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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 10 Mar 2008 11:43:04 -0600

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/2008/Mar/10/t1205171047i3xo7gva8f85ux9.htm/, Retrieved Fri, 26 Apr 2024 02:36:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10051, Retrieved Fri, 26 Apr 2024 02:36:30 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

730

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

-       [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-    D    [Exponential Smoothing] [test] [2008-04-27 21:45:34] [e0301d5affa4b14e9a2781a48e0dae1f] 
-    D    [Exponential Smoothing] [exponential smoot...] [2008-05-09 12:58:03] [74be16979710d4c4e7c6647856088456] 
-   PD    [Exponential Smoothing] [exponential smoot...] [2008-05-09 13:01:30] [74be16979710d4c4e7c6647856088456] 
-   PD    [Exponential Smoothing] [exponential smoot...] [2008-05-09 13:04:50] [74be16979710d4c4e7c6647856088456] 
-   PD    [Exponential Smoothing] [exponential smoot...] [2008-05-09 13:06:47] [74be16979710d4c4e7c6647856088456] 
- RMP     [] [] [-0001-11-30 00:00:00] [7789b9488494790f41ddb7f073cada1b] 
F  MPD    [Exponential Smoothing] [] [2010-11-26 12:44:04] [8a9a6f7c332640af31ddca253a8ded58] 
-    D      [Exponential Smoothing] [] [2010-11-30 10:29:51] [fb3a7008aea9486db3846dc25434607b] 
- R PD        [Exponential Smoothing] [Tripple exponenti...] [2010-12-17 14:30:56] [fb3a7008aea9486db3846dc25434607b] 
F    D      [Exponential Smoothing] [ws 8] [2010-11-30 13:07:26] [af8eb90b4bf1bcfcc4325c143dbee260] 
-    D      [Exponential Smoothing] [holt winter model ] [2010-12-18 18:52:24] [74deae64b71f9d77c839af86f7c687b5] 
- RM        [Exponential Smoothing] [] [2011-11-29 22:31:59] [46d7ccc24e5d35a2decd922dfb3b3a39] 
- RM D    [Exponential Smoothing] [] [2010-11-27 13:17:09] [0175b38674e1402e67841c9c82e4a5a3] 
-   PD      [Exponential Smoothing] [] [2010-12-21 15:53:05] [0175b38674e1402e67841c9c82e4a5a3] 
-  M D    [Exponential Smoothing] [single exponentia...] [2010-11-28 15:28:50] [26379b86c25fbf0febe6a7a428e65173] 
-   PD      [Exponential Smoothing] [single exponentia...] [2010-11-30 15:01:36] [3fb95cad3bbcce10c72dbbcc5bec5662] 
-  M D    [Exponential Smoothing] [exponential smoot...] [2010-11-29 09:42:21] [95e8426e0df851c9330605aa1e892ab5] 
-    D      [Exponential Smoothing] [exponential smoot...] [2010-12-18 19:54:43] [95e8426e0df851c9330605aa1e892ab5] 
-   P         [Exponential Smoothing] [ES faillissemten] [2010-12-19 20:22:31] [95e8426e0df851c9330605aa1e892ab5] 
-  M D    [Exponential Smoothing] [W8 Single Exponen...] [2010-11-29 17:05:06] [56d90b683fcd93137645f9226b43c62b] 
- RMPD    [Exponential Smoothing] [triple Exponentia...] [2010-11-29 20:40:32] [97ad38b1c3b35a5feca8b85f7bc7b3ff] 
- R         [Exponential Smoothing] [] [2011-11-29 15:44:51] [9401a40688cf36283be626153bc5a38b] 
-  M          [Exponential Smoothing] [C8.7] [2011-11-29 20:31:08] [74be16979710d4c4e7c6647856088456] 
- RM        [Exponential Smoothing] [Exponential smoot...] [2011-11-29 21:16:02] [74be16979710d4c4e7c6647856088456] 
- RM D    [Exponential Smoothing] [WS8 Single Expone...] [2010-11-30 09:43:55] [f4dc4aa51d65be851b8508203d9f6001] 
- RMPD    [Exponential Smoothing] [Triple Exponentia...] [2010-11-30 10:00:50] [f4dc4aa51d65be851b8508203d9f6001] 
-   PD      [Exponential Smoothing] [Triple Exponentia...] [2010-12-18 15:43:31] [f4dc4aa51d65be851b8508203d9f6001] 
- RM D    [Exponential Smoothing] [Personal Standard...] [2010-11-30 12:15:29] [7b479c2bada71feddb7d988499871dfc] 
-  MPD    [Exponential Smoothing] [Workshop 8 - Expo...] [2010-12-07 13:26:31] [ed447cc2ebcc70947ad11d93fa385845] 
