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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 26 Nov 2016 00:06:44 +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/2016/Nov/26/t14801188220cnx2tlgooutb8d.htm/, Retrieved Sat, 04 May 2024 00:36:30 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 00:36:30 +0200

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Estimated Impact

Dataseries X:

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-5
-3
-7
-10
-10
-11
-11
-19
-30
-38
-36
-40
-34
-35
-38
-32
-37
-39
-31
-30
-29
-36
-41
-42
-33
-43
-41
-34
-32
-36
-37
-30
-32
-30
-21
-19
-9
-8
-6
-4
-1
-2
-1
-4
-8
-6
-11
-11
-3
-6
2
2
4
8
6
8
5
3
5
3

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	'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.766478963787488
beta	0.0670128473525945
gamma	0.992047281987758

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.766478963787488 \tabularnewline
beta & 0.0670128473525945 \tabularnewline
gamma & 0.992047281987758 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.766478963787488[/C][/ROW]
[ROW][C]beta[/C][C]0.0670128473525945[/C][/ROW]
[ROW][C]gamma[/C][C]0.992047281987758[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.766478963787488
beta	0.0670128473525945
gamma	0.992047281987758

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	-34	-20.4935897435898	-13.5064102564102
14	-35	-32.7113315443334	-2.28866845566655
15	-38	-39.3234652578075	1.32346525780751
16	-32	-34.6406627450013	2.64066274500127
17	-37	-39.5626212301242	2.5626212301242
18	-39	-41.2461039105687	2.24610391056867
19	-31	-29.0568217165737	-1.94317828342628
20	-30	-37.9283454861282	7.92834548612819
21	-29	-41.7429895680571	12.7429895680571
22	-36	-38.6294467861798	2.62944678617983
23	-41	-33.2993297214711	-7.70067027852885
24	-42	-42.0325668295228	0.0325668295228283
25	-33	-38.2573820784236	5.25738207842364
26	-43	-32.1880861178979	-10.8119138821021
27	-41	-43.6278548479301	2.62785484793013
28	-34	-36.704667159622	2.70466715962198
29	-32	-40.6569086160616	8.65690861606157
30	-36	-36.4908088635765	0.490808863576547
31	-37	-25.455822762085	-11.544177237915
32	-30	-38.730973461569	8.73097346156902
33	-32	-40.1053536682378	8.1053536682378
34	-30	-42.4179241978911	12.4179241978911
35	-21	-31.0040057622917	10.0040057622917
36	-19	-22.491832656122	3.49183265612195
37	-9	-12.793474249745	3.79347424974502
38	-8	-9.58278279346753	1.58278279346753
39	-6	-5.78600149383874	-0.213998506161261
40	-4	1.45355764362049	-5.45355764362049
41	-1	-5.31511291020716	4.31511291020716
42	-2	-4.53395147649685	2.53395147649685
43	-1	7.21867972662685	-8.21867972662685
44	-4	3.2999754298959	-7.2999754298959
45	-8	-9.21963421607926	1.21963421607926
46	-6	-14.8774853915441	8.87748539154407
47	-11	-5.98489596670296	-5.01510403329704
48	-11	-10.5130700362578	-0.486929963742188
49	-3	-4.01871490788864	1.01871490788864
50	-6	-3.81372300664488	-2.18627699335512
51	2	-3.88245734428076	5.88245734428076
52	2	6.56886696526081	-4.56886696526081
53	4	2.5395595732683	1.4604404267317
54	8	0.371634517879166	7.62836548212083
55	6	13.4512902126296	-7.45129021262961
56	8	10.2862805143649	-2.28628051436489
57	5	3.79344779186783	1.20655220813217
58	3	0.109144492822566	2.89085550717743
59	5	1.09672680684589	3.90327319315411
60	3	4.81342908784275	-1.81342908784275

