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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 17 Dec 2012 03:03:25 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/17/t1355731444penh75mqaaw64dy.htm/, Retrieved Fri, 26 Apr 2024 12:53:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200693, Retrieved Fri, 26 Apr 2024 12:53:57 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

120

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Exponential Smoothing] [] [2012-12-17 08:00:17] [2f0f353a58a70fd7baf0f5141860d820]
- R PD    [Exponential Smoothing] [] [2012-12-17 08:03:25] [76c30f62b7052b57088120e90a652e05] [Current]

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Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200693&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200693&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200693&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 Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.967277668528082
beta	0.112371825427416
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.967277668528082 \tabularnewline
beta & 0.112371825427416 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200693&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]0.967277668528082[/C][/ROW]
[ROW][C]beta[/C][C]0.112371825427416[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200693&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200693&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
Parameter	Value
alpha	0.967277668528082
beta	0.112371825427416
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	0.99	1	-0.01
4	0.99	0.999240275741642	-0.00924027574164232
5	1	0.998211046263439	0.00178895373656063
6	1	1.0080445940528	-0.00804459405280378
7	1	1.0074919654649	-0.00749196546490416
8	1	1.0066595448011	-0.00665954480110487
9	1	1.00590844845028	-0.00590844845028404
10	1.01	1.00524165345616	0.00475834654384322
11	1.02	1.01540981837738	0.00459018162261526
12	1.02	1.02591424980315	-0.00591424980314748
13	1.01	1.02561513134318	-0.0156151313431752
14	1.03	1.01423528389282	0.0157647161071761
15	1.03	1.03492200411431	-0.00492200411430921
16	1.03	1.03506392578779	-0.00506392578779136
17	1.03	1.03451814761131	-0.00451814761130587
18	1.03	1.03400918951881	-0.00400918951881368
19	1.03	1.03355675734166	-0.00355675734165772
20	1.03	1.03315535182993	-0.00315535182993454
21	1.04	1.03279924670435	0.00720075329564973
22	1.06	1.04324305493158	0.016756945068424
23	1.07	1.06475174613421	0.00524825386579164
24	1.08	1.07569879502278	0.00430120497721975
25	1.08	1.08619730310156	-0.00619730310156164
26	1.09	1.08586722440629	0.00413277559371017
27	1.09	1.09597841118726	-0.00597841118725762
28	1.09	1.09565945083959	-0.00565945083959418
29	1.1	1.09503386107787	0.00496613892213271
30	1.1	1.1052259602725	-0.00522596027249689
31	1.1	1.10499143503722	-0.00499143503721955
32	1.1	1.10444121800474	-0.00444121800474462
33	1.1	1.10394047650745	-0.00394047650745044
34	1.11	1.10349578194054	0.00650421805945989
35	1.12	1.11386098158625	0.00613901841375175
36	1.13	1.1245402108867	0.00545978911330125
37	1.13	1.13515588730563	-0.00515588730563454
38	1.13	1.13494283906882	-0.00494283906882198
