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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 18 Dec 2016 13:33:21 +0100

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/2016/Dec/18/t14820644187mp9x45v0inmshg.htm/, Retrieved Mon, 05 May 2025 02:31:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301030, Retrieved Mon, 05 May 2025 02:31:42 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

143

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

-     [Exponential Smoothing] [] [2016-12-18 12:31:12] [683f400e1b95307fc738e729f07c4fce]
- R       [Exponential Smoothing] [] [2016-12-18 12:33:21] [404ac5ee4f7301873f6a96ef36861981] [Current]

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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	1 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301030&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301030&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301030&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	1 seconds
R Server	Big Analytics Cloud Computing Center

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.506936910736287
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.506936910736287 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301030&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]0.506936910736287[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301030&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301030&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	0.506936910736287
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	6160	9290	-3130
3	8320	7703.28746939542	616.712530604578
4	8310	8015.92181447246	294.078185527535
5	6750	8165.00090135873	-1415.00090135873
6	8710	7447.68471573487	1262.31528426513
7	6300	8087.59892631543	-1787.59892631543
8	5710	7181.39904897358	-1471.39904897358
9	5740	6435.4925606266	-695.492560626604
10	6710	6082.92171050248	627.078289497516
11	7310	6400.81084137015	909.18915862985
12	7240	6861.71238472089	378.28761527911
13	8650	7053.48033978028	1596.51966021972
14	8330	7862.81508426181	467.184915738188
15	7810	8099.64836218872	-289.648362188722
16	8260	7952.81491626095	307.185083739054
17	6680	8108.53837363589	-1428.53837363589
18	5580	7384.35954363667	-1804.35954363667
19	6340	6469.66309072796	-129.66309072796
20	4490	6403.93208407781	-1913.93208407781
21	5000	5433.68926601634	-433.689266016341
22	7030	5213.83616928253	1816.16383071747
23	6100	6134.51665101742	-34.5166510174249
24	9740	6117.01888658169	3622.98111341831
25	7940	7953.64173987388	-13.6417398738822
26	7740	7946.72623840515	-206.726238405148
27	7820	7841.92907773991	-21.9290777399092
28	7820	7830.81241881514	-10.8124188151432
29	5380	7825.33120462341	-2445.33120462341
30	7070	6585.70255802457	484.297441975426
31	6970	6831.21080713708	138.789192862918
32	4080	6901.56817181059	-2821.56817181059
33	4930	5471.2111193611	-541.211119361096
34	4820	5196.85122645605	-376.851226456054
35	6220	5005.81142990924	1214.18857009076
36	6360	5621.32843268236	738.67156731764
37	7630	5995.7883150671	1634.2116849329
38	5130	6824.23053811612	-1694.23053811612
39	6960	5965.36254304846	994.637456951541
40	5350	6469.58098277807	-1119.58098277807
41	6290	5902.02405804946	387.975941950541
42	4630	6098.70338350187	-1468.70338350187
43	5130	5354.1634274815	-224.163427481499
44	3620	5240.52671205397	-1620.52671205397
45	3980	4419.0219068797	-439.021906879698
46	3120	4196.46549766055	-1076.46549766055
47	4310	3650.76540376231	659.234596237689
48	4250	3984.95575342953	265.044246570471
49	5730	4119.31646499439	1610.68353500561
50	3630	4935.83140040394	-1305.83140040394
51	5680	4273.85726434073	1406.14273565927