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & -34 & -20.4935897435898 & -13.5064102564102 \tabularnewline
14 & -35 & -32.7113315443334 & -2.28866845566655 \tabularnewline
15 & -38 & -39.3234652578075 & 1.32346525780751 \tabularnewline
16 & -32 & -34.6406627450013 & 2.64066274500127 \tabularnewline
17 & -37 & -39.5626212301242 & 2.5626212301242 \tabularnewline
18 & -39 & -41.2461039105687 & 2.24610391056867 \tabularnewline
19 & -31 & -29.0568217165737 & -1.94317828342628 \tabularnewline
20 & -30 & -37.9283454861282 & 7.92834548612819 \tabularnewline
21 & -29 & -41.7429895680571 & 12.7429895680571 \tabularnewline
22 & -36 & -38.6294467861798 & 2.62944678617983 \tabularnewline
23 & -41 & -33.2993297214711 & -7.70067027852885 \tabularnewline
24 & -42 & -42.0325668295228 & 0.0325668295228283 \tabularnewline
25 & -33 & -38.2573820784236 & 5.25738207842364 \tabularnewline
26 & -43 & -32.1880861178979 & -10.8119138821021 \tabularnewline
27 & -41 & -43.6278548479301 & 2.62785484793013 \tabularnewline
28 & -34 & -36.704667159622 & 2.70466715962198 \tabularnewline
29 & -32 & -40.6569086160616 & 8.65690861606157 \tabularnewline
30 & -36 & -36.4908088635765 & 0.490808863576547 \tabularnewline
31 & -37 & -25.455822762085 & -11.544177237915 \tabularnewline
32 & -30 & -38.730973461569 & 8.73097346156902 \tabularnewline
33 & -32 & -40.1053536682378 & 8.1053536682378 \tabularnewline
34 & -30 & -42.4179241978911 & 12.4179241978911 \tabularnewline
35 & -21 & -31.0040057622917 & 10.0040057622917 \tabularnewline
36 & -19 & -22.491832656122 & 3.49183265612195 \tabularnewline
37 & -9 & -12.793474249745 & 3.79347424974502 \tabularnewline
38 & -8 & -9.58278279346753 & 1.58278279346753 \tabularnewline
39 & -6 & -5.78600149383874 & -0.213998506161261 \tabularnewline
40 & -4 & 1.45355764362049 & -5.45355764362049 \tabularnewline
41 & -1 & -5.31511291020716 & 4.31511291020716 \tabularnewline
42 & -2 & -4.53395147649685 & 2.53395147649685 \tabularnewline
43 & -1 & 7.21867972662685 & -8.21867972662685 \tabularnewline
44 & -4 & 3.2999754298959 & -7.2999754298959 \tabularnewline
45 & -8 & -9.21963421607926 & 1.21963421607926 \tabularnewline
46 & -6 & -14.8774853915441 & 8.87748539154407 \tabularnewline
47 & -11 & -5.98489596670296 & -5.01510403329704 \tabularnewline
48 & -11 & -10.5130700362578 & -0.486929963742188 \tabularnewline
49 & -3 & -4.01871490788864 & 1.01871490788864 \tabularnewline
50 & -6 & -3.81372300664488 & -2.18627699335512 \tabularnewline
51 & 2 & -3.88245734428076 & 5.88245734428076 \tabularnewline
52 & 2 & 6.56886696526081 & -4.56886696526081 \tabularnewline
53 & 4 & 2.5395595732683 & 1.4604404267317 \tabularnewline
54 & 8 & 0.371634517879166 & 7.62836548212083 \tabularnewline
55 & 6 & 13.4512902126296 & -7.45129021262961 \tabularnewline
56 & 8 & 10.2862805143649 & -2.28628051436489 \tabularnewline
57 & 5 & 3.79344779186783 & 1.20655220813217 \tabularnewline
58 & 3 & 0.109144492822566 & 2.89085550717743 \tabularnewline
59 & 5 & 1.09672680684589 & 3.90327319315411 \tabularnewline
60 & 3 & 4.81342908784275 & -1.81342908784275 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]-34[/C][C]-20.4935897435898[/C][C]-13.5064102564102[/C][/ROW]
[ROW][C]14[/C][C]-35[/C][C]-32.7113315443334[/C][C]-2.28866845566655[/C][/ROW]
[ROW][C]15[/C][C]-38[/C][C]-39.3234652578075[/C][C]1.32346525780751[/C][/ROW]
[ROW][C]16[/C][C]-32[/C][C]-34.6406627450013[/C][C]2.64066274500127[/C][/ROW]
[ROW][C]17[/C][C]-37[/C][C]-39.5626212301242[/C][C]2.5626212301242[/C][/ROW]
[ROW][C]18[/C][C]-39[/C][C]-41.2461039105687[/C][C]2.24610391056867[/C][/ROW]
[ROW][C]19[/C][C]-31[/C][C]-29.0568217165737[/C][C]-1.94317828342628[/C][/ROW]
[ROW][C]20[/C][C]-30[/C][C]-37.9283454861282[/C][C]7.92834548612819[/C][/ROW]
[ROW][C]21[/C][C]-29[/C][C]-41.7429895680571[/C][C]12.7429895680571[/C][/ROW]
