Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 12 Aug 2010 10:59:46 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/12/t12816107728yhhb92ajyv9j1b.htm/, Retrieved Sat, 04 May 2024 15:38:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78680, Retrieved Sat, 04 May 2024 15:38:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsHoes Isabelle
Estimated Impact163
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [TIJDREEKS B - STA...] [2010-08-12 10:59:46] [35611de12c9fa8a4a915f3548e0dcd01] [Current]
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Dataseries X:
158
157
156
154
152
151
152
154
155
155
156
158
156
152
145
141
140
145
143
141
144
139
141
142
141
132
122
122
127
128
122
123
128
128
128
129
124
121
109
110
107
107
104
110
114
118
117
122
113
106
102
111
106
110
105
104
106
110
107
111
101
105
108
124
122
128
124
121
125
134
126
126
111
117
118
128
127
129
124
113
120
127
114
107




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78680&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78680&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78680&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.651858880178058
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.651858880178058 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78680&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]0.651858880178058[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78680&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78680&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
alpha0.651858880178058
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13156160.703792735043-4.70379273504273
14152153.644722364827-1.64472236482683
15145145.663067513859-0.663067513859033
16141141.446313094764-0.446313094764434
17140140.537518635241-0.537518635241184
18145145.569271034237-0.569271034236692
19143141.2886586833131.7113413166866
20141143.78635041225-2.7863504122499
21144142.7271818473761.27281815262432
22139143.647351690988-4.64735169098773
23141141.750072916546-0.75007291654552
24142143.101603253086-1.10160325308632
25141138.4614017479132.53859825208713
26132137.188336440680-5.18833644068019
27122127.238499705538-5.23849970553798
28122120.1146703078351.88532969216513
29127120.6940255053796.30597449462076
30128130.175715356769-2.17571535676947
31122125.641902946422-3.64190294642171
32123123.084203429563-0.0842034295629617
33128125.1996168606212.80038313937911
34128125.0544889470072.94551105299306
35128129.463488174994-1.46348817499435
36129130.227590275046-1.22759027504605
37124126.772566839210-2.77256683920956
38121119.3473077063921.65269229360759
39109113.839392406047-4.83939240604742
40110109.4558225895980.544177410402057
41107110.699943994466-3.69994399446594
42107110.706362021562-3.7063620215618
43104104.664343801024-0.664343801023676
44110105.2861741481374.71382585186279
45114111.5334687719822.46653122801831
46118111.2212415196466.77875848035424
47117116.5940231945530.405976805447352
48122118.6588784023393.34112159766116
49113117.644140500555-4.64414050055491
50106110.539494126684-4.53949412668369
5110298.7349854832373.26501451676295
52111101.5085873125369.49141268746362
53106107.107490307248-1.10749030724834
54110108.8015879126671.19841208733287
55105107.015841880096-2.01584188009632
56104108.629048208371-4.62904820837105
57106108.003731742752-2.00373174275182
58110106.2787875007433.72121249925684
59107107.439853327636-0.439853327636115
60111109.9751912468511.02480875314947
61101104.670546159156-3.67054615915649