- R         [Exponential Smoothing] [workshop 8] [2010-12-10 17:02:41] [83d13bd1a1b3e64dad996f4022b3c29f] 
-  MPD    [Exponential Smoothing] [] [2010-12-07 13:28:05] [253127ae8da904b75450fbd69fe4eb21] 
- RMPD    [Exponential Smoothing] [] [2010-12-07 18:46:49] [43e84bd88d5f94b739fa54f225367516] 
- R         [Exponential Smoothing] [] [2010-12-09 20:27:06] [1253bc7c4737195066123d9caa6dfc18] 
- RMPD    [Exponential Smoothing] [] [2010-12-07 18:46:49] [e71d94d32f847f62b540eebe6fadd003] 
-    D      [Exponential Smoothing] [] [2010-12-09 17:15:47] [6ba840d2473f9a55d7b3e13093db69b8] 
-  MPD    [Exponential Smoothing] [] [2010-12-07 19:37:06] [1ec36cc0fd92fd0f07d0b885ce2c369b] 
-  M D    [Exponential Smoothing] [Workshop 8 - Smoo...] [2010-12-08 20:58:19] [8677c3f87cec9201607d40be65aa9670] 
-  MPD    [Exponential Smoothing] [] [2010-12-21 15:34:15] [5f6607fc345873e3e6f60671bd6cbc8b] 
- RM D    [Exponential Smoothing] [ws8 smoothing] [2011-11-28 17:17:18] [620e5553455d245695b6e856984b13e0] 
- R  D      [Exponential Smoothing] [ws 8 smoothing si...] [2011-11-28 20:34:45] [620e5553455d245695b6e856984b13e0] 
- RM D    [Exponential Smoothing] [ws 8 double smoot...] [2011-11-28 17:18:20] [620e5553455d245695b6e856984b13e0] 
- R  D      [Exponential Smoothing] [ws 8 smoothing do...] [2011-11-28 20:35:48] [620e5553455d245695b6e856984b13e0] 
- RM D    [Exponential Smoothing] [ws 8 triple smoot...] [2011-11-28 17:19:23] [620e5553455d245695b6e856984b13e0] 
- R  D      [Exponential Smoothing] [WS 8 smoothing tr...] [2011-11-28 20:36:47] [620e5553455d245695b6e856984b13e0] 
- RMPD    [Exponential Smoothing] [WS8 Exponential S...] [2011-11-28 17:31:17] [9d4f280afcb4ecc352d7c6f913a0a151] 
- RMPD    [Exponential Smoothing] [WS8 Exponential S...] [2011-11-28 17:36:59] [9d4f280afcb4ecc352d7c6f913a0a151] 
- RM D    [Exponential Smoothing] [exponential Smoot...] [2011-11-28 17:38:17] [74be16979710d4c4e7c6647856088456] 
- R P       [Exponential Smoothing] [exponential Smoot...] [2011-11-28 17:55:22] [74be16979710d4c4e7c6647856088456] 

[Truncated]

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Dataseries X:

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10051&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10051&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10051&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.283890683571503
beta	0
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.283890683571503 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10051&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]0.283890683571503[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10051&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10051&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	0.283890683571503
beta	0
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	12873	13328	-455
3	14000	13198.8297389750	801.170261025034
4	13477	13426.2745120345	50.7254879654774
5	14237	13440.6750054875	796.324994512461
6	13674	13666.7442525248	7.25574747524479
7	13529	13668.8040916353	-139.804091635324
8	14058	13629.1150124949	428.884987505124
9	12975	13750.8714647713	-775.87146477126
10	14326	13530.6087842737	795.391215726278
11	14008	13756.4129402130	251.587059786978
12	16193	13827.8361625937	2365.16383740631
13	14483	14499.2841411536	-16.2841411535665
14	14011	14494.6612251901	-483.661225190106
15	15057	14357.3543093539	699.645690646146
16	14884	14555.9772027292	328.022797270754
17	15414	14649.0998188735	764.900181126524
18	14440	14866.2478541575	-426.247854157451
19	14900	14745.2400594698	154.759940530195
20	15074	14789.1749647764	284.825035223594
21	14442	14870.0341387243	-428.03413872431
22	15307	14748.5192344899	558.480765510074
23	14938	14907.0667207721	30.9332792278838