39	1.13	1.1343986069408	-0.00439860694080085
40	1.13	1.13390269288279	-0.00390269288278788
41	1.14	1.13346226316286	0.00653773683714109
42	1.14	1.14383124567971	-0.00383124567970872
43	1.14	1.14375410664331	-0.00375410664330955
44	1.14	1.14334353076369	-0.00334353076368954
45	1.14	1.14296667149875	-0.00296667149875218
46	1.14	1.1426318781464	-0.00263187814639831
47	1.15	1.14233485157096	0.0076651484290382
48	1.15	1.15283107030241	-0.00283107030240681
49	1.15	1.1528668085515	-0.00286680855149779
50	1.15	1.15255637093058	-0.00255637093057826
51	1.15	1.15226834856996	-0.0022683485699575
52	1.15	1.1520123662095	-0.00201236620950129
53	1.16	1.1517852562131	0.00821474378690468
54	1.15	1.16234350091206	-0.0123435009120556
55	1.16	1.15167454077361	0.00832545922638706
56	1.16	1.16190313797887	-0.0019031379788701
57	1.16	1.16203098040638	-0.00203098040637695
58	1.17	1.1618144067863	0.00818559321370183
59	1.17	1.17236982774558	-0.00236982774557748
60	1.17	1.17245763787737	-0.00245763787736597
61	1.18	1.17219337887697	0.00780662112302544
62	1.19	1.18270604718001	0.00729395281998957
63	1.2	1.19351563731374	0.00648436268626029
64	1.21	1.20424694521893	0.00575305478107002
65	1.21	1.21489620221182	-0.00489620221181797
66	1.21	1.21471247921793	-0.00471247921792606
67	1.21	1.21419424558831	-0.00419424558831083
68	1.22	1.21372139526939	0.0062786047306076
69	1.22	1.22406115060723	-0.00406115060722523
70	1.22	1.22395806572909	-0.00395806572908608
71	1.23	1.2235244715577	0.00647552844229704
72	1.22	1.23388691602326	-0.0138869160232582

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 0.99 & 1 & -0.01 \tabularnewline
4 & 0.99 & 0.999240275741642 & -0.00924027574164232 \tabularnewline
5 & 1 & 0.998211046263439 & 0.00178895373656063 \tabularnewline
6 & 1 & 1.0080445940528 & -0.00804459405280378 \tabularnewline
7 & 1 & 1.0074919654649 & -0.00749196546490416 \tabularnewline
8 & 1 & 1.0066595448011 & -0.00665954480110487 \tabularnewline
9 & 1 & 1.00590844845028 & -0.00590844845028404 \tabularnewline
10 & 1.01 & 1.00524165345616 & 0.00475834654384322 \tabularnewline
11 & 1.02 & 1.01540981837738 & 0.00459018162261526 \tabularnewline
12 & 1.02 & 1.02591424980315 & -0.00591424980314748 \tabularnewline
13 & 1.01 & 1.02561513134318 & -0.0156151313431752 \tabularnewline
14 & 1.03 & 1.01423528389282 & 0.0157647161071761 \tabularnewline
15 & 1.03 & 1.03492200411431 & -0.00492200411430921 \tabularnewline
16 & 1.03 & 1.03506392578779 & -0.00506392578779136 \tabularnewline
17 & 1.03 & 1.03451814761131 & -0.00451814761130587 \tabularnewline
18 & 1.03 & 1.03400918951881 & -0.00400918951881368 \tabularnewline
19 & 1.03 & 1.03355675734166 & -0.00355675734165772 \tabularnewline
20 & 1.03 & 1.03315535182993 & -0.00315535182993454 \tabularnewline
21 & 1.04 & 1.03279924670435 & 0.00720075329564973 \tabularnewline
22 & 1.06 & 1.04324305493158 & 0.016756945068424 \tabularnewline
23 & 1.07 & 1.06475174613421 & 0.00524825386579164 \tabularnewline
24 & 1.08 & 1.07569879502278 & 0.00430120497721975 \tabularnewline
25 & 1.08 & 1.08619730310156 & -0.00619730310156164 \tabularnewline
26 & 1.09 & 1.08586722440629 & 0.00413277559371017 \tabularnewline