6210598.23697760820186.76302239179823
6310896.517185104476311.4828148955237
64124106.81529831780617.1847016821935
65122113.7392261040468.26077389595392
66128122.3428893640265.65711063597391
67124122.3445715988111.65542840118896
68121125.441163484024-4.441163484024
69125125.852301958648-0.852301958647857
70134126.871015945647.12898405436003
71126128.804829805718-2.80482980571782
72126130.308445903248-4.30844590324787
73111119.892625290399-8.8926252903986
74117113.6873523238203.31264767618043
75118111.3615562693516.63844373064903
76128120.4868843709887.51311562901176
77127117.9995166903439.00048330965656
78129126.1789238574282.82107614257187
79124122.9387616888081.06123831119189
80113123.525551161327-10.5255511613273
81120121.219957768385-1.21995776838538
82127124.7776259011392.22237409886121
83114120.054653408804-6.05465340880444
84107118.916372539674-11.9163725396738

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 156 & 160.703792735043 & -4.70379273504273 \tabularnewline
14 & 152 & 153.644722364827 & -1.64472236482683 \tabularnewline
15 & 145 & 145.663067513859 & -0.663067513859033 \tabularnewline
16 & 141 & 141.446313094764 & -0.446313094764434 \tabularnewline
17 & 140 & 140.537518635241 & -0.537518635241184 \tabularnewline
18 & 145 & 145.569271034237 & -0.569271034236692 \tabularnewline
19 & 143 & 141.288658683313 & 1.7113413166866 \tabularnewline
20 & 141 & 143.78635041225 & -2.7863504122499 \tabularnewline
21 & 144 & 142.727181847376 & 1.27281815262432 \tabularnewline
22 & 139 & 143.647351690988 & -4.64735169098773 \tabularnewline
23 & 141 & 141.750072916546 & -0.75007291654552 \tabularnewline
24 & 142 & 143.101603253086 & -1.10160325308632 \tabularnewline
25 & 141 & 138.461401747913 & 2.53859825208713 \tabularnewline
26 & 132 & 137.188336440680 & -5.18833644068019 \tabularnewline
27 & 122 & 127.238499705538 & -5.23849970553798 \tabularnewline
28 & 122 & 120.114670307835 & 1.88532969216513 \tabularnewline
29 & 127 & 120.694025505379 & 6.30597449462076 \tabularnewline
30 & 128 & 130.175715356769 & -2.17571535676947 \tabularnewline
31 & 122 & 125.641902946422 & -3.64190294642171 \tabularnewline
32 & 123 & 123.084203429563 & -0.0842034295629617 \tabularnewline
33 & 128 & 125.199616860621 & 2.80038313937911 \tabularnewline
34 & 128 & 125.054488947007 & 2.94551105299306 \tabularnewline
35 & 128 & 129.463488174994 & -1.46348817499435 \tabularnewline
36 & 129 & 130.227590275046 & -1.22759027504605 \tabularnewline
37 & 124 & 126.772566839210 & -2.77256683920956 \tabularnewline
38 & 121 & 119.347307706392 & 1.65269229360759 \tabularnewline
39 & 109 & 113.839392406047 & -4.83939240604742 \tabularnewline
40 & 110 & 109.455822589598 & 0.544177410402057 \tabularnewline
41 & 107 & 110.699943994466 & -3.69994399446594 \tabularnewline
42 & 107 & 110.706362021562 & -3.7063620215618 \tabularnewline
43 & 104 & 104.664343801024 & -0.664343801023676 \tabularnewline
44 & 110 & 105.286174148137 & 4.71382585186279 \tabularnewline
45 & 114 & 111.533468771982 & 2.46653122801831 \tabularnewline
46 & 118 & 111.221241519646 & 6.77875848035424 \tabularnewline
47 & 117 & 116.594023194553 & 0.405976805447352 \tabularnewline
48 & 122 & 118.658878402339 & 3.34112159766116 \tabularnewline
49 & 113 & 117.644140500555 & -4.64414050055491 \tabularnewline
50 & 106 & 110.539494126684 & -4.53949412668369 \tabularnewline
51 & 102 & 98.734985483237 & 3.26501451676295 \tabularnewline
52 & 111 & 101.508587312536 & 9.49141268746362 \tabularnewline
53 & 106 & 107.107490307248 & -1.10749030724834 \tabularnewline
