882.141721767743-92.141721767743
981000877.966674130569122.033325869431
99890883.4961448095736.5038551904272
100970883.790841986186.2091580138999
101900887.69707832034112.3029216796588
102990888.254537884842101.745462115158
103910892.86474206865217.1352579313483
104730893.641160359586-163.641160359586
105850886.226390733012-36.2263907330116
106840884.584931205975-44.5849312059752
107830882.56473657412-52.5647365741202
108950880.18296776166469.8170322383364

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 950 & 940 & 10 \tabularnewline
3 & 920 & 940.453111528315 & -20.4531115283148 \tabularnewline
4 & 930 & 939.526357465976 & -9.52635746597605 \tabularnewline
5 & 930 & 939.094707226908 & -9.09470722690787 \tabularnewline
6 & 900 & 938.682615557792 & -38.6826155577919 \tabularnewline
7 & 940 & 936.929861652331 & 3.07013834766872 \tabularnewline
8 & 840 & 937.068973160216 & -97.0689731602163 \tabularnewline
9 & 890 & 932.670666082159 & -42.6706660821587 \tabularnewline
10 & 850 & 930.737209009889 & -80.7372090098889 \tabularnewline
11 & 830 & 927.078912993255 & -97.0789129932546 \tabularnewline
12 & 940 & 922.680155529903 & 17.319844470097 \tabularnewline
13 & 960 & 923.464937649705 & 36.5350623502949 \tabularnewline
14 & 900 & 925.120383443567 & -25.1203834435671 \tabularnewline
15 & 940 & 923.98214991017 & 16.0178500898298 \tabularnewline
16 & 920 & 924.707937163622 & -4.7079371636222 \tabularnewline
17 & 930 & 924.49461510328 & 5.50538489671965 \tabularnewline
18 & 970 & 924.744070439732 & 45.2559295602682 \tabularnewline
19 & 930 & 926.794668780568 & 3.20533121943208 \tabularnewline
20 & 780 & 926.939906033327 & -146.939906033327 \tabularnewline
21 & 810 & 920.281889494007 & -110.281889494007 \tabularnewline
22 & 870 & 915.2848899446 & -45.2848899445997 \tabularnewline
23 & 720 & 913.232979375363 & -193.232979375363 \tabularnewline
24 & 880 & 904.477370314803 & -24.4773703148035 \tabularnewline
25 & 920 & 903.368272447557 & 16.6317275524434 \tabularnewline
26 & 920 & 904.121875196537 & 15.878124803463 \tabularnewline
27 & 950 & 904.841331336184 & 45.158668663816 \tabularnewline
28 & 950 & 906.887522673676 & 43.1124773263235 \tabularnewline
29 & 890 & 908.840998722753 & -18.8409987227533 \tabularnewline
30 & 960 & 907.987291350129 & 52.0127086498711 \tabularnewline
31 & 780 & 910.344047140943 & -130.344047140943 \tabularnewline
32 & 780 & 904.438008100265 & -124.438008100265 \tabularnewline
33 & 760 & 898.799578497189 & -138.799578497189 \tabularnewline
34 & 860 & 892.510409582958 & -32.5104095829575 \tabularnewline
35 & 740 & 891.03732544573 & -151.03732544573 \tabularnewline
36 & 1020 & 884.1936501092 & 135.8063498908 \tabularnewline
37 & 890 & 890.347192384588 & -0.34719238458797 \tabularnewline
38 & 1040 & 890.331460697388 & 149.668539302612 \tabularnewline
39 & 920 & 897.113114755793 & 22.8868852442066 \tabularnewline
40 & 900 & 898.15014591093 & 1.84985408906982 \tabularnewline