27 & 1.09 & 1.09597841118726 & -0.00597841118725762 \tabularnewline
28 & 1.09 & 1.09565945083959 & -0.00565945083959418 \tabularnewline
29 & 1.1 & 1.09503386107787 & 0.00496613892213271 \tabularnewline
30 & 1.1 & 1.1052259602725 & -0.00522596027249689 \tabularnewline
31 & 1.1 & 1.10499143503722 & -0.00499143503721955 \tabularnewline
32 & 1.1 & 1.10444121800474 & -0.00444121800474462 \tabularnewline
33 & 1.1 & 1.10394047650745 & -0.00394047650745044 \tabularnewline
34 & 1.11 & 1.10349578194054 & 0.00650421805945989 \tabularnewline
35 & 1.12 & 1.11386098158625 & 0.00613901841375175 \tabularnewline
36 & 1.13 & 1.1245402108867 & 0.00545978911330125 \tabularnewline
37 & 1.13 & 1.13515588730563 & -0.00515588730563454 \tabularnewline
38 & 1.13 & 1.13494283906882 & -0.00494283906882198 \tabularnewline
39 & 1.13 & 1.1343986069408 & -0.00439860694080085 \tabularnewline
40 & 1.13 & 1.13390269288279 & -0.00390269288278788 \tabularnewline
41 & 1.14 & 1.13346226316286 & 0.00653773683714109 \tabularnewline
42 & 1.14 & 1.14383124567971 & -0.00383124567970872 \tabularnewline
43 & 1.14 & 1.14375410664331 & -0.00375410664330955 \tabularnewline
44 & 1.14 & 1.14334353076369 & -0.00334353076368954 \tabularnewline
45 & 1.14 & 1.14296667149875 & -0.00296667149875218 \tabularnewline
46 & 1.14 & 1.1426318781464 & -0.00263187814639831 \tabularnewline
47 & 1.15 & 1.14233485157096 & 0.0076651484290382 \tabularnewline
48 & 1.15 & 1.15283107030241 & -0.00283107030240681 \tabularnewline
49 & 1.15 & 1.1528668085515 & -0.00286680855149779 \tabularnewline
50 & 1.15 & 1.15255637093058 & -0.00255637093057826 \tabularnewline
51 & 1.15 & 1.15226834856996 & -0.0022683485699575 \tabularnewline
52 & 1.15 & 1.1520123662095 & -0.00201236620950129 \tabularnewline
53 & 1.16 & 1.1517852562131 & 0.00821474378690468 \tabularnewline
54 & 1.15 & 1.16234350091206 & -0.0123435009120556 \tabularnewline
55 & 1.16 & 1.15167454077361 & 0.00832545922638706 \tabularnewline
56 & 1.16 & 1.16190313797887 & -0.0019031379788701 \tabularnewline
57 & 1.16 & 1.16203098040638 & -0.00203098040637695 \tabularnewline
58 & 1.17 & 1.1618144067863 & 0.00818559321370183 \tabularnewline
59 & 1.17 & 1.17236982774558 & -0.00236982774557748 \tabularnewline
60 & 1.17 & 1.17245763787737 & -0.00245763787736597 \tabularnewline
61 & 1.18 & 1.17219337887697 & 0.00780662112302544 \tabularnewline
62 & 1.19 & 1.18270604718001 & 0.00729395281998957 \tabularnewline
63 & 1.2 & 1.19351563731374 & 0.00648436268626029 \tabularnewline
64 & 1.21 & 1.20424694521893 & 0.00575305478107002 \tabularnewline
65 & 1.21 & 1.21489620221182 & -0.00489620221181797 \tabularnewline
66 & 1.21 & 1.21471247921793 & -0.00471247921792606 \tabularnewline
67 & 1.21 & 1.21419424558831 & -0.00419424558831083 \tabularnewline
68 & 1.22 & 1.21372139526939 & 0.0062786047306076 \tabularnewline
69 & 1.22 & 1.22406115060723 & -0.00406115060722523 \tabularnewline
70 & 1.22 & 1.22395806572909 & -0.00395806572908608 \tabularnewline
71 & 1.23 & 1.2235244715577 & 0.00647552844229704 \tabularnewline
72 & 1.22 & 1.23388691602326 & -0.0138869160232582 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200693&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]3[/C][C]0.99[/C][C]1[/C][C]-0.01[/C][/ROW]