24	17193	14915.8483905572	2277.15160944277
25	15528	15562.3105175579	-34.3105175578839
26	14765	15552.5700812747	-787.570081274684
27	15838	15328.9862725411	509.013727458852
28	15723	15473.4905275767	249.509472423280
29	16150	15544.3239422605	605.676057739471
30	15486	15716.2697323151	-230.269732315079
31	15986	15650.8983006023	335.101699397677
32	15983	15746.0305511103	236.969448889700
33	15692	15813.3039699412	-121.303969941160
34	16490	15778.8669029946	711.133097005375
35	15686	15980.7509640138	-294.750964013800
36	18897	15897.0739113566	2999.92608864344
37	16316	16748.7249793255	-432.724979325532
38	15636	16625.8783891463	-989.878389146343
39	17163	16344.8611365989	818.138863401073
40	16534	16577.1231377863	-43.1231377862714
41	16518	16564.8808807224	-46.8808807223795
42	16375	16551.5718354477	-176.571835447670
43	16290	16501.4447363830	-211.444736382953
44	16352	16441.4175456336	-89.4175456335979
45	15943	16416.0327374804	-473.032737480389
46	16362	16281.7431502854	80.2568497146203
47	16393	16304.5273222122	88.4726777878423
48	19051	16329.6438911867	2721.35610881325
49	16747	17102.2115371592	-355.21153715923
50	16320	17001.3702910626	-681.370291062609
51	17910	16807.9356133675	1102.06438663247
52	16961	17120.8014254284	-159.801425428432
53	17480	17075.4352895279	404.564710472147
54	17049	17190.2874417327	-141.287441732697
55	16879	17150.1772533191	-271.177253319132
56	17473	17073.1925575053	399.807442494679
57	16998	17186.6941656521	-188.694165652108
58	17307	17133.1256499792	173.874350020822
59	17418	17182.4869580621	235.513041937862
60	20169	17249.3469165279	2919.65308347212
61	17871	18078.2092261864	-207.209226186427
62	17226	18019.3844573220	-793.384457322041
63	19062	17794.1500013979	1267.84999860212
64	17804	18154.0808041672	-350.080804167166
65	19100	18054.6961253669	1045.30387463311
66	18522	18351.4481568764	170.551843123576
67	18060	18399.8662362052	-339.866236205155
68	18869	18303.381378086	565.618621914
69	18127	18463.9552353019	-336.955235301935
70	18871	18368.2967832191	502.70321678093
71	18890	18511.0095430646	378.990456935397
72	21263	18618.6014029511	2644.39859704893
73	19547	19369.3215283028	177.678471697189
74	18450	19419.7627910889	-969.762791088866
75	20254	19144.4561694244	1109.54383057556
76	19240	19459.4453259391	-219.445325939076
77	20216	19397.1468423517	818.85315764834
78	19420	19629.6116250211	-209.611625021127
79	19415	19570.1048375093	-155.104837509345
80	20018	19526.0720191636	491.92798083643
81	18652	19665.7257899112	-1013.72578991117
82	19978	19377.9384824592	600.061517540773
83	19509	19548.2903568588	-39.2903568588299
84	21971	19537.1361905924	2433.86380940759

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 12873 & 13328 & -455 \tabularnewline
3 & 14000 & 13198.8297389750 & 801.170261025034 \tabularnewline
4 & 13477 & 13426.2745120345 & 50.7254879654774 \tabularnewline
5 & 14237 & 13440.6750054875 & 796.324994512461 \tabularnewline
6 & 13674 & 13666.7442525248 & 7.25574747524479 \tabularnewline
7 & 13529 & 13668.8040916353 & -139.804091635324 \tabularnewline
8 & 14058 & 13629.1150124949 & 428.884987505124 \tabularnewline
9 & 12975 & 13750.8714647713 & -775.87146477126 \tabularnewline
10 & 14326 & 13530.6087842737 & 795.391215726278 \tabularnewline
11 & 14008 & 13756.4129402130 & 251.587059786978 \tabularnewline
12 & 16193 & 13827.8361625937 & 2365.16383740631 \tabularnewline
13 & 14483 & 14499.2841411536 & -16.2841411535665 \tabularnewline
14 & 14011 & 14494.6612251901 & -483.661225190106 \tabularnewline
15 & 15057 & 14357.3543093539 & 699.645690646146 \tabularnewline
16 & 14884 & 14555.9772027292 & 328.022797270754 \tabularnewline
17 & 15414 & 14649.0998188735 & 764.900181126524 \tabularnewline