41 & 950 & 898.233964932276 & 51.766035067724 \tabularnewline
42 & 990 & 900.579543658709 & 89.4204563412906 \tabularnewline
43 & 840 & 904.631287622251 & -64.6312876222505 \tabularnewline
44 & 740 & 901.702769471103 & -161.702769471103 \tabularnewline
45 & 840 & 894.375830570324 & -54.3758305703242 \tabularnewline
46 & 960 & 891.911999001013 & 68.0880009989866 \tabularnewline
47 & 790 & 894.997144820269 & -104.997144820269 \tabularnewline
48 & 1010 & 890.239603144448 & 119.760396855552 \tabularnewline
49 & 900 & 895.666084789529 & 4.33391521047088 \tabularnewline
50 & 970 & 895.862459483989 & 74.1375405160105 \tabularnewline
51 & 920 & 899.221716912861 & 20.7782830871394 \tabularnewline
52 & 980 & 900.163204873398 & 79.8367951266022 \tabularnewline
53 & 890 & 903.780702098955 & -13.780702098955 \tabularnewline
54 & 1000 & 903.156282600024 & 96.8437173999758 \tabularnewline
55 & 880 & 907.544383079903 & -27.5443830799034 \tabularnewline
56 & 740 & 906.296315328521 & -166.296315328521 \tabularnewline
57 & 860 & 898.761237569358 & -38.7612375693581 \tabularnewline
58 & 940 & 897.004921209915 & 42.9950787900846 \tabularnewline
59 & 760 & 898.953077795975 & -138.953077795975 \tabularnewline
60 & 1010 & 892.656953651556 & 117.343046348444 \tabularnewline
61 & 870 & 897.973902358362 & -27.9739023583624 \tabularnewline
62 & 980 & 896.70637259331 & 83.2936274066903 \tabularnewline
63 & 920 & 900.480502874623 & 19.5194971253773 \tabularnewline
64 & 950 & 901.364953792064 & 48.6350462079356 \tabularnewline
65 & 880 & 903.568663803758 & -23.5686638037583 \tabularnewline
66 & 980 & 902.500740476112 & 77.4992595238875 \tabularnewline
67 & 910 & 906.012321268726 & 3.98767873127395 \tabularnewline
68 & 730 & 906.193007589162 & -176.193007589162 \tabularnewline
69 & 880 & 898.209499294451 & -18.2094992944507 \tabularnewline
70 & 820 & 897.384405888935 & -77.384405888935 \tabularnewline
71 & 690 & 893.878029246928 & -203.878029246928 \tabularnewline
72 & 990 & 884.640080704739 & 105.359919295261 \tabularnewline
73 & 800 & 889.414060110239 & -89.4140601102392 \tabularnewline
74 & 960 & 885.362605967301 & 74.6373940326991 \tabularnewline
75 & 910 & 888.74451233526 & 21.2554876647399 \tabularnewline
76 & 950 & 889.707622985345 & 60.2923770146552 \tabularnewline
77 & 940 & 892.439540094829 & 47.5604599051709 \tabularnewline
78 & 1010 & 894.594559362328 & 115.405440637672 \tabularnewline
79 & 890 & 899.823712920646 & -9.82371292064602 \tabularnewline
80 & 660 & 899.378589163126 & -239.378589163126 \tabularnewline
81 & 860 & 888.532069324971 & -28.532069324971 \tabularnewline
82 & 840 & 887.239248371189 & -47.2392483711888 \tabularnewline
83 & 740 & 885.098783568597 & -145.098783568597 \tabularnewline
84 & 980 & 878.524190410659 & 101.475809589341 \tabularnewline
85 & 820 & 883.12217632766 & -63.1221763276595 \tabularnewline
86 & 1080 & 880.262037749021 & 199.737962250979 \tabularnewline