[ROW][C]4[/C][C]0.99[/C][C]0.999240275741642[/C][C]-0.00924027574164232[/C][/ROW]
[ROW][C]5[/C][C]1[/C][C]0.998211046263439[/C][C]0.00178895373656063[/C][/ROW]
[ROW][C]6[/C][C]1[/C][C]1.0080445940528[/C][C]-0.00804459405280378[/C][/ROW]
[ROW][C]7[/C][C]1[/C][C]1.0074919654649[/C][C]-0.00749196546490416[/C][/ROW]
[ROW][C]8[/C][C]1[/C][C]1.0066595448011[/C][C]-0.00665954480110487[/C][/ROW]
[ROW][C]9[/C][C]1[/C][C]1.00590844845028[/C][C]-0.00590844845028404[/C][/ROW]
[ROW][C]10[/C][C]1.01[/C][C]1.00524165345616[/C][C]0.00475834654384322[/C][/ROW]
[ROW][C]11[/C][C]1.02[/C][C]1.01540981837738[/C][C]0.00459018162261526[/C][/ROW]
[ROW][C]12[/C][C]1.02[/C][C]1.02591424980315[/C][C]-0.00591424980314748[/C][/ROW]
[ROW][C]13[/C][C]1.01[/C][C]1.02561513134318[/C][C]-0.0156151313431752[/C][/ROW]
[ROW][C]14[/C][C]1.03[/C][C]1.01423528389282[/C][C]0.0157647161071761[/C][/ROW]
[ROW][C]15[/C][C]1.03[/C][C]1.03492200411431[/C][C]-0.00492200411430921[/C][/ROW]
[ROW][C]16[/C][C]1.03[/C][C]1.03506392578779[/C][C]-0.00506392578779136[/C][/ROW]
[ROW][C]17[/C][C]1.03[/C][C]1.03451814761131[/C][C]-0.00451814761130587[/C][/ROW]
[ROW][C]18[/C][C]1.03[/C][C]1.03400918951881[/C][C]-0.00400918951881368[/C][/ROW]
[ROW][C]19[/C][C]1.03[/C][C]1.03355675734166[/C][C]-0.00355675734165772[/C][/ROW]
[ROW][C]20[/C][C]1.03[/C][C]1.03315535182993[/C][C]-0.00315535182993454[/C][/ROW]
[ROW][C]21[/C][C]1.04[/C][C]1.03279924670435[/C][C]0.00720075329564973[/C][/ROW]
[ROW][C]22[/C][C]1.06[/C][C]1.04324305493158[/C][C]0.016756945068424[/C][/ROW]
[ROW][C]23[/C][C]1.07[/C][C]1.06475174613421[/C][C]0.00524825386579164[/C][/ROW]
[ROW][C]24[/C][C]1.08[/C][C]1.07569879502278[/C][C]0.00430120497721975[/C][/ROW]
[ROW][C]25[/C][C]1.08[/C][C]1.08619730310156[/C][C]-0.00619730310156164[/C][/ROW]
[ROW][C]26[/C][C]1.09[/C][C]1.08586722440629[/C][C]0.00413277559371017[/C][/ROW]
[ROW][C]27[/C][C]1.09[/C][C]1.09597841118726[/C][C]-0.00597841118725762[/C][/ROW]
[ROW][C]28[/C][C]1.09[/C][C]1.09565945083959[/C][C]-0.00565945083959418[/C][/ROW]
[ROW][C]29[/C][C]1.1[/C][C]1.09503386107787[/C][C]0.00496613892213271[/C][/ROW]
[ROW][C]30[/C][C]1.1[/C][C]1.1052259602725[/C][C]-0.00522596027249689[/C][/ROW]
[ROW][C]31[/C][C]1.1[/C][C]1.10499143503722[/C][C]-0.00499143503721955[/C][/ROW]
[ROW][C]32[/C][C]1.1[/C][C]1.10444121800474[/C][C]-0.00444121800474462[/C][/ROW]
[ROW][C]33[/C][C]1.1[/C][C]1.10394047650745[/C][C]-0.00394047650745044[/C][/ROW]
[ROW][C]34[/C][C]1.11[/C][C]1.10349578194054[/C][C]0.00650421805945989[/C][/ROW]
[ROW][C]35[/C][C]1.12[/C][C]1.11386098158625[/C][C]0.00613901841375175[/C][/ROW]
[ROW][C]36[/C][C]1.13[/C][C]1.1245402108867[/C][C]0.00545978911330125[/C][/ROW]
[ROW][C]37[/C][C]1.13[/C][C]1.13515588730563[/C][C]-0.00515588730563454[/C][/ROW]
[ROW][C]38[/C][C]1.13[/C][C]1.13494283906882[/C][C]-0.00494283906882198[/C][/ROW]
[ROW][C]39[/C][C]1.13[/C][C]1.1343986069408[/C][C]-0.00439860694080085[/C][/ROW]
[ROW][C]40[/C][C]1.13[/C][C]1.13390269288279[/C][C]-0.00390269288278788[/C][/ROW]
[ROW][C]41[/C][C]1.14[/C][C]1.13346226316286[/C][C]0.00653773683714109[/C][/ROW]