18 & 14440 & 14866.2478541575 & -426.247854157451 \tabularnewline
19 & 14900 & 14745.2400594698 & 154.759940530195 \tabularnewline
20 & 15074 & 14789.1749647764 & 284.825035223594 \tabularnewline
21 & 14442 & 14870.0341387243 & -428.03413872431 \tabularnewline
22 & 15307 & 14748.5192344899 & 558.480765510074 \tabularnewline
23 & 14938 & 14907.0667207721 & 30.9332792278838 \tabularnewline
24 & 17193 & 14915.8483905572 & 2277.15160944277 \tabularnewline
25 & 15528 & 15562.3105175579 & -34.3105175578839 \tabularnewline
26 & 14765 & 15552.5700812747 & -787.570081274684 \tabularnewline
27 & 15838 & 15328.9862725411 & 509.013727458852 \tabularnewline
28 & 15723 & 15473.4905275767 & 249.509472423280 \tabularnewline
29 & 16150 & 15544.3239422605 & 605.676057739471 \tabularnewline
30 & 15486 & 15716.2697323151 & -230.269732315079 \tabularnewline
31 & 15986 & 15650.8983006023 & 335.101699397677 \tabularnewline
32 & 15983 & 15746.0305511103 & 236.969448889700 \tabularnewline
33 & 15692 & 15813.3039699412 & -121.303969941160 \tabularnewline
34 & 16490 & 15778.8669029946 & 711.133097005375 \tabularnewline
35 & 15686 & 15980.7509640138 & -294.750964013800 \tabularnewline
36 & 18897 & 15897.0739113566 & 2999.92608864344 \tabularnewline
37 & 16316 & 16748.7249793255 & -432.724979325532 \tabularnewline
38 & 15636 & 16625.8783891463 & -989.878389146343 \tabularnewline
39 & 17163 & 16344.8611365989 & 818.138863401073 \tabularnewline
40 & 16534 & 16577.1231377863 & -43.1231377862714 \tabularnewline
41 & 16518 & 16564.8808807224 & -46.8808807223795 \tabularnewline
42 & 16375 & 16551.5718354477 & -176.571835447670 \tabularnewline
43 & 16290 & 16501.4447363830 & -211.444736382953 \tabularnewline
44 & 16352 & 16441.4175456336 & -89.4175456335979 \tabularnewline
45 & 15943 & 16416.0327374804 & -473.032737480389 \tabularnewline
46 & 16362 & 16281.7431502854 & 80.2568497146203 \tabularnewline
47 & 16393 & 16304.5273222122 & 88.4726777878423 \tabularnewline
48 & 19051 & 16329.6438911867 & 2721.35610881325 \tabularnewline
49 & 16747 & 17102.2115371592 & -355.21153715923 \tabularnewline
50 & 16320 & 17001.3702910626 & -681.370291062609 \tabularnewline
51 & 17910 & 16807.9356133675 & 1102.06438663247 \tabularnewline
52 & 16961 & 17120.8014254284 & -159.801425428432 \tabularnewline
53 & 17480 & 17075.4352895279 & 404.564710472147 \tabularnewline
54 & 17049 & 17190.2874417327 & -141.287441732697 \tabularnewline
55 & 16879 & 17150.1772533191 & -271.177253319132 \tabularnewline
56 & 17473 & 17073.1925575053 & 399.807442494679 \tabularnewline
57 & 16998 & 17186.6941656521 & -188.694165652108 \tabularnewline
58 & 17307 & 17133.1256499792 & 173.874350020822 \tabularnewline
59 & 17418 & 17182.4869580621 & 235.513041937862 \tabularnewline
60 & 20169 & 17249.3469165279 & 2919.65308347212 \tabularnewline
61 & 17871 & 18078.2092261864 & -207.209226186427 \tabularnewline
62 & 17226 & 18019.3844573220 & -793.384457322041 \tabularnewline
63 & 19062 & 17794.1500013979 & 1267.84999860212 \tabularnewline
64 & 17804 & 18154.0808041672 & -350.080804167166 \tabularnewline
65 & 19100 & 18054.6961253669 & 1045.30387463311 \tabularnewline
66 & 18522 & 18351.4481568764 & 170.551843123576 \tabularnewline
67 & 18060 & 18399.8662362052 & -339.866236205155 \tabularnewline
68 & 18869 & 18303.381378086 & 565.618621914 \tabularnewline
69 & 18127 & 18463.9552353019 & -336.955235301935 \tabularnewline
70 & 18871 & 18368.2967832191 & 502.70321678093 \tabularnewline
71 & 18890 & 18511.0095430646 & 378.990456935397 \tabularnewline
72 & 21263 & 18618.6014029511 & 2644.39859704893 \tabularnewline
73 & 19547 & 19369.3215283028 & 177.678471697189 \tabularnewline
74 & 18450 & 19419.7627910889 & -969.762791088866 \tabularnewline