54 & 110 & 108.801587912667 & 1.19841208733287 \tabularnewline
55 & 105 & 107.015841880096 & -2.01584188009632 \tabularnewline
56 & 104 & 108.629048208371 & -4.62904820837105 \tabularnewline
57 & 106 & 108.003731742752 & -2.00373174275182 \tabularnewline
58 & 110 & 106.278787500743 & 3.72121249925684 \tabularnewline
59 & 107 & 107.439853327636 & -0.439853327636115 \tabularnewline
60 & 111 & 109.975191246851 & 1.02480875314947 \tabularnewline
61 & 101 & 104.670546159156 & -3.67054615915649 \tabularnewline
62 & 105 & 98.2369776082018 & 6.76302239179823 \tabularnewline
63 & 108 & 96.5171851044763 & 11.4828148955237 \tabularnewline
64 & 124 & 106.815298317806 & 17.1847016821935 \tabularnewline
65 & 122 & 113.739226104046 & 8.26077389595392 \tabularnewline
66 & 128 & 122.342889364026 & 5.65711063597391 \tabularnewline
67 & 124 & 122.344571598811 & 1.65542840118896 \tabularnewline
68 & 121 & 125.441163484024 & -4.441163484024 \tabularnewline
69 & 125 & 125.852301958648 & -0.852301958647857 \tabularnewline
70 & 134 & 126.87101594564 & 7.12898405436003 \tabularnewline
71 & 126 & 128.804829805718 & -2.80482980571782 \tabularnewline
72 & 126 & 130.308445903248 & -4.30844590324787 \tabularnewline
73 & 111 & 119.892625290399 & -8.8926252903986 \tabularnewline
74 & 117 & 113.687352323820 & 3.31264767618043 \tabularnewline
75 & 118 & 111.361556269351 & 6.63844373064903 \tabularnewline
76 & 128 & 120.486884370988 & 7.51311562901176 \tabularnewline
77 & 127 & 117.999516690343 & 9.00048330965656 \tabularnewline
78 & 129 & 126.178923857428 & 2.82107614257187 \tabularnewline
79 & 124 & 122.938761688808 & 1.06123831119189 \tabularnewline
80 & 113 & 123.525551161327 & -10.5255511613273 \tabularnewline
81 & 120 & 121.219957768385 & -1.21995776838538 \tabularnewline
82 & 127 & 124.777625901139 & 2.22237409886121 \tabularnewline
83 & 114 & 120.054653408804 & -6.05465340880444 \tabularnewline
84 & 107 & 118.916372539674 & -11.9163725396738 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78680&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]156[/C][C]160.703792735043[/C][C]-4.70379273504273[/C][/ROW]
[ROW][C]14[/C][C]152[/C][C]153.644722364827[/C][C]-1.64472236482683[/C][/ROW]
[ROW][C]15[/C][C]145[/C][C]145.663067513859[/C][C]-0.663067513859033[/C][/ROW]
[ROW][C]16[/C][C]141[/C][C]141.446313094764[/C][C]-0.446313094764434[/C][/ROW]
[ROW][C]17[/C][C]140[/C][C]140.537518635241[/C][C]-0.537518635241184[/C][/ROW]
[ROW][C]18[/C][C]145[/C][C]145.569271034237[/C][C]-0.569271034236692[/C][/ROW]
[ROW][C]19[/C][C]143[/C][C]141.288658683313[/C][C]1.7113413166866[/C][/ROW]
[ROW][C]20[/C][C]141[/C][C]143.78635041225[/C][C]-2.7863504122499[/C][/ROW]
[ROW][C]21[/C][C]144[/C][C]142.727181847376[/C][C]1.27281815262432[/C][/ROW]
[ROW][C]22[/C][C]139[/C][C]143.647351690988[/C][C]-4.64735169098773[/C][/ROW]
[ROW][C]23[/C][C]141[/C][C]141.750072916546[/C][C]-0.75007291654552[/C][/ROW]
[ROW][C]24[/C][C]142[/C][C]143.101603253086[/C][C]-1.10160325308632[/C][/ROW]
[ROW][C]25[/C][C]141[/C][C]138.461401747913[/C][C]2.53859825208713[/C][/ROW]
[ROW][C]26[/C][C]132[/C][C]137.188336440680[/C][C]-5.18833644068019[/C][/ROW]
[ROW][C]27[/C][C]122[/C][C]127.238499705538[/C][C]-5.23849970553798[/C][/ROW]
[ROW][C]28[/C][C]122[/C][C]120.114670307835[/C][C]1.88532969216513[/C][/ROW]
[ROW][C]29[/C][C]127[/C][C]120.694025505379[/C][C]6.30597449462076[/C][/ROW]
[ROW][C]30[/C][C]128[/C][C]130.175715356769[/C][C]-2.17571535676947[/C][/ROW]
[ROW][C]31[/C][C]122[/C][C]125.641902946422[/C][C]-3.64190294642171[/C][/ROW]