[ROW][C]42[/C][C]1.14[/C][C]1.14383124567971[/C][C]-0.00383124567970872[/C][/ROW]
[ROW][C]43[/C][C]1.14[/C][C]1.14375410664331[/C][C]-0.00375410664330955[/C][/ROW]
[ROW][C]44[/C][C]1.14[/C][C]1.14334353076369[/C][C]-0.00334353076368954[/C][/ROW]
[ROW][C]45[/C][C]1.14[/C][C]1.14296667149875[/C][C]-0.00296667149875218[/C][/ROW]
[ROW][C]46[/C][C]1.14[/C][C]1.1426318781464[/C][C]-0.00263187814639831[/C][/ROW]
[ROW][C]47[/C][C]1.15[/C][C]1.14233485157096[/C][C]0.0076651484290382[/C][/ROW]
[ROW][C]48[/C][C]1.15[/C][C]1.15283107030241[/C][C]-0.00283107030240681[/C][/ROW]
[ROW][C]49[/C][C]1.15[/C][C]1.1528668085515[/C][C]-0.00286680855149779[/C][/ROW]
[ROW][C]50[/C][C]1.15[/C][C]1.15255637093058[/C][C]-0.00255637093057826[/C][/ROW]
[ROW][C]51[/C][C]1.15[/C][C]1.15226834856996[/C][C]-0.0022683485699575[/C][/ROW]
[ROW][C]52[/C][C]1.15[/C][C]1.1520123662095[/C][C]-0.00201236620950129[/C][/ROW]
[ROW][C]53[/C][C]1.16[/C][C]1.1517852562131[/C][C]0.00821474378690468[/C][/ROW]
[ROW][C]54[/C][C]1.15[/C][C]1.16234350091206[/C][C]-0.0123435009120556[/C][/ROW]
[ROW][C]55[/C][C]1.16[/C][C]1.15167454077361[/C][C]0.00832545922638706[/C][/ROW]
[ROW][C]56[/C][C]1.16[/C][C]1.16190313797887[/C][C]-0.0019031379788701[/C][/ROW]
[ROW][C]57[/C][C]1.16[/C][C]1.16203098040638[/C][C]-0.00203098040637695[/C][/ROW]
[ROW][C]58[/C][C]1.17[/C][C]1.1618144067863[/C][C]0.00818559321370183[/C][/ROW]
[ROW][C]59[/C][C]1.17[/C][C]1.17236982774558[/C][C]-0.00236982774557748[/C][/ROW]
[ROW][C]60[/C][C]1.17[/C][C]1.17245763787737[/C][C]-0.00245763787736597[/C][/ROW]
[ROW][C]61[/C][C]1.18[/C][C]1.17219337887697[/C][C]0.00780662112302544[/C][/ROW]
[ROW][C]62[/C][C]1.19[/C][C]1.18270604718001[/C][C]0.00729395281998957[/C][/ROW]
[ROW][C]63[/C][C]1.2[/C][C]1.19351563731374[/C][C]0.00648436268626029[/C][/ROW]
[ROW][C]64[/C][C]1.21[/C][C]1.20424694521893[/C][C]0.00575305478107002[/C][/ROW]
[ROW][C]65[/C][C]1.21[/C][C]1.21489620221182[/C][C]-0.00489620221181797[/C][/ROW]
[ROW][C]66[/C][C]1.21[/C][C]1.21471247921793[/C][C]-0.00471247921792606[/C][/ROW]
[ROW][C]67[/C][C]1.21[/C][C]1.21419424558831[/C][C]-0.00419424558831083[/C][/ROW]
[ROW][C]68[/C][C]1.22[/C][C]1.21372139526939[/C][C]0.0062786047306076[/C][/ROW]
[ROW][C]69[/C][C]1.22[/C][C]1.22406115060723[/C][C]-0.00406115060722523[/C][/ROW]
[ROW][C]70[/C][C]1.22[/C][C]1.22395806572909[/C][C]-0.00395806572908608[/C][/ROW]
[ROW][C]71[/C][C]1.23[/C][C]1.2235244715577[/C][C]0.00647552844229704[/C][/ROW]
[ROW][C]72[/C][C]1.22[/C][C]1.23388691602326[/C][C]-0.0138869160232582[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200693&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200693&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
t	Observed	Fitted	Residuals
3	0.99	1	-0.01
4	0.99	0.999240275741642	-0.00924027574164232
5	1	0.998211046263439	0.00178895373656063
6	1	1.0080445940528	-0.00804459405280378
7	1	1.0074919654649	-0.00749196546490416
8	1	1.0066595448011	-0.00665954480110487
9	1	1.00590844845028	-0.00590844845028404
10	1.01	1.00524165345616	0.00475834654384322
11	1.02	1.01540981837738	0.00459018162261526
12	1.02	1.02591424980315	-0.00591424980314748
13	1.01	1.02561513134318	-0.0156151313431752
14	1.03	1.01423528389282	0.0157647161071761
