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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

Wed, 18 May 2011 12:52:56 +0000

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/2011/May/18/t13057230432jbjxcg74d6l8go.htm/, Retrieved Thu, 12 Feb 2026 11:40:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121829, Retrieved Thu, 12 Feb 2026 11:40:35 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

276

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

-       [Exponential Smoothing] [Exponential Smoot...] [2011-05-18 12:52:56] [8b50cbc1ebd04aa753862408f533fbe8] [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' @ www.wessa.org

\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' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121829&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' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121829&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121829&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' @ www.wessa.org

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121829&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121829&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121829&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	1
beta	0
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	1.2261	1.2642	-0.0381
4	1.1989	1.2263	-0.0273999999999999
5	1.2	1.1991	0.000899999999999901
6	1.2146	1.2002	0.0144
7	1.2266	1.2148	0.0118
8	1.2191	1.2268	-0.00769999999999982
9	1.2224	1.2193	0.00309999999999988
10	1.2507	1.2226	0.0281
11	1.2997	1.2509	0.0488000000000002
12	1.3406	1.2999	0.0407
13	1.3123	1.3408	-0.0285
14	1.3013	1.3125	-0.0112000000000001
15	1.3185	1.3015	0.0170000000000001
16	1.2943	1.3187	-0.0244
17	1.2697	1.2945	-0.0247999999999999
18	1.2155	1.2699	-0.0544
19	1.2041	1.2157	-0.0116000000000001
20	1.2295	1.2043	0.0252000000000001
21	1.2234	1.2297	-0.00629999999999997
22	1.2022	1.2236	-0.0214000000000001
23	1.1789	1.2024	-0.0234999999999999
24	1.1861	1.1791	0.0069999999999999
25	1.2126	1.1863	0.0263
26	1.194	1.2128	-0.0187999999999999
27	1.2028	1.1942	0.00860000000000016
28	1.2273	1.203	0.0243
29	1.2767	1.2275	0.0491999999999999
30	1.2661	1.2769	-0.0107999999999999
31	1.2681	1.2663	0.00180000000000002
32	1.281	1.2683	0.0126999999999999
33	1.2722	1.2812	-0.0089999999999999
34	1.2617	1.2724	-0.0106999999999999
35	1.2888	1.2619	0.0268999999999999
36	1.3205	1.289	0.0315000000000001
37	1.2993	1.3207	-0.0214000000000001
38	1.308	1.2995	0.00850000000000017
39	1.3246	1.3082	0.0164
40	1.3513	1.3248	0.0265
41	1.3518	1.3515	0.000299999999999967
42	1.3421	1.352	-0.0098999999999998
43	1.3726	1.3423	0.0303
44	1.3626	1.3728	-0.0102
45	1.391	1.3628	0.0282
46	1.4233	1.3912	0.0321
47	1.4683	1.4235	0.0448
48	1.4559	1.4685	-0.0125999999999999
49	1.4728	1.4561	0.0167000000000002
50	1.4759	1.473	0.0028999999999999
51	1.552	1.4761	0.0759000000000001