[ROW][C]32[/C][C]123[/C][C]123.084203429563[/C][C]-0.0842034295629617[/C][/ROW]
[ROW][C]33[/C][C]128[/C][C]125.199616860621[/C][C]2.80038313937911[/C][/ROW]
[ROW][C]34[/C][C]128[/C][C]125.054488947007[/C][C]2.94551105299306[/C][/ROW]
[ROW][C]35[/C][C]128[/C][C]129.463488174994[/C][C]-1.46348817499435[/C][/ROW]
[ROW][C]36[/C][C]129[/C][C]130.227590275046[/C][C]-1.22759027504605[/C][/ROW]
[ROW][C]37[/C][C]124[/C][C]126.772566839210[/C][C]-2.77256683920956[/C][/ROW]
[ROW][C]38[/C][C]121[/C][C]119.347307706392[/C][C]1.65269229360759[/C][/ROW]
[ROW][C]39[/C][C]109[/C][C]113.839392406047[/C][C]-4.83939240604742[/C][/ROW]
[ROW][C]40[/C][C]110[/C][C]109.455822589598[/C][C]0.544177410402057[/C][/ROW]
[ROW][C]41[/C][C]107[/C][C]110.699943994466[/C][C]-3.69994399446594[/C][/ROW]
[ROW][C]42[/C][C]107[/C][C]110.706362021562[/C][C]-3.7063620215618[/C][/ROW]
[ROW][C]43[/C][C]104[/C][C]104.664343801024[/C][C]-0.664343801023676[/C][/ROW]
[ROW][C]44[/C][C]110[/C][C]105.286174148137[/C][C]4.71382585186279[/C][/ROW]
[ROW][C]45[/C][C]114[/C][C]111.533468771982[/C][C]2.46653122801831[/C][/ROW]
[ROW][C]46[/C][C]118[/C][C]111.221241519646[/C][C]6.77875848035424[/C][/ROW]
[ROW][C]47[/C][C]117[/C][C]116.594023194553[/C][C]0.405976805447352[/C][/ROW]
[ROW][C]48[/C][C]122[/C][C]118.658878402339[/C][C]3.34112159766116[/C][/ROW]
[ROW][C]49[/C][C]113[/C][C]117.644140500555[/C][C]-4.64414050055491[/C][/ROW]
[ROW][C]50[/C][C]106[/C][C]110.539494126684[/C][C]-4.53949412668369[/C][/ROW]
[ROW][C]51[/C][C]102[/C][C]98.734985483237[/C][C]3.26501451676295[/C][/ROW]
[ROW][C]52[/C][C]111[/C][C]101.508587312536[/C][C]9.49141268746362[/C][/ROW]
[ROW][C]53[/C][C]106[/C][C]107.107490307248[/C][C]-1.10749030724834[/C][/ROW]
[ROW][C]54[/C][C]110[/C][C]108.801587912667[/C][C]1.19841208733287[/C][/ROW]
[ROW][C]55[/C][C]105[/C][C]107.015841880096[/C][C]-2.01584188009632[/C][/ROW]
[ROW][C]56[/C][C]104[/C][C]108.629048208371[/C][C]-4.62904820837105[/C][/ROW]
[ROW][C]57[/C][C]106[/C][C]108.003731742752[/C][C]-2.00373174275182[/C][/ROW]
[ROW][C]58[/C][C]110[/C][C]106.278787500743[/C][C]3.72121249925684[/C][/ROW]
[ROW][C]59[/C][C]107[/C][C]107.439853327636[/C][C]-0.439853327636115[/C][/ROW]
[ROW][C]60[/C][C]111[/C][C]109.975191246851[/C][C]1.02480875314947[/C][/ROW]
[ROW][C]61[/C][C]101[/C][C]104.670546159156[/C][C]-3.67054615915649[/C][/ROW]
[ROW][C]62[/C][C]105[/C][C]98.2369776082018[/C][C]6.76302239179823[/C][/ROW]
[ROW][C]63[/C][C]108[/C][C]96.5171851044763[/C][C]11.4828148955237[/C][/ROW]
[ROW][C]64[/C][C]124[/C][C]106.815298317806[/C][C]17.1847016821935[/C][/ROW]
[ROW][C]65[/C][C]122[/C][C]113.739226104046[/C][C]8.26077389595392[/C][/ROW]
[ROW][C]66[/C][C]128[/C][C]122.342889364026[/C][C]5.65711063597391[/C][/ROW]
[ROW][C]67[/C][C]124[/C][C]122.344571598811[/C][C]1.65542840118896[/C][/ROW]
[ROW][C]68[/C][C]121[/C][C]125.441163484024[/C][C]-4.441163484024[/C][/ROW]
[ROW][C]69[/C][C]125[/C][C]125.852301958648[/C][C]-0.852301958647857[/C][/ROW]
[ROW][C]70[/C][C]134[/C][C]126.87101594564[/C][C]7.12898405436003[/C][/ROW]
[ROW][C]71[/C][C]126[/C][C]128.804829805718[/C][C]-2.80482980571782[/C][/ROW]
[ROW][C]72[/C][C]126[/C][C]130.308445903248[/C][C]-4.30844590324787[/C][/ROW]
[ROW][C]73[/C][C]111[/C][C]119.892625290399[/C][C]-8.8926252903986[/C][/ROW]
[ROW][C]74[/C][C]117[/C][C]113.687352323820[/C][C]3.31264767618043[/C][/ROW]
[ROW][C]75[/C][C]118[/C][C]111.361556269351[/C][C]6.63844373064903[/C][/ROW]
[ROW][C]76[/C][C]128[/C][C]120.486884370988[/C][C]7.51311562901176[/C][/ROW]
[ROW][C]77[/C][C]127[/C][C]117.999516690343[/C][C]9.00048330965656[/C][/ROW]