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 6160 & 9290 & -3130 \tabularnewline
3 & 8320 & 7703.28746939542 & 616.712530604578 \tabularnewline
4 & 8310 & 8015.92181447246 & 294.078185527535 \tabularnewline
5 & 6750 & 8165.00090135873 & -1415.00090135873 \tabularnewline
6 & 8710 & 7447.68471573487 & 1262.31528426513 \tabularnewline
7 & 6300 & 8087.59892631543 & -1787.59892631543 \tabularnewline
8 & 5710 & 7181.39904897358 & -1471.39904897358 \tabularnewline
9 & 5740 & 6435.4925606266 & -695.492560626604 \tabularnewline
10 & 6710 & 6082.92171050248 & 627.078289497516 \tabularnewline
11 & 7310 & 6400.81084137015 & 909.18915862985 \tabularnewline
12 & 7240 & 6861.71238472089 & 378.28761527911 \tabularnewline
13 & 8650 & 7053.48033978028 & 1596.51966021972 \tabularnewline
14 & 8330 & 7862.81508426181 & 467.184915738188 \tabularnewline
15 & 7810 & 8099.64836218872 & -289.648362188722 \tabularnewline
16 & 8260 & 7952.81491626095 & 307.185083739054 \tabularnewline
17 & 6680 & 8108.53837363589 & -1428.53837363589 \tabularnewline
18 & 5580 & 7384.35954363667 & -1804.35954363667 \tabularnewline
19 & 6340 & 6469.66309072796 & -129.66309072796 \tabularnewline
20 & 4490 & 6403.93208407781 & -1913.93208407781 \tabularnewline
21 & 5000 & 5433.68926601634 & -433.689266016341 \tabularnewline
22 & 7030 & 5213.83616928253 & 1816.16383071747 \tabularnewline
23 & 6100 & 6134.51665101742 & -34.5166510174249 \tabularnewline
24 & 9740 & 6117.01888658169 & 3622.98111341831 \tabularnewline
25 & 7940 & 7953.64173987388 & -13.6417398738822 \tabularnewline
26 & 7740 & 7946.72623840515 & -206.726238405148 \tabularnewline
27 & 7820 & 7841.92907773991 & -21.9290777399092 \tabularnewline
28 & 7820 & 7830.81241881514 & -10.8124188151432 \tabularnewline
29 & 5380 & 7825.33120462341 & -2445.33120462341 \tabularnewline
30 & 7070 & 6585.70255802457 & 484.297441975426 \tabularnewline
31 & 6970 & 6831.21080713708 & 138.789192862918 \tabularnewline
32 & 4080 & 6901.56817181059 & -2821.56817181059 \tabularnewline
33 & 4930 & 5471.2111193611 & -541.211119361096 \tabularnewline
34 & 4820 & 5196.85122645605 & -376.851226456054 \tabularnewline
35 & 6220 & 5005.81142990924 & 1214.18857009076 \tabularnewline
36 & 6360 & 5621.32843268236 & 738.67156731764 \tabularnewline
37 & 7630 & 5995.7883150671 & 1634.2116849329 \tabularnewline
38 & 5130 & 6824.23053811612 & -1694.23053811612 \tabularnewline
39 & 6960 & 5965.36254304846 & 994.637456951541 \tabularnewline
40 & 5350 & 6469.58098277807 & -1119.58098277807 \tabularnewline
41 & 6290 & 5902.02405804946 & 387.975941950541 \tabularnewline
42 & 4630 & 6098.70338350187 & -1468.70338350187 \tabularnewline
43 & 5130 & 5354.1634274815 & -224.163427481499 \tabularnewline
44 & 3620 & 5240.52671205397 & -1620.52671205397 \tabularnewline
45 & 3980 & 4419.0219068797 & -439.021906879698 \tabularnewline
46 & 3120 & 4196.46549766055 & -1076.46549766055 \tabularnewline
47 & 4310 & 3650.76540376231 & 659.234596237689 \tabularnewline
48 & 4250 & 3984.95575342953 & 265.044246570471 \tabularnewline
49 & 5730 & 4119.31646499439 & 1610.68353500561 \tabularnewline
50 & 3630 & 4935.83140040394 & -1305.83140040394 \tabularnewline