87 & 930 & 889.312395082824 & 40.6876049171759 \tabularnewline
88 & 970 & 891.155997367573 & 78.8440026324269 \tabularnewline
89 & 930 & 894.728510020697 & 35.2714899793032 \tabularnewline
90 & 1010 & 896.326701893743 & 113.673298106257 \tabularnewline
91 & 880 & 901.477370077094 & -21.4773700770944 \tabularnewline
92 & 740 & 900.504205679113 & -160.504205679113 \tabularnewline
93 & 860 & 893.231575085491 & -33.2315750854909 \tabularnewline
94 & 810 & 891.725814107961 & -81.7258141079614 \tabularnewline
95 & 750 & 888.022723254638 & -138.022723254638 \tabularnewline
96 & 890 & 881.76875454703 & 8.23124545297003 \tabularnewline
97 & 790 & 882.141721767743 & -92.141721767743 \tabularnewline
98 & 1000 & 877.966674130569 & 122.033325869431 \tabularnewline
99 & 890 & 883.496144809573 & 6.5038551904272 \tabularnewline
100 & 970 & 883.7908419861 & 86.2091580138999 \tabularnewline
101 & 900 & 887.697078320341 & 12.3029216796588 \tabularnewline
102 & 990 & 888.254537884842 & 101.745462115158 \tabularnewline
103 & 910 & 892.864742068652 & 17.1352579313483 \tabularnewline
104 & 730 & 893.641160359586 & -163.641160359586 \tabularnewline
105 & 850 & 886.226390733012 & -36.2263907330116 \tabularnewline
106 & 840 & 884.584931205975 & -44.5849312059752 \tabularnewline
107 & 830 & 882.56473657412 & -52.5647365741202 \tabularnewline
108 & 950 & 880.182967761664 & 69.8170322383364 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168946&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]950[/C][C]940[/C][C]10[/C][/ROW]
[ROW][C]3[/C][C]920[/C][C]940.453111528315[/C][C]-20.4531115283148[/C][/ROW]
[ROW][C]4[/C][C]930[/C][C]939.526357465976[/C][C]-9.52635746597605[/C][/ROW]
[ROW][C]5[/C][C]930[/C][C]939.094707226908[/C][C]-9.09470722690787[/C][/ROW]
[ROW][C]6[/C][C]900[/C][C]938.682615557792[/C][C]-38.6826155577919[/C][/ROW]
[ROW][C]7[/C][C]940[/C][C]936.929861652331[/C][C]3.07013834766872[/C][/ROW]
[ROW][C]8[/C][C]840[/C][C]937.068973160216[/C][C]-97.0689731602163[/C][/ROW]
[ROW][C]9[/C][C]890[/C][C]932.670666082159[/C][C]-42.6706660821587[/C][/ROW]
[ROW][C]10[/C][C]850[/C][C]930.737209009889[/C][C]-80.7372090098889[/C][/ROW]
[ROW][C]11[/C][C]830[/C][C]927.078912993255[/C][C]-97.0789129932546[/C][/ROW]
[ROW][C]12[/C][C]940[/C][C]922.680155529903[/C][C]17.319844470097[/C][/ROW]
[ROW][C]13[/C][C]960[/C][C]923.464937649705[/C][C]36.5350623502949[/C][/ROW]
[ROW][C]14[/C][C]900[/C][C]925.120383443567[/C][C]-25.1203834435671[/C][/ROW]
[ROW][C]15[/C][C]940[/C][C]923.98214991017[/C][C]16.0178500898298[/C][/ROW]
[ROW][C]16[/C][C]920[/C][C]924.707937163622[/C][C]-4.7079371636222[/C][/ROW]
[ROW][C]17[/C][C]930[/C][C]924.49461510328[/C][C]5.50538489671965[/C][/ROW]
[ROW][C]18[/C][C]970[/C][C]924.744070439732[/C][C]45.2559295602682[/C][/ROW]
[ROW][C]19[/C][C]930[/C][C]926.794668780568[/C][C]3.20533121943208[/C][/ROW]
[ROW][C]20[/C][C]780[/C][C]926.939906033327[/C][C]-146.939906033327[/C][/ROW]
[ROW][C]21[/C][C]810[/C][C]920.281889494007[/C][C]-110.281889494007[/C][/ROW]