[ROW][C]78[/C][C]129[/C][C]126.178923857428[/C][C]2.82107614257187[/C][/ROW]
[ROW][C]79[/C][C]124[/C][C]122.938761688808[/C][C]1.06123831119189[/C][/ROW]
[ROW][C]80[/C][C]113[/C][C]123.525551161327[/C][C]-10.5255511613273[/C][/ROW]
[ROW][C]81[/C][C]120[/C][C]121.219957768385[/C][C]-1.21995776838538[/C][/ROW]
[ROW][C]82[/C][C]127[/C][C]124.777625901139[/C][C]2.22237409886121[/C][/ROW]
[ROW][C]83[/C][C]114[/C][C]120.054653408804[/C][C]-6.05465340880444[/C][/ROW]
[ROW][C]84[/C][C]107[/C][C]118.916372539674[/C][C]-11.9163725396738[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78680&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78680&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
13156160.703792735043-4.70379273504273
14152153.644722364827-1.64472236482683
15145145.663067513859-0.663067513859033
16141141.446313094764-0.446313094764434
17140140.537518635241-0.537518635241184
18145145.569271034237-0.569271034236692
19143141.2886586833131.7113413166866
20141143.78635041225-2.7863504122499
21144142.7271818473761.27281815262432
22139143.647351690988-4.64735169098773
23141141.750072916546-0.75007291654552
24142143.101603253086-1.10160325308632
25141138.4614017479132.53859825208713
26132137.188336440680-5.18833644068019
27122127.238499705538-5.23849970553798
28122120.1146703078351.88532969216513
29127120.6940255053796.30597449462076
30128130.175715356769-2.17571535676947
31122125.641902946422-3.64190294642171
32123123.084203429563-0.0842034295629617
33128125.1996168606212.80038313937911
34128125.0544889470072.94551105299306
35128129.463488174994-1.46348817499435
36129130.227590275046-1.22759027504605
37124126.772566839210-2.77256683920956
38121119.3473077063921.65269229360759
39109113.839392406047-4.83939240604742
40110109.4558225895980.544177410402057
41107110.699943994466-3.69994399446594
42107110.706362021562-3.7063620215618
43104104.664343801024-0.664343801023676
44110105.2861741481374.71382585186279
45114111.5334687719822.46653122801831
46118111.2212415196466.77875848035424
47117116.5940231945530.405976805447352
48122118.6588784023393.34112159766116
49113117.644140500555-4.64414050055491
50106110.539494126684-4.53949412668369
5110298.7349854832373.26501451676295
52111101.5085873125369.49141268746362
53106107.107490307248-1.10749030724834
54110108.8015879126671.19841208733287
55105107.015841880096-2.01584188009632
56104108.629048208371-4.62904820837105
57106108.003731742752-2.00373174275182
58110106.2787875007433.72121249925684
59107107.439853327636-0.439853327636115
60111109.9751912468511.02480875314947
61101104.670546159156-3.67054615915649
6210598.23697760820186.76302239179823
6310896.517185104476311.4828148955237
64124106.81529831780617.1847016821935
65122113.7392261040468.26077389595392
66128122.3428893640265.65711063597391
67124122.3445715988111.65542840118896
68121125.441163484024-4.441163484024
69125125.852301958648-0.852301958647857
70134126.871015945647.12898405436003
71126128.804829805718-2.80482980571782
72126130.308445903248-4.30844590324787
73111119.892625290399-8.8926252903986
74117113.6873523238203.31264767618043
75118111.3615562693516.63844373064903
76128120.4868843709887.51311562901176
77127117.9995166903439.00048330965656
78129126.1789238574282.82107614257187
79124122.9387616888081.06123831119189
80113123.525551161327-10.5255511613273
81120121.219957768385-1.21995776838538
82127124.7776259011392.22237409886121
83114120.054653408804-6.05465340880444
84107118.916372539674-11.9163725396738







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85101.94531604382092.080500692086111.810131395554