15	1.03	1.03492200411431	-0.00492200411430921
16	1.03	1.03506392578779	-0.00506392578779136
17	1.03	1.03451814761131	-0.00451814761130587
18	1.03	1.03400918951881	-0.00400918951881368
19	1.03	1.03355675734166	-0.00355675734165772
20	1.03	1.03315535182993	-0.00315535182993454
21	1.04	1.03279924670435	0.00720075329564973
22	1.06	1.04324305493158	0.016756945068424
23	1.07	1.06475174613421	0.00524825386579164
24	1.08	1.07569879502278	0.00430120497721975
25	1.08	1.08619730310156	-0.00619730310156164
26	1.09	1.08586722440629	0.00413277559371017
27	1.09	1.09597841118726	-0.00597841118725762
28	1.09	1.09565945083959	-0.00565945083959418
29	1.1	1.09503386107787	0.00496613892213271
30	1.1	1.1052259602725	-0.00522596027249689
31	1.1	1.10499143503722	-0.00499143503721955
32	1.1	1.10444121800474	-0.00444121800474462
33	1.1	1.10394047650745	-0.00394047650745044
34	1.11	1.10349578194054	0.00650421805945989
35	1.12	1.11386098158625	0.00613901841375175
36	1.13	1.1245402108867	0.00545978911330125
37	1.13	1.13515588730563	-0.00515588730563454
38	1.13	1.13494283906882	-0.00494283906882198
39	1.13	1.1343986069408	-0.00439860694080085
40	1.13	1.13390269288279	-0.00390269288278788
41	1.14	1.13346226316286	0.00653773683714109
42	1.14	1.14383124567971	-0.00383124567970872
43	1.14	1.14375410664331	-0.00375410664330955
44	1.14	1.14334353076369	-0.00334353076368954
45	1.14	1.14296667149875	-0.00296667149875218
46	1.14	1.1426318781464	-0.00263187814639831
47	1.15	1.14233485157096	0.0076651484290382
48	1.15	1.15283107030241	-0.00283107030240681
49	1.15	1.1528668085515	-0.00286680855149779
50	1.15	1.15255637093058	-0.00255637093057826
51	1.15	1.15226834856996	-0.0022683485699575
52	1.15	1.1520123662095	-0.00201236620950129
53	1.16	1.1517852562131	0.00821474378690468
54	1.15	1.16234350091206	-0.0123435009120556
55	1.16	1.15167454077361	0.00832545922638706
56	1.16	1.16190313797887	-0.0019031379788701
57	1.16	1.16203098040638	-0.00203098040637695
58	1.17	1.1618144067863	0.00818559321370183
59	1.17	1.17236982774558	-0.00236982774557748
60	1.17	1.17245763787737	-0.00245763787736597
61	1.18	1.17219337887697	0.00780662112302544
62	1.19	1.18270604718001	0.00729395281998957
63	1.2	1.19351563731374	0.00648436268626029
64	1.21	1.20424694521893	0.00575305478107002
65	1.21	1.21489620221182	-0.00489620221181797
66	1.21	1.21471247921793	-0.00471247921792606
67	1.21	1.21419424558831	-0.00419424558831083
68	1.22	1.21372139526939	0.0062786047306076
69	1.22	1.22406115060723	-0.00406115060722523
70	1.22	1.22395806572909	-0.00395806572908608
71	1.23	1.2235244715577	0.00647552844229704
72	1.22	1.23388691602326	-0.0138869160232582

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.22304378771374	1.21025897715961	1.23582859826787
74	1.22563316315824	1.2068533397334	1.24441298658308
75	1.22822253860274	1.20409630029657	1.25234877690892
76	1.23081191404725	1.20156307798782	1.26006075010667
77	1.23340128949175	1.19909675502393	1.26770582395957
78	1.23599066493625	1.19662243400589	1.27535889586661
79	1.23858004038075	1.19409941331076	1.28306066745075
80	1.24116941582526	1.19150384396681	1.2908349876837
81	1.24375879126976	1.18882111434256	1.29869646819696