52	1.5754	1.5522	0.0231999999999999
53	1.5554	1.5756	-0.0202
54	1.5562	1.5556	0.000600000000000156
55	1.5759	1.5564	0.0195000000000001
56	1.4955	1.5761	-0.0806
57	1.4342	1.4957	-0.0615000000000001
58	1.3266	1.4344	-0.1078
59	1.2744	1.3268	-0.0524
60	1.3511	1.2746	0.0765
61	1.3244	1.3513	-0.0268999999999999
62	1.2797	1.3246	-0.0448999999999999
63	1.305	1.2799	0.0250999999999999
64	1.3199	1.3052	0.0147000000000002
65	1.3646	1.3201	0.0445
66	1.4014	1.3648	0.0366
67	1.4092	1.4016	0.00760000000000005
68	1.4266	1.4094	0.0172000000000001
69	1.4575	1.4268	0.0306999999999999
70	1.4821	1.4577	0.0244
71	1.4908	1.4823	0.00849999999999995
72	1.4579	1.491	-0.0330999999999999
73	1.4266	1.4581	-0.0314999999999999
74	1.368	1.4268	-0.0588
75	1.357	1.3682	-0.0112000000000001
76	1.3417	1.3572	-0.0155000000000001
77	1.2563	1.3419	-0.0855999999999999
78	1.2223	1.2565	-0.0342
79	1.2811	1.2225	0.0586
80	1.2903	1.2813	0.00900000000000012
81	1.3103	1.2905	0.0198
82	1.3901	1.3105	0.0795999999999999
83	1.3654	1.3903	-0.0248999999999999
84	1.3221	1.3656	-0.0434999999999999

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.2261 & 1.2642 & -0.0381 \tabularnewline
4 & 1.1989 & 1.2263 & -0.0273999999999999 \tabularnewline
5 & 1.2 & 1.1991 & 0.000899999999999901 \tabularnewline
6 & 1.2146 & 1.2002 & 0.0144 \tabularnewline
7 & 1.2266 & 1.2148 & 0.0118 \tabularnewline
8 & 1.2191 & 1.2268 & -0.00769999999999982 \tabularnewline
9 & 1.2224 & 1.2193 & 0.00309999999999988 \tabularnewline
10 & 1.2507 & 1.2226 & 0.0281 \tabularnewline
11 & 1.2997 & 1.2509 & 0.0488000000000002 \tabularnewline
12 & 1.3406 & 1.2999 & 0.0407 \tabularnewline
13 & 1.3123 & 1.3408 & -0.0285 \tabularnewline
14 & 1.3013 & 1.3125 & -0.0112000000000001 \tabularnewline
15 & 1.3185 & 1.3015 & 0.0170000000000001 \tabularnewline
16 & 1.2943 & 1.3187 & -0.0244 \tabularnewline
17 & 1.2697 & 1.2945 & -0.0247999999999999 \tabularnewline
18 & 1.2155 & 1.2699 & -0.0544 \tabularnewline
19 & 1.2041 & 1.2157 & -0.0116000000000001 \tabularnewline
20 & 1.2295 & 1.2043 & 0.0252000000000001 \tabularnewline
21 & 1.2234 & 1.2297 & -0.00629999999999997 \tabularnewline
22 & 1.2022 & 1.2236 & -0.0214000000000001 \tabularnewline
23 & 1.1789 & 1.2024 & -0.0234999999999999 \tabularnewline
24 & 1.1861 & 1.1791 & 0.0069999999999999 \tabularnewline
25 & 1.2126 & 1.1863 & 0.0263 \tabularnewline
26 & 1.194 & 1.2128 & -0.0187999999999999 \tabularnewline
27 & 1.2028 & 1.1942 & 0.00860000000000016 \tabularnewline
28 & 1.2273 & 1.203 & 0.0243 \tabularnewline
29 & 1.2767 & 1.2275 & 0.0491999999999999 \tabularnewline
30 & 1.2661 & 1.2769 & -0.0107999999999999 \tabularnewline
31 & 1.2681 & 1.2663 & 0.00180000000000002 \tabularnewline
32 & 1.281 & 1.2683 & 0.0126999999999999 \tabularnewline
33 & 1.2722 & 1.2812 & -0.0089999999999999 \tabularnewline
34 & 1.2617 & 1.2724 & -0.0106999999999999 \tabularnewline