75 & 20254 & 19144.4561694244 & 1109.54383057556 \tabularnewline
76 & 19240 & 19459.4453259391 & -219.445325939076 \tabularnewline
77 & 20216 & 19397.1468423517 & 818.85315764834 \tabularnewline
78 & 19420 & 19629.6116250211 & -209.611625021127 \tabularnewline
79 & 19415 & 19570.1048375093 & -155.104837509345 \tabularnewline
80 & 20018 & 19526.0720191636 & 491.92798083643 \tabularnewline
81 & 18652 & 19665.7257899112 & -1013.72578991117 \tabularnewline
82 & 19978 & 19377.9384824592 & 600.061517540773 \tabularnewline
83 & 19509 & 19548.2903568588 & -39.2903568588299 \tabularnewline
84 & 21971 & 19537.1361905924 & 2433.86380940759 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10051&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]12873[/C][C]13328[/C][C]-455[/C][/ROW]
[ROW][C]3[/C][C]14000[/C][C]13198.8297389750[/C][C]801.170261025034[/C][/ROW]
[ROW][C]4[/C][C]13477[/C][C]13426.2745120345[/C][C]50.7254879654774[/C][/ROW]
[ROW][C]5[/C][C]14237[/C][C]13440.6750054875[/C][C]796.324994512461[/C][/ROW]
[ROW][C]6[/C][C]13674[/C][C]13666.7442525248[/C][C]7.25574747524479[/C][/ROW]
[ROW][C]7[/C][C]13529[/C][C]13668.8040916353[/C][C]-139.804091635324[/C][/ROW]
[ROW][C]8[/C][C]14058[/C][C]13629.1150124949[/C][C]428.884987505124[/C][/ROW]
[ROW][C]9[/C][C]12975[/C][C]13750.8714647713[/C][C]-775.87146477126[/C][/ROW]
[ROW][C]10[/C][C]14326[/C][C]13530.6087842737[/C][C]795.391215726278[/C][/ROW]
[ROW][C]11[/C][C]14008[/C][C]13756.4129402130[/C][C]251.587059786978[/C][/ROW]
[ROW][C]12[/C][C]16193[/C][C]13827.8361625937[/C][C]2365.16383740631[/C][/ROW]
[ROW][C]13[/C][C]14483[/C][C]14499.2841411536[/C][C]-16.2841411535665[/C][/ROW]
[ROW][C]14[/C][C]14011[/C][C]14494.6612251901[/C][C]-483.661225190106[/C][/ROW]
[ROW][C]15[/C][C]15057[/C][C]14357.3543093539[/C][C]699.645690646146[/C][/ROW]
[ROW][C]16[/C][C]14884[/C][C]14555.9772027292[/C][C]328.022797270754[/C][/ROW]
[ROW][C]17[/C][C]15414[/C][C]14649.0998188735[/C][C]764.900181126524[/C][/ROW]
[ROW][C]18[/C][C]14440[/C][C]14866.2478541575[/C][C]-426.247854157451[/C][/ROW]
[ROW][C]19[/C][C]14900[/C][C]14745.2400594698[/C][C]154.759940530195[/C][/ROW]
[ROW][C]20[/C][C]15074[/C][C]14789.1749647764[/C][C]284.825035223594[/C][/ROW]
[ROW][C]21[/C][C]14442[/C][C]14870.0341387243[/C][C]-428.03413872431[/C][/ROW]
[ROW][C]22[/C][C]15307[/C][C]14748.5192344899[/C][C]558.480765510074[/C][/ROW]
[ROW][C]23[/C][C]14938[/C][C]14907.0667207721[/C][C]30.9332792278838[/C][/ROW]
[ROW][C]24[/C][C]17193[/C][C]14915.8483905572[/C][C]2277.15160944277[/C][/ROW]
[ROW][C]25[/C][C]15528[/C][C]15562.3105175579[/C][C]-34.3105175578839[/C][/ROW]
[ROW][C]26[/C][C]14765[/C][C]15552.5700812747[/C][C]-787.570081274684[/C][/ROW]
[ROW][C]27[/C][C]15838[/C][C]15328.9862725411[/C][C]509.013727458852[/C][/ROW]
[ROW][C]28[/C][C]15723[/C][C]15473.4905275767[/C][C]249.509472423280[/C][/ROW]
[ROW][C]29[/C][C]16150[/C][C]15544.3239422605[/C][C]605.676057739471[/C][/ROW]
[ROW][C]30[/C][C]15486[/C][C]15716.2697323151[/C][C]-230.269732315079[/C][/ROW]
[ROW][C]31[/C][C]15986[/C][C]15650.8983006023[/C][C]335.101699397677[/C][/ROW]
[ROW][C]32[/C][C]15983[/C][C]15746.0305511103[/C][C]236.969448889700[/C][/ROW]
[ROW][C]33[/C][C]15692[/C][C]15813.3039699412[/C][C]-121.303969941160[/C][/ROW]
[ROW][C]34[/C][C]16490[/C][C]15778.8669029946[/C][C]711.133097005375[/C][/ROW]
[ROW][C]35[/C][C]15686[/C][C]15980.7509640138[/C][C]-294.750964013800[/C][/ROW]
[ROW][C]36[/C][C]18897[/C][C]15897.0739113566[/C][C]2999.92608864344[/C][/ROW]
[ROW][C]37[/C][C]16316[/C][C]16748.7249793255[/C][C]-432.724979325532[/C][/ROW]
[ROW][C]38[/C][C]15636[/C][C]16625.8783891463[/C][C]-989.878389146343[/C][/ROW]
[ROW][C]39[/C][C]17163[/C][C]16344.8611365989[/C][C]818.138863401073[/C][/ROW]