[ROW][C]22[/C][C]870[/C][C]915.2848899446[/C][C]-45.2848899445997[/C][/ROW]
[ROW][C]23[/C][C]720[/C][C]913.232979375363[/C][C]-193.232979375363[/C][/ROW]
[ROW][C]24[/C][C]880[/C][C]904.477370314803[/C][C]-24.4773703148035[/C][/ROW]
[ROW][C]25[/C][C]920[/C][C]903.368272447557[/C][C]16.6317275524434[/C][/ROW]
[ROW][C]26[/C][C]920[/C][C]904.121875196537[/C][C]15.878124803463[/C][/ROW]
[ROW][C]27[/C][C]950[/C][C]904.841331336184[/C][C]45.158668663816[/C][/ROW]
[ROW][C]28[/C][C]950[/C][C]906.887522673676[/C][C]43.1124773263235[/C][/ROW]
[ROW][C]29[/C][C]890[/C][C]908.840998722753[/C][C]-18.8409987227533[/C][/ROW]
[ROW][C]30[/C][C]960[/C][C]907.987291350129[/C][C]52.0127086498711[/C][/ROW]
[ROW][C]31[/C][C]780[/C][C]910.344047140943[/C][C]-130.344047140943[/C][/ROW]
[ROW][C]32[/C][C]780[/C][C]904.438008100265[/C][C]-124.438008100265[/C][/ROW]
[ROW][C]33[/C][C]760[/C][C]898.799578497189[/C][C]-138.799578497189[/C][/ROW]
[ROW][C]34[/C][C]860[/C][C]892.510409582958[/C][C]-32.5104095829575[/C][/ROW]
[ROW][C]35[/C][C]740[/C][C]891.03732544573[/C][C]-151.03732544573[/C][/ROW]
[ROW][C]36[/C][C]1020[/C][C]884.1936501092[/C][C]135.8063498908[/C][/ROW]
[ROW][C]37[/C][C]890[/C][C]890.347192384588[/C][C]-0.34719238458797[/C][/ROW]
[ROW][C]38[/C][C]1040[/C][C]890.331460697388[/C][C]149.668539302612[/C][/ROW]
[ROW][C]39[/C][C]920[/C][C]897.113114755793[/C][C]22.8868852442066[/C][/ROW]
[ROW][C]40[/C][C]900[/C][C]898.15014591093[/C][C]1.84985408906982[/C][/ROW]
[ROW][C]41[/C][C]950[/C][C]898.233964932276[/C][C]51.766035067724[/C][/ROW]
[ROW][C]42[/C][C]990[/C][C]900.579543658709[/C][C]89.4204563412906[/C][/ROW]
[ROW][C]43[/C][C]840[/C][C]904.631287622251[/C][C]-64.6312876222505[/C][/ROW]
[ROW][C]44[/C][C]740[/C][C]901.702769471103[/C][C]-161.702769471103[/C][/ROW]
[ROW][C]45[/C][C]840[/C][C]894.375830570324[/C][C]-54.3758305703242[/C][/ROW]
[ROW][C]46[/C][C]960[/C][C]891.911999001013[/C][C]68.0880009989866[/C][/ROW]
[ROW][C]47[/C][C]790[/C][C]894.997144820269[/C][C]-104.997144820269[/C][/ROW]
[ROW][C]48[/C][C]1010[/C][C]890.239603144448[/C][C]119.760396855552[/C][/ROW]
[ROW][C]49[/C][C]900[/C][C]895.666084789529[/C][C]4.33391521047088[/C][/ROW]
[ROW][C]50[/C][C]970[/C][C]895.862459483989[/C][C]74.1375405160105[/C][/ROW]
[ROW][C]51[/C][C]920[/C][C]899.221716912861[/C][C]20.7782830871394[/C][/ROW]
[ROW][C]52[/C][C]980[/C][C]900.163204873398[/C][C]79.8367951266022[/C][/ROW]
[ROW][C]53[/C][C]890[/C][C]903.780702098955[/C][C]-13.780702098955[/C][/ROW]
[ROW][C]54[/C][C]1000[/C][C]903.156282600024[/C][C]96.8437173999758[/C][/ROW]
[ROW][C]55[/C][C]880[/C][C]907.544383079903[/C][C]-27.5443830799034[/C][/ROW]
[ROW][C]56[/C][C]740[/C][C]906.296315328521[/C][C]-166.296315328521[/C][/ROW]
[ROW][C]57[/C][C]860[/C][C]898.761237569358[/C][C]-38.7612375693581[/C][/ROW]
[ROW][C]58[/C][C]940[/C][C]897.004921209915[/C][C]42.9950787900846[/C][/ROW]
[ROW][C]59[/C][C]760[/C][C]898.953077795975[/C][C]-138.953077795975[/C][/ROW]