35 & 1.2888 & 1.2619 & 0.0268999999999999 \tabularnewline
36 & 1.3205 & 1.289 & 0.0315000000000001 \tabularnewline
37 & 1.2993 & 1.3207 & -0.0214000000000001 \tabularnewline
38 & 1.308 & 1.2995 & 0.00850000000000017 \tabularnewline
39 & 1.3246 & 1.3082 & 0.0164 \tabularnewline
40 & 1.3513 & 1.3248 & 0.0265 \tabularnewline
41 & 1.3518 & 1.3515 & 0.000299999999999967 \tabularnewline
42 & 1.3421 & 1.352 & -0.0098999999999998 \tabularnewline
43 & 1.3726 & 1.3423 & 0.0303 \tabularnewline
44 & 1.3626 & 1.3728 & -0.0102 \tabularnewline
45 & 1.391 & 1.3628 & 0.0282 \tabularnewline
46 & 1.4233 & 1.3912 & 0.0321 \tabularnewline
47 & 1.4683 & 1.4235 & 0.0448 \tabularnewline
48 & 1.4559 & 1.4685 & -0.0125999999999999 \tabularnewline
49 & 1.4728 & 1.4561 & 0.0167000000000002 \tabularnewline
50 & 1.4759 & 1.473 & 0.0028999999999999 \tabularnewline
51 & 1.552 & 1.4761 & 0.0759000000000001 \tabularnewline
52 & 1.5754 & 1.5522 & 0.0231999999999999 \tabularnewline
53 & 1.5554 & 1.5756 & -0.0202 \tabularnewline
54 & 1.5562 & 1.5556 & 0.000600000000000156 \tabularnewline
55 & 1.5759 & 1.5564 & 0.0195000000000001 \tabularnewline
56 & 1.4955 & 1.5761 & -0.0806 \tabularnewline
57 & 1.4342 & 1.4957 & -0.0615000000000001 \tabularnewline
58 & 1.3266 & 1.4344 & -0.1078 \tabularnewline
59 & 1.2744 & 1.3268 & -0.0524 \tabularnewline
60 & 1.3511 & 1.2746 & 0.0765 \tabularnewline
61 & 1.3244 & 1.3513 & -0.0268999999999999 \tabularnewline
62 & 1.2797 & 1.3246 & -0.0448999999999999 \tabularnewline
63 & 1.305 & 1.2799 & 0.0250999999999999 \tabularnewline
64 & 1.3199 & 1.3052 & 0.0147000000000002 \tabularnewline
65 & 1.3646 & 1.3201 & 0.0445 \tabularnewline
66 & 1.4014 & 1.3648 & 0.0366 \tabularnewline
67 & 1.4092 & 1.4016 & 0.00760000000000005 \tabularnewline
68 & 1.4266 & 1.4094 & 0.0172000000000001 \tabularnewline
69 & 1.4575 & 1.4268 & 0.0306999999999999 \tabularnewline
70 & 1.4821 & 1.4577 & 0.0244 \tabularnewline
71 & 1.4908 & 1.4823 & 0.00849999999999995 \tabularnewline
72 & 1.4579 & 1.491 & -0.0330999999999999 \tabularnewline
73 & 1.4266 & 1.4581 & -0.0314999999999999 \tabularnewline
74 & 1.368 & 1.4268 & -0.0588 \tabularnewline
75 & 1.357 & 1.3682 & -0.0112000000000001 \tabularnewline
76 & 1.3417 & 1.3572 & -0.0155000000000001 \tabularnewline
77 & 1.2563 & 1.3419 & -0.0855999999999999 \tabularnewline
78 & 1.2223 & 1.2565 & -0.0342 \tabularnewline
79 & 1.2811 & 1.2225 & 0.0586 \tabularnewline
80 & 1.2903 & 1.2813 & 0.00900000000000012 \tabularnewline
81 & 1.3103 & 1.2905 & 0.0198 \tabularnewline
82 & 1.3901 & 1.3105 & 0.0795999999999999 \tabularnewline
83 & 1.3654 & 1.3903 & -0.0248999999999999 \tabularnewline
84 & 1.3221 & 1.3656 & -0.0434999999999999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121829&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]1.2261[/C][C]1.2642[/C][C]-0.0381[/C][/ROW]
[ROW][C]4[/C][C]1.1989[/C][C]1.2263[/C][C]-0.0273999999999999[/C][/ROW]