51 & 5680 & 4273.85726434073 & 1406.14273565927 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301030&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]6160[/C][C]9290[/C][C]-3130[/C][/ROW]
[ROW][C]3[/C][C]8320[/C][C]7703.28746939542[/C][C]616.712530604578[/C][/ROW]
[ROW][C]4[/C][C]8310[/C][C]8015.92181447246[/C][C]294.078185527535[/C][/ROW]
[ROW][C]5[/C][C]6750[/C][C]8165.00090135873[/C][C]-1415.00090135873[/C][/ROW]
[ROW][C]6[/C][C]8710[/C][C]7447.68471573487[/C][C]1262.31528426513[/C][/ROW]
[ROW][C]7[/C][C]6300[/C][C]8087.59892631543[/C][C]-1787.59892631543[/C][/ROW]
[ROW][C]8[/C][C]5710[/C][C]7181.39904897358[/C][C]-1471.39904897358[/C][/ROW]
[ROW][C]9[/C][C]5740[/C][C]6435.4925606266[/C][C]-695.492560626604[/C][/ROW]
[ROW][C]10[/C][C]6710[/C][C]6082.92171050248[/C][C]627.078289497516[/C][/ROW]
[ROW][C]11[/C][C]7310[/C][C]6400.81084137015[/C][C]909.18915862985[/C][/ROW]
[ROW][C]12[/C][C]7240[/C][C]6861.71238472089[/C][C]378.28761527911[/C][/ROW]
[ROW][C]13[/C][C]8650[/C][C]7053.48033978028[/C][C]1596.51966021972[/C][/ROW]
[ROW][C]14[/C][C]8330[/C][C]7862.81508426181[/C][C]467.184915738188[/C][/ROW]
[ROW][C]15[/C][C]7810[/C][C]8099.64836218872[/C][C]-289.648362188722[/C][/ROW]
[ROW][C]16[/C][C]8260[/C][C]7952.81491626095[/C][C]307.185083739054[/C][/ROW]
[ROW][C]17[/C][C]6680[/C][C]8108.53837363589[/C][C]-1428.53837363589[/C][/ROW]
[ROW][C]18[/C][C]5580[/C][C]7384.35954363667[/C][C]-1804.35954363667[/C][/ROW]
[ROW][C]19[/C][C]6340[/C][C]6469.66309072796[/C][C]-129.66309072796[/C][/ROW]
[ROW][C]20[/C][C]4490[/C][C]6403.93208407781[/C][C]-1913.93208407781[/C][/ROW]
[ROW][C]21[/C][C]5000[/C][C]5433.68926601634[/C][C]-433.689266016341[/C][/ROW]
[ROW][C]22[/C][C]7030[/C][C]5213.83616928253[/C][C]1816.16383071747[/C][/ROW]
[ROW][C]23[/C][C]6100[/C][C]6134.51665101742[/C][C]-34.5166510174249[/C][/ROW]
[ROW][C]24[/C][C]9740[/C][C]6117.01888658169[/C][C]3622.98111341831[/C][/ROW]
[ROW][C]25[/C][C]7940[/C][C]7953.64173987388[/C][C]-13.6417398738822[/C][/ROW]
[ROW][C]26[/C][C]7740[/C][C]7946.72623840515[/C][C]-206.726238405148[/C][/ROW]
[ROW][C]27[/C][C]7820[/C][C]7841.92907773991[/C][C]-21.9290777399092[/C][/ROW]
[ROW][C]28[/C][C]7820[/C][C]7830.81241881514[/C][C]-10.8124188151432[/C][/ROW]
[ROW][C]29[/C][C]5380[/C][C]7825.33120462341[/C][C]-2445.33120462341[/C][/ROW]
[ROW][C]30[/C][C]7070[/C][C]6585.70255802457[/C][C]484.297441975426[/C][/ROW]
[ROW][C]31[/C][C]6970[/C][C]6831.21080713708[/C][C]138.789192862918[/C][/ROW]
[ROW][C]32[/C][C]4080[/C][C]6901.56817181059[/C][C]-2821.56817181059[/C][/ROW]
[ROW][C]33[/C][C]4930[/C][C]5471.2111193611[/C][C]-541.211119361096[/C][/ROW]
[ROW][C]34[/C][C]4820[/C][C]5196.85122645605[/C][C]-376.851226456054[/C][/ROW]
[ROW][C]35[/C][C]6220[/C][C]5005.81142990924[/C][C]1214.18857009076[/C][/ROW]
[ROW][C]36[/C][C]6360[/C][C]5621.32843268236[/C][C]738.67156731764[/C][/ROW]
[ROW][C]37[/C][C]7630[/C][C]5995.7883150671[/C][C]1634.2116849329[/C][/ROW]
[ROW][C]38[/C][C]5130[/C][C]6824.23053811612[/C][C]-1694.23053811612[/C][/ROW]
[ROW][C]39[/C][C]6960[/C][C]5965.36254304846[/C][C]994.637456951541[/C][/ROW]