[ROW][C]60[/C][C]1010[/C][C]892.656953651556[/C][C]117.343046348444[/C][/ROW]
[ROW][C]61[/C][C]870[/C][C]897.973902358362[/C][C]-27.9739023583624[/C][/ROW]
[ROW][C]62[/C][C]980[/C][C]896.70637259331[/C][C]83.2936274066903[/C][/ROW]
[ROW][C]63[/C][C]920[/C][C]900.480502874623[/C][C]19.5194971253773[/C][/ROW]
[ROW][C]64[/C][C]950[/C][C]901.364953792064[/C][C]48.6350462079356[/C][/ROW]
[ROW][C]65[/C][C]880[/C][C]903.568663803758[/C][C]-23.5686638037583[/C][/ROW]
[ROW][C]66[/C][C]980[/C][C]902.500740476112[/C][C]77.4992595238875[/C][/ROW]
[ROW][C]67[/C][C]910[/C][C]906.012321268726[/C][C]3.98767873127395[/C][/ROW]
[ROW][C]68[/C][C]730[/C][C]906.193007589162[/C][C]-176.193007589162[/C][/ROW]
[ROW][C]69[/C][C]880[/C][C]898.209499294451[/C][C]-18.2094992944507[/C][/ROW]
[ROW][C]70[/C][C]820[/C][C]897.384405888935[/C][C]-77.384405888935[/C][/ROW]
[ROW][C]71[/C][C]690[/C][C]893.878029246928[/C][C]-203.878029246928[/C][/ROW]
[ROW][C]72[/C][C]990[/C][C]884.640080704739[/C][C]105.359919295261[/C][/ROW]
[ROW][C]73[/C][C]800[/C][C]889.414060110239[/C][C]-89.4140601102392[/C][/ROW]
[ROW][C]74[/C][C]960[/C][C]885.362605967301[/C][C]74.6373940326991[/C][/ROW]
[ROW][C]75[/C][C]910[/C][C]888.74451233526[/C][C]21.2554876647399[/C][/ROW]
[ROW][C]76[/C][C]950[/C][C]889.707622985345[/C][C]60.2923770146552[/C][/ROW]
[ROW][C]77[/C][C]940[/C][C]892.439540094829[/C][C]47.5604599051709[/C][/ROW]
[ROW][C]78[/C][C]1010[/C][C]894.594559362328[/C][C]115.405440637672[/C][/ROW]
[ROW][C]79[/C][C]890[/C][C]899.823712920646[/C][C]-9.82371292064602[/C][/ROW]
[ROW][C]80[/C][C]660[/C][C]899.378589163126[/C][C]-239.378589163126[/C][/ROW]
[ROW][C]81[/C][C]860[/C][C]888.532069324971[/C][C]-28.532069324971[/C][/ROW]
[ROW][C]82[/C][C]840[/C][C]887.239248371189[/C][C]-47.2392483711888[/C][/ROW]
[ROW][C]83[/C][C]740[/C][C]885.098783568597[/C][C]-145.098783568597[/C][/ROW]
[ROW][C]84[/C][C]980[/C][C]878.524190410659[/C][C]101.475809589341[/C][/ROW]
[ROW][C]85[/C][C]820[/C][C]883.12217632766[/C][C]-63.1221763276595[/C][/ROW]
[ROW][C]86[/C][C]1080[/C][C]880.262037749021[/C][C]199.737962250979[/C][/ROW]
[ROW][C]87[/C][C]930[/C][C]889.312395082824[/C][C]40.6876049171759[/C][/ROW]
[ROW][C]88[/C][C]970[/C][C]891.155997367573[/C][C]78.8440026324269[/C][/ROW]
[ROW][C]89[/C][C]930[/C][C]894.728510020697[/C][C]35.2714899793032[/C][/ROW]
[ROW][C]90[/C][C]1010[/C][C]896.326701893743[/C][C]113.673298106257[/C][/ROW]
[ROW][C]91[/C][C]880[/C][C]901.477370077094[/C][C]-21.4773700770944[/C][/ROW]
[ROW][C]92[/C][C]740[/C][C]900.504205679113[/C][C]-160.504205679113[/C][/ROW]
[ROW][C]93[/C][C]860[/C][C]893.231575085491[/C][C]-33.2315750854909[/C][/ROW]
[ROW][C]94[/C][C]810[/C][C]891.725814107961[/C][C]-81.7258141079614[/C][/ROW]
[ROW][C]95[/C][C]750[/C][C]888.022723254638[/C][C]-138.022723254638[/C][/ROW]
[ROW][C]96[/C][C]890[/C][C]881.76875454703[/C][C]8.23124545297003[/C][/ROW]
[ROW][C]97[/C][C]790[/C][C]882.141721767743[/C][C]-92.141721767743[/C][/ROW]