[ROW][C]5[/C][C]1.2[/C][C]1.1991[/C][C]0.000899999999999901[/C][/ROW]
[ROW][C]6[/C][C]1.2146[/C][C]1.2002[/C][C]0.0144[/C][/ROW]
[ROW][C]7[/C][C]1.2266[/C][C]1.2148[/C][C]0.0118[/C][/ROW]
[ROW][C]8[/C][C]1.2191[/C][C]1.2268[/C][C]-0.00769999999999982[/C][/ROW]
[ROW][C]9[/C][C]1.2224[/C][C]1.2193[/C][C]0.00309999999999988[/C][/ROW]
[ROW][C]10[/C][C]1.2507[/C][C]1.2226[/C][C]0.0281[/C][/ROW]
[ROW][C]11[/C][C]1.2997[/C][C]1.2509[/C][C]0.0488000000000002[/C][/ROW]
[ROW][C]12[/C][C]1.3406[/C][C]1.2999[/C][C]0.0407[/C][/ROW]
[ROW][C]13[/C][C]1.3123[/C][C]1.3408[/C][C]-0.0285[/C][/ROW]
[ROW][C]14[/C][C]1.3013[/C][C]1.3125[/C][C]-0.0112000000000001[/C][/ROW]
[ROW][C]15[/C][C]1.3185[/C][C]1.3015[/C][C]0.0170000000000001[/C][/ROW]
[ROW][C]16[/C][C]1.2943[/C][C]1.3187[/C][C]-0.0244[/C][/ROW]
[ROW][C]17[/C][C]1.2697[/C][C]1.2945[/C][C]-0.0247999999999999[/C][/ROW]
[ROW][C]18[/C][C]1.2155[/C][C]1.2699[/C][C]-0.0544[/C][/ROW]
[ROW][C]19[/C][C]1.2041[/C][C]1.2157[/C][C]-0.0116000000000001[/C][/ROW]
[ROW][C]20[/C][C]1.2295[/C][C]1.2043[/C][C]0.0252000000000001[/C][/ROW]
[ROW][C]21[/C][C]1.2234[/C][C]1.2297[/C][C]-0.00629999999999997[/C][/ROW]
[ROW][C]22[/C][C]1.2022[/C][C]1.2236[/C][C]-0.0214000000000001[/C][/ROW]
[ROW][C]23[/C][C]1.1789[/C][C]1.2024[/C][C]-0.0234999999999999[/C][/ROW]
[ROW][C]24[/C][C]1.1861[/C][C]1.1791[/C][C]0.0069999999999999[/C][/ROW]
[ROW][C]25[/C][C]1.2126[/C][C]1.1863[/C][C]0.0263[/C][/ROW]
[ROW][C]26[/C][C]1.194[/C][C]1.2128[/C][C]-0.0187999999999999[/C][/ROW]
[ROW][C]27[/C][C]1.2028[/C][C]1.1942[/C][C]0.00860000000000016[/C][/ROW]
[ROW][C]28[/C][C]1.2273[/C][C]1.203[/C][C]0.0243[/C][/ROW]
[ROW][C]29[/C][C]1.2767[/C][C]1.2275[/C][C]0.0491999999999999[/C][/ROW]
[ROW][C]30[/C][C]1.2661[/C][C]1.2769[/C][C]-0.0107999999999999[/C][/ROW]
[ROW][C]31[/C][C]1.2681[/C][C]1.2663[/C][C]0.00180000000000002[/C][/ROW]
[ROW][C]32[/C][C]1.281[/C][C]1.2683[/C][C]0.0126999999999999[/C][/ROW]
[ROW][C]33[/C][C]1.2722[/C][C]1.2812[/C][C]-0.0089999999999999[/C][/ROW]
[ROW][C]34[/C][C]1.2617[/C][C]1.2724[/C][C]-0.0106999999999999[/C][/ROW]
[ROW][C]35[/C][C]1.2888[/C][C]1.2619[/C][C]0.0268999999999999[/C][/ROW]
[ROW][C]36[/C][C]1.3205[/C][C]1.289[/C][C]0.0315000000000001[/C][/ROW]
[ROW][C]37[/C][C]1.2993[/C][C]1.3207[/C][C]-0.0214000000000001[/C][/ROW]
[ROW][C]38[/C][C]1.308[/C][C]1.2995[/C][C]0.00850000000000017[/C][/ROW]
[ROW][C]39[/C][C]1.3246[/C][C]1.3082[/C][C]0.0164[/C][/ROW]
[ROW][C]40[/C][C]1.3513[/C][C]1.3248[/C][C]0.0265[/C][/ROW]
[ROW][C]41[/C][C]1.3518[/C][C]1.3515[/C][C]0.000299999999999967[/C][/ROW]
[ROW][C]42[/C][C]1.3421[/C][C]1.352[/C][C]-0.0098999999999998[/C][/ROW]
[ROW][C]43[/C][C]1.3726[/C][C]1.3423[/C][C]0.0303[/C][/ROW]
[ROW][C]44[/C][C]1.3626[/C][C]1.3728[/C][C]-0.0102[/C][/ROW]
[ROW][C]45[/C][C]1.391[/C][C]1.3628[/C][C]0.0282[/C][/ROW]
[ROW][C]46[/C][C]1.4233[/C][C]1.3912[/C][C]0.0321[/C][/ROW]
[ROW][C]47[/C][C]1.4683[/C][C]1.4235[/C][C]0.0448[/C][/ROW]