82	1.24634816671426	1.18604206131818	1.30665427211035
83	1.24893754215876	1.18316091072482	1.31471417359271
84	1.25152691760327	1.180174081363	1.32287975384353

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.22304378771374 & 1.21025897715961 & 1.23582859826787 \tabularnewline
74 & 1.22563316315824 & 1.2068533397334 & 1.24441298658308 \tabularnewline
75 & 1.22822253860274 & 1.20409630029657 & 1.25234877690892 \tabularnewline
76 & 1.23081191404725 & 1.20156307798782 & 1.26006075010667 \tabularnewline
77 & 1.23340128949175 & 1.19909675502393 & 1.26770582395957 \tabularnewline
78 & 1.23599066493625 & 1.19662243400589 & 1.27535889586661 \tabularnewline
79 & 1.23858004038075 & 1.19409941331076 & 1.28306066745075 \tabularnewline
80 & 1.24116941582526 & 1.19150384396681 & 1.2908349876837 \tabularnewline
81 & 1.24375879126976 & 1.18882111434256 & 1.29869646819696 \tabularnewline
82 & 1.24634816671426 & 1.18604206131818 & 1.30665427211035 \tabularnewline
83 & 1.24893754215876 & 1.18316091072482 & 1.31471417359271 \tabularnewline
84 & 1.25152691760327 & 1.180174081363 & 1.32287975384353 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200693&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]73[/C][C]1.22304378771374[/C][C]1.21025897715961[/C][C]1.23582859826787[/C][/ROW]
[ROW][C]74[/C][C]1.22563316315824[/C][C]1.2068533397334[/C][C]1.24441298658308[/C][/ROW]
[ROW][C]75[/C][C]1.22822253860274[/C][C]1.20409630029657[/C][C]1.25234877690892[/C][/ROW]
[ROW][C]76[/C][C]1.23081191404725[/C][C]1.20156307798782[/C][C]1.26006075010667[/C][/ROW]
[ROW][C]77[/C][C]1.23340128949175[/C][C]1.19909675502393[/C][C]1.26770582395957[/C][/ROW]
[ROW][C]78[/C][C]1.23599066493625[/C][C]1.19662243400589[/C][C]1.27535889586661[/C][/ROW]
[ROW][C]79[/C][C]1.23858004038075[/C][C]1.19409941331076[/C][C]1.28306066745075[/C][/ROW]
[ROW][C]80[/C][C]1.24116941582526[/C][C]1.19150384396681[/C][C]1.2908349876837[/C][/ROW]
[ROW][C]81[/C][C]1.24375879126976[/C][C]1.18882111434256[/C][C]1.29869646819696[/C][/ROW]
[ROW][C]82[/C][C]1.24634816671426[/C][C]1.18604206131818[/C][C]1.30665427211035[/C][/ROW]
[ROW][C]83[/C][C]1.24893754215876[/C][C]1.18316091072482[/C][C]1.31471417359271[/C][/ROW]
[ROW][C]84[/C][C]1.25152691760327[/C][C]1.180174081363[/C][C]1.32287975384353[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200693&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200693&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
t	Forecast	95% Lower Bound	95% Upper Bound
73	1.22304378771374	1.21025897715961	1.23582859826787
74	1.22563316315824	1.2068533397334	1.24441298658308
75	1.22822253860274	1.20409630029657	1.25234877690892
76	1.23081191404725	1.20156307798782	1.26006075010667
77	1.23340128949175	1.19909675502393	1.26770582395957
78	1.23599066493625	1.19662243400589	1.27535889586661
79	1.23858004038075	1.19409941331076	1.28306066745075
80	1.24116941582526	1.19150384396681	1.2908349876837
81	1.24375879126976	1.18882111434256	1.29869646819696
82	1.24634816671426	1.18604206131818	1.30665427211035
83	1.24893754215876	1.18316091072482	1.31471417359271
84	1.25152691760327	1.180174081363	1.32287975384353

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code