[ROW][C]98[/C][C]1000[/C][C]877.966674130569[/C][C]122.033325869431[/C][/ROW]
[ROW][C]99[/C][C]890[/C][C]883.496144809573[/C][C]6.5038551904272[/C][/ROW]
[ROW][C]100[/C][C]970[/C][C]883.7908419861[/C][C]86.2091580138999[/C][/ROW]
[ROW][C]101[/C][C]900[/C][C]887.697078320341[/C][C]12.3029216796588[/C][/ROW]
[ROW][C]102[/C][C]990[/C][C]888.254537884842[/C][C]101.745462115158[/C][/ROW]
[ROW][C]103[/C][C]910[/C][C]892.864742068652[/C][C]17.1352579313483[/C][/ROW]
[ROW][C]104[/C][C]730[/C][C]893.641160359586[/C][C]-163.641160359586[/C][/ROW]
[ROW][C]105[/C][C]850[/C][C]886.226390733012[/C][C]-36.2263907330116[/C][/ROW]
[ROW][C]106[/C][C]840[/C][C]884.584931205975[/C][C]-44.5849312059752[/C][/ROW]
[ROW][C]107[/C][C]830[/C][C]882.56473657412[/C][C]-52.5647365741202[/C][/ROW]
[ROW][C]108[/C][C]950[/C][C]880.182967761664[/C][C]69.8170322383364[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168946&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168946&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
295094010
3920940.453111528315-20.4531115283148
4930939.526357465976-9.52635746597605
5930939.094707226908-9.09470722690787
6900938.682615557792-38.6826155577919
7940936.9298616523313.07013834766872
8840937.068973160216-97.0689731602163
9890932.670666082159-42.6706660821587
10850930.737209009889-80.7372090098889
11830927.078912993255-97.0789129932546
12940922.68015552990317.319844470097
13960923.46493764970536.5350623502949
14900925.120383443567-25.1203834435671
15940923.9821499101716.0178500898298
16920924.707937163622-4.7079371636222
17930924.494615103285.50538489671965
18970924.74407043973245.2559295602682
19930926.7946687805683.20533121943208
20780926.939906033327-146.939906033327
21810920.281889494007-110.281889494007
22870915.2848899446-45.2848899445997
23720913.232979375363-193.232979375363
24880904.477370314803-24.4773703148035
25920903.36827244755716.6317275524434
26920904.12187519653715.878124803463
27950904.84133133618445.158668663816
28950906.88752267367643.1124773263235
29890908.840998722753-18.8409987227533
30960907.98729135012952.0127086498711
31780910.344047140943-130.344047140943
32780904.438008100265-124.438008100265
33760898.799578497189-138.799578497189
34860892.510409582958-32.5104095829575
35740891.03732544573-151.03732544573
361020884.1936501092135.8063498908
37890890.347192384588-0.34719238458797
381040890.331460697388149.668539302612
39920897.11311475579322.8868852442066
40900898.150145910931.84985408906982
41950898.23396493227651.766035067724
42990900.57954365870989.4204563412906
43840904.631287622251-64.6312876222505
44740901.702769471103-161.702769471103
45840894.375830570324-54.3758305703242
46960891.91199900101368.0880009989866
47790894.997144820269-104.997144820269
481010890.239603144448119.760396855552
49900895.6660847895294.33391521047088
50970895.86245948398974.1375405160105
51920899.22171691286120.7782830871394
52980900.16320487339879.8367951266022