[ROW][C]40[/C][C]16534[/C][C]16577.1231377863[/C][C]-43.1231377862714[/C][/ROW]
[ROW][C]41[/C][C]16518[/C][C]16564.8808807224[/C][C]-46.8808807223795[/C][/ROW]
[ROW][C]42[/C][C]16375[/C][C]16551.5718354477[/C][C]-176.571835447670[/C][/ROW]
[ROW][C]43[/C][C]16290[/C][C]16501.4447363830[/C][C]-211.444736382953[/C][/ROW]
[ROW][C]44[/C][C]16352[/C][C]16441.4175456336[/C][C]-89.4175456335979[/C][/ROW]
[ROW][C]45[/C][C]15943[/C][C]16416.0327374804[/C][C]-473.032737480389[/C][/ROW]
[ROW][C]46[/C][C]16362[/C][C]16281.7431502854[/C][C]80.2568497146203[/C][/ROW]
[ROW][C]47[/C][C]16393[/C][C]16304.5273222122[/C][C]88.4726777878423[/C][/ROW]
[ROW][C]48[/C][C]19051[/C][C]16329.6438911867[/C][C]2721.35610881325[/C][/ROW]
[ROW][C]49[/C][C]16747[/C][C]17102.2115371592[/C][C]-355.21153715923[/C][/ROW]
[ROW][C]50[/C][C]16320[/C][C]17001.3702910626[/C][C]-681.370291062609[/C][/ROW]
[ROW][C]51[/C][C]17910[/C][C]16807.9356133675[/C][C]1102.06438663247[/C][/ROW]
[ROW][C]52[/C][C]16961[/C][C]17120.8014254284[/C][C]-159.801425428432[/C][/ROW]
[ROW][C]53[/C][C]17480[/C][C]17075.4352895279[/C][C]404.564710472147[/C][/ROW]
[ROW][C]54[/C][C]17049[/C][C]17190.2874417327[/C][C]-141.287441732697[/C][/ROW]
[ROW][C]55[/C][C]16879[/C][C]17150.1772533191[/C][C]-271.177253319132[/C][/ROW]
[ROW][C]56[/C][C]17473[/C][C]17073.1925575053[/C][C]399.807442494679[/C][/ROW]
[ROW][C]57[/C][C]16998[/C][C]17186.6941656521[/C][C]-188.694165652108[/C][/ROW]
[ROW][C]58[/C][C]17307[/C][C]17133.1256499792[/C][C]173.874350020822[/C][/ROW]
[ROW][C]59[/C][C]17418[/C][C]17182.4869580621[/C][C]235.513041937862[/C][/ROW]
[ROW][C]60[/C][C]20169[/C][C]17249.3469165279[/C][C]2919.65308347212[/C][/ROW]
[ROW][C]61[/C][C]17871[/C][C]18078.2092261864[/C][C]-207.209226186427[/C][/ROW]
[ROW][C]62[/C][C]17226[/C][C]18019.3844573220[/C][C]-793.384457322041[/C][/ROW]
[ROW][C]63[/C][C]19062[/C][C]17794.1500013979[/C][C]1267.84999860212[/C][/ROW]
[ROW][C]64[/C][C]17804[/C][C]18154.0808041672[/C][C]-350.080804167166[/C][/ROW]
[ROW][C]65[/C][C]19100[/C][C]18054.6961253669[/C][C]1045.30387463311[/C][/ROW]
[ROW][C]66[/C][C]18522[/C][C]18351.4481568764[/C][C]170.551843123576[/C][/ROW]
[ROW][C]67[/C][C]18060[/C][C]18399.8662362052[/C][C]-339.866236205155[/C][/ROW]
[ROW][C]68[/C][C]18869[/C][C]18303.381378086[/C][C]565.618621914[/C][/ROW]
[ROW][C]69[/C][C]18127[/C][C]18463.9552353019[/C][C]-336.955235301935[/C][/ROW]
[ROW][C]70[/C][C]18871[/C][C]18368.2967832191[/C][C]502.70321678093[/C][/ROW]
[ROW][C]71[/C][C]18890[/C][C]18511.0095430646[/C][C]378.990456935397[/C][/ROW]
[ROW][C]72[/C][C]21263[/C][C]18618.6014029511[/C][C]2644.39859704893[/C][/ROW]
[ROW][C]73[/C][C]19547[/C][C]19369.3215283028[/C][C]177.678471697189[/C][/ROW]
[ROW][C]74[/C][C]18450[/C][C]19419.7627910889[/C][C]-969.762791088866[/C][/ROW]
[ROW][C]75[/C][C]20254[/C][C]19144.4561694244[/C][C]1109.54383057556[/C][/ROW]
[ROW][C]76[/C][C]19240[/C][C]19459.4453259391[/C][C]-219.445325939076[/C][/ROW]
[ROW][C]77[/C][C]20216[/C][C]19397.1468423517[/C][C]818.85315764834[/C][/ROW]
[ROW][C]78[/C][C]19420[/C][C]19629.6116250211[/C][C]-209.611625021127[/C][/ROW]
[ROW][C]79[/C][C]19415[/C][C]19570.1048375093[/C][C]-155.104837509345[/C][/ROW]
[ROW][C]80[/C][C]20018[/C][C]19526.0720191636[/C][C]491.92798083643[/C][/ROW]
[ROW][C]81[/C][C]18652[/C][C]19665.7257899112[/C][C]-1013.72578991117[/C][/ROW]
[ROW][C]82[/C][C]19978[/C][C]19377.9384824592[/C][C]600.061517540773[/C][/ROW]
[ROW][C]83[/C][C]19509[/C][C]19548.2903568588[/C][C]-39.2903568588299[/C][/ROW]
[ROW][C]84[/C][C]21971[/C][C]19537.1361905924[/C][C]2433.86380940759[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10051&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10051&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