[ROW][C]48[/C][C]1.4559[/C][C]1.4685[/C][C]-0.0125999999999999[/C][/ROW]
[ROW][C]49[/C][C]1.4728[/C][C]1.4561[/C][C]0.0167000000000002[/C][/ROW]
[ROW][C]50[/C][C]1.4759[/C][C]1.473[/C][C]0.0028999999999999[/C][/ROW]
[ROW][C]51[/C][C]1.552[/C][C]1.4761[/C][C]0.0759000000000001[/C][/ROW]
[ROW][C]52[/C][C]1.5754[/C][C]1.5522[/C][C]0.0231999999999999[/C][/ROW]
[ROW][C]53[/C][C]1.5554[/C][C]1.5756[/C][C]-0.0202[/C][/ROW]
[ROW][C]54[/C][C]1.5562[/C][C]1.5556[/C][C]0.000600000000000156[/C][/ROW]
[ROW][C]55[/C][C]1.5759[/C][C]1.5564[/C][C]0.0195000000000001[/C][/ROW]
[ROW][C]56[/C][C]1.4955[/C][C]1.5761[/C][C]-0.0806[/C][/ROW]
[ROW][C]57[/C][C]1.4342[/C][C]1.4957[/C][C]-0.0615000000000001[/C][/ROW]
[ROW][C]58[/C][C]1.3266[/C][C]1.4344[/C][C]-0.1078[/C][/ROW]
[ROW][C]59[/C][C]1.2744[/C][C]1.3268[/C][C]-0.0524[/C][/ROW]
[ROW][C]60[/C][C]1.3511[/C][C]1.2746[/C][C]0.0765[/C][/ROW]
[ROW][C]61[/C][C]1.3244[/C][C]1.3513[/C][C]-0.0268999999999999[/C][/ROW]
[ROW][C]62[/C][C]1.2797[/C][C]1.3246[/C][C]-0.0448999999999999[/C][/ROW]
[ROW][C]63[/C][C]1.305[/C][C]1.2799[/C][C]0.0250999999999999[/C][/ROW]
[ROW][C]64[/C][C]1.3199[/C][C]1.3052[/C][C]0.0147000000000002[/C][/ROW]
[ROW][C]65[/C][C]1.3646[/C][C]1.3201[/C][C]0.0445[/C][/ROW]
[ROW][C]66[/C][C]1.4014[/C][C]1.3648[/C][C]0.0366[/C][/ROW]
[ROW][C]67[/C][C]1.4092[/C][C]1.4016[/C][C]0.00760000000000005[/C][/ROW]
[ROW][C]68[/C][C]1.4266[/C][C]1.4094[/C][C]0.0172000000000001[/C][/ROW]
[ROW][C]69[/C][C]1.4575[/C][C]1.4268[/C][C]0.0306999999999999[/C][/ROW]
[ROW][C]70[/C][C]1.4821[/C][C]1.4577[/C][C]0.0244[/C][/ROW]
[ROW][C]71[/C][C]1.4908[/C][C]1.4823[/C][C]0.00849999999999995[/C][/ROW]
[ROW][C]72[/C][C]1.4579[/C][C]1.491[/C][C]-0.0330999999999999[/C][/ROW]
[ROW][C]73[/C][C]1.4266[/C][C]1.4581[/C][C]-0.0314999999999999[/C][/ROW]
[ROW][C]74[/C][C]1.368[/C][C]1.4268[/C][C]-0.0588[/C][/ROW]
[ROW][C]75[/C][C]1.357[/C][C]1.3682[/C][C]-0.0112000000000001[/C][/ROW]
[ROW][C]76[/C][C]1.3417[/C][C]1.3572[/C][C]-0.0155000000000001[/C][/ROW]
[ROW][C]77[/C][C]1.2563[/C][C]1.3419[/C][C]-0.0855999999999999[/C][/ROW]
[ROW][C]78[/C][C]1.2223[/C][C]1.2565[/C][C]-0.0342[/C][/ROW]
[ROW][C]79[/C][C]1.2811[/C][C]1.2225[/C][C]0.0586[/C][/ROW]
[ROW][C]80[/C][C]1.2903[/C][C]1.2813[/C][C]0.00900000000000012[/C][/ROW]
[ROW][C]81[/C][C]1.3103[/C][C]1.2905[/C][C]0.0198[/C][/ROW]
[ROW][C]82[/C][C]1.3901[/C][C]1.3105[/C][C]0.0795999999999999[/C][/ROW]
[ROW][C]83[/C][C]1.3654[/C][C]1.3903[/C][C]-0.0248999999999999[/C][/ROW]
[ROW][C]84[/C][C]1.3221[/C][C]1.3656[/C][C]-0.0434999999999999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121829&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121829&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	1.2261	1.2642	-0.0381
4	1.1989	1.2263	-0.0273999999999999
5	1.2	1.1991	0.000899999999999901
6	1.2146	1.2002	0.0144
7	1.2266	1.2148	0.0118
8	1.2191	1.2268	-0.00769999999999982