53890903.780702098955-13.780702098955
541000903.15628260002496.8437173999758
55880907.544383079903-27.5443830799034
56740906.296315328521-166.296315328521
57860898.761237569358-38.7612375693581
58940897.00492120991542.9950787900846
59760898.953077795975-138.953077795975
601010892.656953651556117.343046348444
61870897.973902358362-27.9739023583624
62980896.7063725933183.2936274066903
63920900.48050287462319.5194971253773
64950901.36495379206448.6350462079356
65880903.568663803758-23.5686638037583
66980902.50074047611277.4992595238875
67910906.0123212687263.98767873127395
68730906.193007589162-176.193007589162
69880898.209499294451-18.2094992944507
70820897.384405888935-77.384405888935
71690893.878029246928-203.878029246928
72990884.640080704739105.359919295261
73800889.414060110239-89.4140601102392
74960885.36260596730174.6373940326991
75910888.7445123352621.2554876647399
76950889.70762298534560.2923770146552
77940892.43954009482947.5604599051709
781010894.594559362328115.405440637672
79890899.823712920646-9.82371292064602
80660899.378589163126-239.378589163126
81860888.532069324971-28.532069324971
82840887.239248371189-47.2392483711888
83740885.098783568597-145.098783568597
84980878.524190410659101.475809589341
85820883.12217632766-63.1221763276595
861080880.262037749021199.737962250979
87930889.31239508282440.6876049171759
88970891.15599736757378.8440026324269
89930894.72851002069735.2714899793032
901010896.326701893743113.673298106257
91880901.477370077094-21.4773700770944
92740900.504205679113-160.504205679113
93860893.231575085491-33.2315750854909
94810891.725814107961-81.7258141079614
95750888.022723254638-138.022723254638
96890881.768754547038.23124545297003
97790882.141721767743-92.141721767743
981000877.966674130569122.033325869431
99890883.4961448095736.5038551904272
100970883.790841986186.2091580138999
101900887.69707832034112.3029216796588
102990888.254537884842101.745462115158
103910892.86474206865217.1352579313483
104730893.641160359586-163.641160359586
105850886.226390733012-36.2263907330116
106840884.584931205975-44.5849312059752
107830882.56473657412-52.5647365741202
108950880.18296776166469.8170322383364







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109883.346457979655712.1394054224191054.55351053689
110883.346457979655711.9637428907241054.72917306859
111883.346457979655711.7882602239911054.90465573532
112883.346457979655711.6129568708471055.07995908846
113883.346457979655711.4378322827271055.25508367658
114883.346457979655711.2628859138581055.43003004545
115883.346457979655711.0881172212411055.60479873807
116883.346457979655710.9135256646251055.77939029469
117883.346457979655710.7391107064951055.95380525282
118883.346457979655710.5648718120461056.12804414726
119883.346457979655710.3908084491691056.30210751014
120883.346457979655710.2169200884271056.47599587088

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 883.346457979655 & 712.139405422419 & 1054.55351053689 \tabularnewline