2	12873	13328	-455
3	14000	13198.8297389750	801.170261025034
4	13477	13426.2745120345	50.7254879654774
5	14237	13440.6750054875	796.324994512461
6	13674	13666.7442525248	7.25574747524479
7	13529	13668.8040916353	-139.804091635324
8	14058	13629.1150124949	428.884987505124
9	12975	13750.8714647713	-775.87146477126
10	14326	13530.6087842737	795.391215726278
11	14008	13756.4129402130	251.587059786978
12	16193	13827.8361625937	2365.16383740631
13	14483	14499.2841411536	-16.2841411535665
14	14011	14494.6612251901	-483.661225190106
15	15057	14357.3543093539	699.645690646146
16	14884	14555.9772027292	328.022797270754
17	15414	14649.0998188735	764.900181126524
18	14440	14866.2478541575	-426.247854157451
19	14900	14745.2400594698	154.759940530195
20	15074	14789.1749647764	284.825035223594
21	14442	14870.0341387243	-428.03413872431
22	15307	14748.5192344899	558.480765510074
23	14938	14907.0667207721	30.9332792278838
24	17193	14915.8483905572	2277.15160944277
25	15528	15562.3105175579	-34.3105175578839
26	14765	15552.5700812747	-787.570081274684
27	15838	15328.9862725411	509.013727458852
28	15723	15473.4905275767	249.509472423280
29	16150	15544.3239422605	605.676057739471
30	15486	15716.2697323151	-230.269732315079
31	15986	15650.8983006023	335.101699397677
32	15983	15746.0305511103	236.969448889700
33	15692	15813.3039699412	-121.303969941160
34	16490	15778.8669029946	711.133097005375
35	15686	15980.7509640138	-294.750964013800
36	18897	15897.0739113566	2999.92608864344
37	16316	16748.7249793255	-432.724979325532
38	15636	16625.8783891463	-989.878389146343
39	17163	16344.8611365989	818.138863401073
40	16534	16577.1231377863	-43.1231377862714
41	16518	16564.8808807224	-46.8808807223795
42	16375	16551.5718354477	-176.571835447670
43	16290	16501.4447363830	-211.444736382953
44	16352	16441.4175456336	-89.4175456335979
45	15943	16416.0327374804	-473.032737480389
46	16362	16281.7431502854	80.2568497146203
47	16393	16304.5273222122	88.4726777878423
48	19051	16329.6438911867	2721.35610881325
49	16747	17102.2115371592	-355.21153715923
50	16320	17001.3702910626	-681.370291062609
51	17910	16807.9356133675	1102.06438663247
52	16961	17120.8014254284	-159.801425428432
53	17480	17075.4352895279	404.564710472147
54	17049	17190.2874417327	-141.287441732697
55	16879	17150.1772533191	-271.177253319132
56	17473	17073.1925575053	399.807442494679
57	16998	17186.6941656521	-188.694165652108
58	17307	17133.1256499792	173.874350020822
59	17418	17182.4869580621	235.513041937862
60	20169	17249.3469165279	2919.65308347212
61	17871	18078.2092261864	-207.209226186427
62	17226	18019.3844573220	-793.384457322041
63	19062	17794.1500013979	1267.84999860212
64	17804	18154.0808041672	-350.080804167166
65	19100	18054.6961253669	1045.30387463311
66	18522	18351.4481568764	170.551843123576
67	18060	18399.8662362052	-339.866236205155
68	18869	18303.381378086	565.618621914
69	18127	18463.9552353019	-336.955235301935
70	18871	18368.2967832191	502.70321678093
71	18890	18511.0095430646	378.990456935397
72	21263	18618.6014029511	2644.39859704893
73	19547	19369.3215283028	177.678471697189
74	18450	19419.7627910889	-969.762791088866
75	20254	19144.4561694244	1109.54383057556
76	19240	19459.4453259391	-219.445325939076
77	20216	19397.1468423517	818.85315764834
78	19420	19629.6116250211	-209.611625021127
79	19415	19570.1048375093	-155.104837509345
80	20018	19526.0720191636	491.92798083643
81	18652	19665.7257899112	-1013.72578991117
82	19978	19377.9384824592	600.061517540773
83	19509	19548.2903568588	-39.2903568588299
84	21971	19537.1361905924	2433.86380940759

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	20228.0874511651	18517.5865739587	21938.5883283714
86	20228.0874511651	18449.9940872937	22006.1808150364