86105.78593723920094.0103058742817117.561568604119
87102.45860874281489.0415894702222115.875628015407
88107.56111760223992.6826997334002122.439535471077
89100.69407263094584.4854875477726116.902657714116
90100.85512909575183.417550636656118.292707554845
9195.16335147861576.5778718066847113.748831150545
9291.024525471894671.3580319676019110.691018976187
9398.819765776658978.1286595019078119.51087205141
94104.37109148523882.703770677356126.038412293121
9595.31787107616872.7164617592613117.919280393075
9696.085664335664372.5872683217018119.584060349627

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 101.945316043820 & 92.080500692086 & 111.810131395554 \tabularnewline
86 & 105.785937239200 & 94.0103058742817 & 117.561568604119 \tabularnewline
87 & 102.458608742814 & 89.0415894702222 & 115.875628015407 \tabularnewline
88 & 107.561117602239 & 92.6826997334002 & 122.439535471077 \tabularnewline
89 & 100.694072630945 & 84.4854875477726 & 116.902657714116 \tabularnewline
90 & 100.855129095751 & 83.417550636656 & 118.292707554845 \tabularnewline
91 & 95.163351478615 & 76.5778718066847 & 113.748831150545 \tabularnewline
92 & 91.0245254718946 & 71.3580319676019 & 110.691018976187 \tabularnewline
93 & 98.8197657766589 & 78.1286595019078 & 119.51087205141 \tabularnewline
94 & 104.371091485238 & 82.703770677356 & 126.038412293121 \tabularnewline
95 & 95.317871076168 & 72.7164617592613 & 117.919280393075 \tabularnewline
96 & 96.0856643356643 & 72.5872683217018 & 119.584060349627 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78680&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]85[/C][C]101.945316043820[/C][C]92.080500692086[/C][C]111.810131395554[/C][/ROW]
[ROW][C]86[/C][C]105.785937239200[/C][C]94.0103058742817[/C][C]117.561568604119[/C][/ROW]
[ROW][C]87[/C][C]102.458608742814[/C][C]89.0415894702222[/C][C]115.875628015407[/C][/ROW]
[ROW][C]88[/C][C]107.561117602239[/C][C]92.6826997334002[/C][C]122.439535471077[/C][/ROW]
[ROW][C]89[/C][C]100.694072630945[/C][C]84.4854875477726[/C][C]116.902657714116[/C][/ROW]
[ROW][C]90[/C][C]100.855129095751[/C][C]83.417550636656[/C][C]118.292707554845[/C][/ROW]
[ROW][C]91[/C][C]95.163351478615[/C][C]76.5778718066847[/C][C]113.748831150545[/C][/ROW]
[ROW][C]92[/C][C]91.0245254718946[/C][C]71.3580319676019[/C][C]110.691018976187[/C][/ROW]
[ROW][C]93[/C][C]98.8197657766589[/C][C]78.1286595019078[/C][C]119.51087205141[/C][/ROW]
[ROW][C]94[/C][C]104.371091485238[/C][C]82.703770677356[/C][C]126.038412293121[/C][/ROW]
[ROW][C]95[/C][C]95.317871076168[/C][C]72.7164617592613[/C][C]117.919280393075[/C][/ROW]
[ROW][C]96[/C][C]96.0856643356643[/C][C]72.5872683217018[/C][C]119.584060349627[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78680&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78680&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
85101.94531604382092.080500692086111.810131395554
86105.78593723920094.0103058742817117.561568604119
87102.45860874281489.0415894702222115.875628015407
88107.56111760223992.6826997334002122.439535471077
89100.69407263094584.4854875477726116.902657714116
90100.85512909575183.417550636656118.292707554845
9195.16335147861576.5778718066847113.748831150545
9291.024525471894671.3580319676019110.691018976187
9398.819765776658978.1286595019078119.51087205141
94104.37109148523882.703770677356126.038412293121
9595.31787107616872.7164617592613117.919280393075
9696.085664335664372.5872683217018119.584060349627



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