110 & 883.346457979655 & 711.963742890724 & 1054.72917306859 \tabularnewline
111 & 883.346457979655 & 711.788260223991 & 1054.90465573532 \tabularnewline
112 & 883.346457979655 & 711.612956870847 & 1055.07995908846 \tabularnewline
113 & 883.346457979655 & 711.437832282727 & 1055.25508367658 \tabularnewline
114 & 883.346457979655 & 711.262885913858 & 1055.43003004545 \tabularnewline
115 & 883.346457979655 & 711.088117221241 & 1055.60479873807 \tabularnewline
116 & 883.346457979655 & 710.913525664625 & 1055.77939029469 \tabularnewline
117 & 883.346457979655 & 710.739110706495 & 1055.95380525282 \tabularnewline
118 & 883.346457979655 & 710.564871812046 & 1056.12804414726 \tabularnewline
119 & 883.346457979655 & 710.390808449169 & 1056.30210751014 \tabularnewline
120 & 883.346457979655 & 710.216920088427 & 1056.47599587088 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168946&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]109[/C][C]883.346457979655[/C][C]712.139405422419[/C][C]1054.55351053689[/C][/ROW]
[ROW][C]110[/C][C]883.346457979655[/C][C]711.963742890724[/C][C]1054.72917306859[/C][/ROW]
[ROW][C]111[/C][C]883.346457979655[/C][C]711.788260223991[/C][C]1054.90465573532[/C][/ROW]
[ROW][C]112[/C][C]883.346457979655[/C][C]711.612956870847[/C][C]1055.07995908846[/C][/ROW]
[ROW][C]113[/C][C]883.346457979655[/C][C]711.437832282727[/C][C]1055.25508367658[/C][/ROW]
[ROW][C]114[/C][C]883.346457979655[/C][C]711.262885913858[/C][C]1055.43003004545[/C][/ROW]
[ROW][C]115[/C][C]883.346457979655[/C][C]711.088117221241[/C][C]1055.60479873807[/C][/ROW]
[ROW][C]116[/C][C]883.346457979655[/C][C]710.913525664625[/C][C]1055.77939029469[/C][/ROW]
[ROW][C]117[/C][C]883.346457979655[/C][C]710.739110706495[/C][C]1055.95380525282[/C][/ROW]
[ROW][C]118[/C][C]883.346457979655[/C][C]710.564871812046[/C][C]1056.12804414726[/C][/ROW]
[ROW][C]119[/C][C]883.346457979655[/C][C]710.390808449169[/C][C]1056.30210751014[/C][/ROW]
[ROW][C]120[/C][C]883.346457979655[/C][C]710.216920088427[/C][C]1056.47599587088[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168946&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168946&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
109883.346457979655712.1394054224191054.55351053689
110883.346457979655711.9637428907241054.72917306859
111883.346457979655711.7882602239911054.90465573532
112883.346457979655711.6129568708471055.07995908846
113883.346457979655711.4378322827271055.25508367658
114883.346457979655711.2628859138581055.43003004545
115883.346457979655711.0881172212411055.60479873807
116883.346457979655710.9135256646251055.77939029469
117883.346457979655710.7391107064951055.95380525282
118883.346457979655710.5648718120461056.12804414726
119883.346457979655710.3908084491691056.30210751014
120883.346457979655710.2169200884271056.47599587088



Parameters (Session):
par1 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')