87	20228.0874511651	18384.8786267604	22071.2962755697
88	20228.0874511651	18321.9863179397	22134.1885843904
89	20228.0874511651	18261.1039001910	22195.0710021392
90	20228.0874511651	18202.0501737384	22254.1247285917
91	20228.0874511651	18144.6696319934	22311.5052703368
92	20228.0874511651	18088.8276331528	22367.3472691773
93	20228.0874511651	18034.4066793385	22421.7682229916
94	20228.0874511651	17981.3035077470	22474.8713945832
95	20228.0874511651	17929.4267871868	22526.7481151434
96	20228.0874511651	17878.6952727834	22577.4796295467

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 20228.0874511651 & 18517.5865739587 & 21938.5883283714 \tabularnewline
86 & 20228.0874511651 & 18449.9940872937 & 22006.1808150364 \tabularnewline
87 & 20228.0874511651 & 18384.8786267604 & 22071.2962755697 \tabularnewline
88 & 20228.0874511651 & 18321.9863179397 & 22134.1885843904 \tabularnewline
89 & 20228.0874511651 & 18261.1039001910 & 22195.0710021392 \tabularnewline
90 & 20228.0874511651 & 18202.0501737384 & 22254.1247285917 \tabularnewline
91 & 20228.0874511651 & 18144.6696319934 & 22311.5052703368 \tabularnewline
92 & 20228.0874511651 & 18088.8276331528 & 22367.3472691773 \tabularnewline
93 & 20228.0874511651 & 18034.4066793385 & 22421.7682229916 \tabularnewline
94 & 20228.0874511651 & 17981.3035077470 & 22474.8713945832 \tabularnewline
95 & 20228.0874511651 & 17929.4267871868 & 22526.7481151434 \tabularnewline
96 & 20228.0874511651 & 17878.6952727834 & 22577.4796295467 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10051&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]20228.0874511651[/C][C]18517.5865739587[/C][C]21938.5883283714[/C][/ROW]
[ROW][C]86[/C][C]20228.0874511651[/C][C]18449.9940872937[/C][C]22006.1808150364[/C][/ROW]
[ROW][C]87[/C][C]20228.0874511651[/C][C]18384.8786267604[/C][C]22071.2962755697[/C][/ROW]
[ROW][C]88[/C][C]20228.0874511651[/C][C]18321.9863179397[/C][C]22134.1885843904[/C][/ROW]
[ROW][C]89[/C][C]20228.0874511651[/C][C]18261.1039001910[/C][C]22195.0710021392[/C][/ROW]
[ROW][C]90[/C][C]20228.0874511651[/C][C]18202.0501737384[/C][C]22254.1247285917[/C][/ROW]
[ROW][C]91[/C][C]20228.0874511651[/C][C]18144.6696319934[/C][C]22311.5052703368[/C][/ROW]
[ROW][C]92[/C][C]20228.0874511651[/C][C]18088.8276331528[/C][C]22367.3472691773[/C][/ROW]
[ROW][C]93[/C][C]20228.0874511651[/C][C]18034.4066793385[/C][C]22421.7682229916[/C][/ROW]
[ROW][C]94[/C][C]20228.0874511651[/C][C]17981.3035077470[/C][C]22474.8713945832[/C][/ROW]
[ROW][C]95[/C][C]20228.0874511651[/C][C]17929.4267871868[/C][C]22526.7481151434[/C][/ROW]
[ROW][C]96[/C][C]20228.0874511651[/C][C]17878.6952727834[/C][C]22577.4796295467[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10051&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10051&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
85	20228.0874511651	18517.5865739587	21938.5883283714
86	20228.0874511651	18449.9940872937	22006.1808150364
87	20228.0874511651	18384.8786267604	22071.2962755697
88	20228.0874511651	18321.9863179397	22134.1885843904
89	20228.0874511651	18261.1039001910	22195.0710021392
90	20228.0874511651	18202.0501737384	22254.1247285917
91	20228.0874511651	18144.6696319934	22311.5052703368
92	20228.0874511651	18088.8276331528	22367.3472691773
93	20228.0874511651	18034.4066793385	22421.7682229916
94	20228.0874511651	17981.3035077470	22474.8713945832
95	20228.0874511651	17929.4267871868	22526.7481151434
96	20228.0874511651	17878.6952727834	22577.4796295467

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 = Single ; par3 = additive ;

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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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