9	1.2224	1.2193	0.00309999999999988
10	1.2507	1.2226	0.0281
11	1.2997	1.2509	0.0488000000000002
12	1.3406	1.2999	0.0407
13	1.3123	1.3408	-0.0285
14	1.3013	1.3125	-0.0112000000000001
15	1.3185	1.3015	0.0170000000000001
16	1.2943	1.3187	-0.0244
17	1.2697	1.2945	-0.0247999999999999
18	1.2155	1.2699	-0.0544
19	1.2041	1.2157	-0.0116000000000001
20	1.2295	1.2043	0.0252000000000001
21	1.2234	1.2297	-0.00629999999999997
22	1.2022	1.2236	-0.0214000000000001
23	1.1789	1.2024	-0.0234999999999999
24	1.1861	1.1791	0.0069999999999999
25	1.2126	1.1863	0.0263
26	1.194	1.2128	-0.0187999999999999
27	1.2028	1.1942	0.00860000000000016
28	1.2273	1.203	0.0243
29	1.2767	1.2275	0.0491999999999999
30	1.2661	1.2769	-0.0107999999999999
31	1.2681	1.2663	0.00180000000000002
32	1.281	1.2683	0.0126999999999999
33	1.2722	1.2812	-0.0089999999999999
34	1.2617	1.2724	-0.0106999999999999
35	1.2888	1.2619	0.0268999999999999
36	1.3205	1.289	0.0315000000000001
37	1.2993	1.3207	-0.0214000000000001
38	1.308	1.2995	0.00850000000000017
39	1.3246	1.3082	0.0164
40	1.3513	1.3248	0.0265
41	1.3518	1.3515	0.000299999999999967
42	1.3421	1.352	-0.0098999999999998
43	1.3726	1.3423	0.0303
44	1.3626	1.3728	-0.0102
45	1.391	1.3628	0.0282
46	1.4233	1.3912	0.0321
47	1.4683	1.4235	0.0448
48	1.4559	1.4685	-0.0125999999999999
49	1.4728	1.4561	0.0167000000000002
50	1.4759	1.473	0.0028999999999999
51	1.552	1.4761	0.0759000000000001
52	1.5754	1.5522	0.0231999999999999
53	1.5554	1.5756	-0.0202
54	1.5562	1.5556	0.000600000000000156
55	1.5759	1.5564	0.0195000000000001
56	1.4955	1.5761	-0.0806
57	1.4342	1.4957	-0.0615000000000001
58	1.3266	1.4344	-0.1078
59	1.2744	1.3268	-0.0524
60	1.3511	1.2746	0.0765
61	1.3244	1.3513	-0.0268999999999999
62	1.2797	1.3246	-0.0448999999999999
63	1.305	1.2799	0.0250999999999999
64	1.3199	1.3052	0.0147000000000002
65	1.3646	1.3201	0.0445
66	1.4014	1.3648	0.0366
67	1.4092	1.4016	0.00760000000000005
68	1.4266	1.4094	0.0172000000000001
69	1.4575	1.4268	0.0306999999999999
70	1.4821	1.4577	0.0244
71	1.4908	1.4823	0.00849999999999995
72	1.4579	1.491	-0.0330999999999999
73	1.4266	1.4581	-0.0314999999999999
74	1.368	1.4268	-0.0588
75	1.357	1.3682	-0.0112000000000001
76	1.3417	1.3572	-0.0155000000000001
77	1.2563	1.3419	-0.0855999999999999
78	1.2223	1.2565	-0.0342
79	1.2811	1.2225	0.0586
80	1.2903	1.2813	0.00900000000000012
81	1.3103	1.2905	0.0198
82	1.3901	1.3105	0.0795999999999999
83	1.3654	1.3903	-0.0248999999999999
84	1.3221	1.3656	-0.0434999999999999

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	1.3223	1.25290875043269	1.39169124956731
86	1.3225	1.22436595375189	1.42063404624811
87	1.3227	1.20251083014873	1.44288916985127
88	1.3229	1.18411750086538	1.46168249913462
89	1.3231	1.16793644892384	1.47826355107616
90	1.3233	1.15332684594596	1.49327315405404
91	1.3235	1.13990801048088	1.50709198951912
92	1.3237	1.12743190750378	1.51996809249622
93	1.3239	1.11572625129807	1.53207374870193