[ROW][C]40[/C][C]5350[/C][C]6469.58098277807[/C][C]-1119.58098277807[/C][/ROW]
[ROW][C]41[/C][C]6290[/C][C]5902.02405804946[/C][C]387.975941950541[/C][/ROW]
[ROW][C]42[/C][C]4630[/C][C]6098.70338350187[/C][C]-1468.70338350187[/C][/ROW]
[ROW][C]43[/C][C]5130[/C][C]5354.1634274815[/C][C]-224.163427481499[/C][/ROW]
[ROW][C]44[/C][C]3620[/C][C]5240.52671205397[/C][C]-1620.52671205397[/C][/ROW]
[ROW][C]45[/C][C]3980[/C][C]4419.0219068797[/C][C]-439.021906879698[/C][/ROW]
[ROW][C]46[/C][C]3120[/C][C]4196.46549766055[/C][C]-1076.46549766055[/C][/ROW]
[ROW][C]47[/C][C]4310[/C][C]3650.76540376231[/C][C]659.234596237689[/C][/ROW]
[ROW][C]48[/C][C]4250[/C][C]3984.95575342953[/C][C]265.044246570471[/C][/ROW]
[ROW][C]49[/C][C]5730[/C][C]4119.31646499439[/C][C]1610.68353500561[/C][/ROW]
[ROW][C]50[/C][C]3630[/C][C]4935.83140040394[/C][C]-1305.83140040394[/C][/ROW]
[ROW][C]51[/C][C]5680[/C][C]4273.85726434073[/C][C]1406.14273565927[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301030&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301030&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	6160	9290	-3130
3	8320	7703.28746939542	616.712530604578
4	8310	8015.92181447246	294.078185527535
5	6750	8165.00090135873	-1415.00090135873
6	8710	7447.68471573487	1262.31528426513
7	6300	8087.59892631543	-1787.59892631543
8	5710	7181.39904897358	-1471.39904897358
9	5740	6435.4925606266	-695.492560626604
10	6710	6082.92171050248	627.078289497516
11	7310	6400.81084137015	909.18915862985
12	7240	6861.71238472089	378.28761527911
13	8650	7053.48033978028	1596.51966021972
14	8330	7862.81508426181	467.184915738188
15	7810	8099.64836218872	-289.648362188722
16	8260	7952.81491626095	307.185083739054
17	6680	8108.53837363589	-1428.53837363589
18	5580	7384.35954363667	-1804.35954363667
19	6340	6469.66309072796	-129.66309072796
20	4490	6403.93208407781	-1913.93208407781
21	5000	5433.68926601634	-433.689266016341
22	7030	5213.83616928253	1816.16383071747
23	6100	6134.51665101742	-34.5166510174249
24	9740	6117.01888658169	3622.98111341831
25	7940	7953.64173987388	-13.6417398738822
26	7740	7946.72623840515	-206.726238405148
27	7820	7841.92907773991	-21.9290777399092
28	7820	7830.81241881514	-10.8124188151432
29	5380	7825.33120462341	-2445.33120462341
30	7070	6585.70255802457	484.297441975426
31	6970	6831.21080713708	138.789192862918
32	4080	6901.56817181059	-2821.56817181059
33	4930	5471.2111193611	-541.211119361096
34	4820	5196.85122645605	-376.851226456054
35	6220	5005.81142990924	1214.18857009076
36	6360	5621.32843268236	738.67156731764
37	7630	5995.7883150671	1634.2116849329
38	5130	6824.23053811612	-1694.23053811612
39	6960	5965.36254304846	994.637456951541
40	5350	6469.58098277807	-1119.58098277807
41	6290	5902.02405804946	387.975941950541
42	4630	6098.70338350187	-1468.70338350187
43	5130	5354.1634274815	-224.163427481499
44	3620	5240.52671205397	-1620.52671205397
45	3980	4419.0219068797	-439.021906879698
46	3120	4196.46549766055	-1076.46549766055
47	4310	3650.76540376231	659.234596237689
48	4250	3984.95575342953	265.044246570471
49	5730	4119.31646499439	1610.68353500561
50	3630	4935.83140040394	-1305.83140040394
51	5680	4273.85726434073	1406.14273565927