94	1.3241	1.10466560168212	1.54353439831788
95	1.3243	1.09415526145132	1.55444473854868
96	1.3245	1.08412166029745	1.56487833970255

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 1.3223 & 1.25290875043269 & 1.39169124956731 \tabularnewline
86 & 1.3225 & 1.22436595375189 & 1.42063404624811 \tabularnewline
87 & 1.3227 & 1.20251083014873 & 1.44288916985127 \tabularnewline
88 & 1.3229 & 1.18411750086538 & 1.46168249913462 \tabularnewline
89 & 1.3231 & 1.16793644892384 & 1.47826355107616 \tabularnewline
90 & 1.3233 & 1.15332684594596 & 1.49327315405404 \tabularnewline
91 & 1.3235 & 1.13990801048088 & 1.50709198951912 \tabularnewline
92 & 1.3237 & 1.12743190750378 & 1.51996809249622 \tabularnewline
93 & 1.3239 & 1.11572625129807 & 1.53207374870193 \tabularnewline
94 & 1.3241 & 1.10466560168212 & 1.54353439831788 \tabularnewline
95 & 1.3243 & 1.09415526145132 & 1.55444473854868 \tabularnewline
96 & 1.3245 & 1.08412166029745 & 1.56487833970255 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121829&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]1.3223[/C][C]1.25290875043269[/C][C]1.39169124956731[/C][/ROW]
[ROW][C]86[/C][C]1.3225[/C][C]1.22436595375189[/C][C]1.42063404624811[/C][/ROW]
[ROW][C]87[/C][C]1.3227[/C][C]1.20251083014873[/C][C]1.44288916985127[/C][/ROW]
[ROW][C]88[/C][C]1.3229[/C][C]1.18411750086538[/C][C]1.46168249913462[/C][/ROW]
[ROW][C]89[/C][C]1.3231[/C][C]1.16793644892384[/C][C]1.47826355107616[/C][/ROW]
[ROW][C]90[/C][C]1.3233[/C][C]1.15332684594596[/C][C]1.49327315405404[/C][/ROW]
[ROW][C]91[/C][C]1.3235[/C][C]1.13990801048088[/C][C]1.50709198951912[/C][/ROW]
[ROW][C]92[/C][C]1.3237[/C][C]1.12743190750378[/C][C]1.51996809249622[/C][/ROW]
[ROW][C]93[/C][C]1.3239[/C][C]1.11572625129807[/C][C]1.53207374870193[/C][/ROW]
[ROW][C]94[/C][C]1.3241[/C][C]1.10466560168212[/C][C]1.54353439831788[/C][/ROW]
[ROW][C]95[/C][C]1.3243[/C][C]1.09415526145132[/C][C]1.55444473854868[/C][/ROW]
[ROW][C]96[/C][C]1.3245[/C][C]1.08412166029745[/C][C]1.56487833970255[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121829&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121829&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	1.3223	1.25290875043269	1.39169124956731
86	1.3225	1.22436595375189	1.42063404624811
87	1.3227	1.20251083014873	1.44288916985127
88	1.3229	1.18411750086538	1.46168249913462
89	1.3231	1.16793644892384	1.47826355107616
90	1.3233	1.15332684594596	1.49327315405404
91	1.3235	1.13990801048088	1.50709198951912
92	1.3237	1.12743190750378	1.51996809249622
93	1.3239	1.11572625129807	1.53207374870193
94	1.3241	1.10466560168212	1.54353439831788
95	1.3243	1.09415526145132	1.55444473854868
96	1.3245	1.08412166029745	1.56487833970255

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 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

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