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
52	4986.68291881011	2393.82195750902	7579.5438801112
53	4986.68291881011	2079.68793787509	7893.67789974513
54	4986.68291881011	1796.33628032025	8177.02955729997
55	4986.68291881011	1536.17519844985	8437.19063917037
56	4986.68291881011	1294.29949034444	8679.06634727578
57	4986.68291881011	1067.32235395389	8906.04348366633
58	4986.68291881011	852.788980657817	9120.5768569624
59	4986.68291881011	648.852707006696	9324.51313061352
60	4986.68291881011	454.082914289898	9519.28292333032
61	4986.68291881011	267.344548284132	9706.02128933609
62	4986.68291881011	87.7190987701033	9885.64673885012
63	4986.68291881011	-85.5491701821857	10058.9150078024

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
52 & 4986.68291881011 & 2393.82195750902 & 7579.5438801112 \tabularnewline
53 & 4986.68291881011 & 2079.68793787509 & 7893.67789974513 \tabularnewline
54 & 4986.68291881011 & 1796.33628032025 & 8177.02955729997 \tabularnewline
55 & 4986.68291881011 & 1536.17519844985 & 8437.19063917037 \tabularnewline
56 & 4986.68291881011 & 1294.29949034444 & 8679.06634727578 \tabularnewline
57 & 4986.68291881011 & 1067.32235395389 & 8906.04348366633 \tabularnewline
58 & 4986.68291881011 & 852.788980657817 & 9120.5768569624 \tabularnewline
59 & 4986.68291881011 & 648.852707006696 & 9324.51313061352 \tabularnewline
60 & 4986.68291881011 & 454.082914289898 & 9519.28292333032 \tabularnewline
61 & 4986.68291881011 & 267.344548284132 & 9706.02128933609 \tabularnewline
62 & 4986.68291881011 & 87.7190987701033 & 9885.64673885012 \tabularnewline
63 & 4986.68291881011 & -85.5491701821857 & 10058.9150078024 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301030&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]52[/C][C]4986.68291881011[/C][C]2393.82195750902[/C][C]7579.5438801112[/C][/ROW]
[ROW][C]53[/C][C]4986.68291881011[/C][C]2079.68793787509[/C][C]7893.67789974513[/C][/ROW]
[ROW][C]54[/C][C]4986.68291881011[/C][C]1796.33628032025[/C][C]8177.02955729997[/C][/ROW]
[ROW][C]55[/C][C]4986.68291881011[/C][C]1536.17519844985[/C][C]8437.19063917037[/C][/ROW]
[ROW][C]56[/C][C]4986.68291881011[/C][C]1294.29949034444[/C][C]8679.06634727578[/C][/ROW]
[ROW][C]57[/C][C]4986.68291881011[/C][C]1067.32235395389[/C][C]8906.04348366633[/C][/ROW]
[ROW][C]58[/C][C]4986.68291881011[/C][C]852.788980657817[/C][C]9120.5768569624[/C][/ROW]
[ROW][C]59[/C][C]4986.68291881011[/C][C]648.852707006696[/C][C]9324.51313061352[/C][/ROW]
[ROW][C]60[/C][C]4986.68291881011[/C][C]454.082914289898[/C][C]9519.28292333032[/C][/ROW]
[ROW][C]61[/C][C]4986.68291881011[/C][C]267.344548284132[/C][C]9706.02128933609[/C][/ROW]
[ROW][C]62[/C][C]4986.68291881011[/C][C]87.7190987701033[/C][C]9885.64673885012[/C][/ROW]
[ROW][C]63[/C][C]4986.68291881011[/C][C]-85.5491701821857[/C][C]10058.9150078024[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301030&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301030&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
52	4986.68291881011	2393.82195750902	7579.5438801112
53	4986.68291881011	2079.68793787509	7893.67789974513
54	4986.68291881011	1796.33628032025	8177.02955729997
55	4986.68291881011	1536.17519844985	8437.19063917037
56	4986.68291881011	1294.29949034444	8679.06634727578
57	4986.68291881011	1067.32235395389	8906.04348366633
58	4986.68291881011	852.788980657817	9120.5768569624
59	4986.68291881011	648.852707006696	9324.51313061352
60	4986.68291881011	454.082914289898	9519.28292333032
61	4986.68291881011	267.344548284132	9706.02128933609
62	4986.68291881011	87.7190987701033	9885.64673885012
63	4986.68291881011	-85.5491701821857	10058.9150078024

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 ; par4 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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