[ROW][C]22[/C][C]-36[/C][C]-38.6294467861798[/C][C]2.62944678617983[/C][/ROW]
[ROW][C]23[/C][C]-41[/C][C]-33.2993297214711[/C][C]-7.70067027852885[/C][/ROW]
[ROW][C]24[/C][C]-42[/C][C]-42.0325668295228[/C][C]0.0325668295228283[/C][/ROW]
[ROW][C]25[/C][C]-33[/C][C]-38.2573820784236[/C][C]5.25738207842364[/C][/ROW]
[ROW][C]26[/C][C]-43[/C][C]-32.1880861178979[/C][C]-10.8119138821021[/C][/ROW]
[ROW][C]27[/C][C]-41[/C][C]-43.6278548479301[/C][C]2.62785484793013[/C][/ROW]
[ROW][C]28[/C][C]-34[/C][C]-36.704667159622[/C][C]2.70466715962198[/C][/ROW]
[ROW][C]29[/C][C]-32[/C][C]-40.6569086160616[/C][C]8.65690861606157[/C][/ROW]
[ROW][C]30[/C][C]-36[/C][C]-36.4908088635765[/C][C]0.490808863576547[/C][/ROW]
[ROW][C]31[/C][C]-37[/C][C]-25.455822762085[/C][C]-11.544177237915[/C][/ROW]
[ROW][C]32[/C][C]-30[/C][C]-38.730973461569[/C][C]8.73097346156902[/C][/ROW]
[ROW][C]33[/C][C]-32[/C][C]-40.1053536682378[/C][C]8.1053536682378[/C][/ROW]
[ROW][C]34[/C][C]-30[/C][C]-42.4179241978911[/C][C]12.4179241978911[/C][/ROW]
[ROW][C]35[/C][C]-21[/C][C]-31.0040057622917[/C][C]10.0040057622917[/C][/ROW]
[ROW][C]36[/C][C]-19[/C][C]-22.491832656122[/C][C]3.49183265612195[/C][/ROW]
[ROW][C]37[/C][C]-9[/C][C]-12.793474249745[/C][C]3.79347424974502[/C][/ROW]
[ROW][C]38[/C][C]-8[/C][C]-9.58278279346753[/C][C]1.58278279346753[/C][/ROW]
[ROW][C]39[/C][C]-6[/C][C]-5.78600149383874[/C][C]-0.213998506161261[/C][/ROW]
[ROW][C]40[/C][C]-4[/C][C]1.45355764362049[/C][C]-5.45355764362049[/C][/ROW]
[ROW][C]41[/C][C]-1[/C][C]-5.31511291020716[/C][C]4.31511291020716[/C][/ROW]
[ROW][C]42[/C][C]-2[/C][C]-4.53395147649685[/C][C]2.53395147649685[/C][/ROW]
[ROW][C]43[/C][C]-1[/C][C]7.21867972662685[/C][C]-8.21867972662685[/C][/ROW]
[ROW][C]44[/C][C]-4[/C][C]3.2999754298959[/C][C]-7.2999754298959[/C][/ROW]
[ROW][C]45[/C][C]-8[/C][C]-9.21963421607926[/C][C]1.21963421607926[/C][/ROW]
[ROW][C]46[/C][C]-6[/C][C]-14.8774853915441[/C][C]8.87748539154407[/C][/ROW]
[ROW][C]47[/C][C]-11[/C][C]-5.98489596670296[/C][C]-5.01510403329704[/C][/ROW]
[ROW][C]48[/C][C]-11[/C][C]-10.5130700362578[/C][C]-0.486929963742188[/C][/ROW]
[ROW][C]49[/C][C]-3[/C][C]-4.01871490788864[/C][C]1.01871490788864[/C][/ROW]
[ROW][C]50[/C][C]-6[/C][C]-3.81372300664488[/C][C]-2.18627699335512[/C][/ROW]
[ROW][C]51[/C][C]2[/C][C]-3.88245734428076[/C][C]5.88245734428076[/C][/ROW]
[ROW][C]52[/C][C]2[/C][C]6.56886696526081[/C][C]-4.56886696526081[/C][/ROW]
[ROW][C]53[/C][C]4[/C][C]2.5395595732683[/C][C]1.4604404267317[/C][/ROW]
[ROW][C]54[/C][C]8[/C][C]0.371634517879166[/C][C]7.62836548212083[/C][/ROW]
[ROW][C]55[/C][C]6[/C][C]13.4512902126296[/C][C]-7.45129021262961[/C][/ROW]
[ROW][C]56[/C][C]8[/C][C]10.2862805143649[/C][C]-2.28628051436489[/C][/ROW]
[ROW][C]57[/C][C]5[/C][C]3.79344779186783[/C][C]1.20655220813217[/C][/ROW]
[ROW][C]58[/C][C]3[/C][C]0.109144492822566[/C][C]2.89085550717743[/C][/ROW]
[ROW][C]59[/C][C]5[/C][C]1.09672680684589[/C][C]3.90327319315411[/C][/ROW]
[ROW][C]60[/C][C]3[/C][C]4.81342908784275[/C][C]-1.81342908784275[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
13	-34	-20.4935897435898	-13.5064102564102
14	-35	-32.7113315443334	-2.28866845566655
15	-38	-39.3234652578075	1.32346525780751
16	-32	-34.6406627450013	2.64066274500127
17	-37	-39.5626212301242	2.5626212301242
18	-39	-41.2461039105687	2.24610391056867
19	-31	-29.0568217165737	-1.94317828342628
20	-30	-37.9283454861282	7.92834548612819
21	-29	-41.7429895680571	12.7429895680571
22	-36	-38.6294467861798	2.62944678617983
23	-41	-33.2993297214711	-7.70067027852885
24	-42	-42.0325668295228	0.0325668295228283
25	-33	-38.2573820784236	5.25738207842364
26	-43	-32.1880861178979	-10.8119138821021
27	-41	-43.6278548479301	2.62785484793013
28	-34	-36.704667159622	2.70466715962198
29	-32	-40.6569086160616	8.65690861606157
30	-36	-36.4908088635765	0.490808863576547
31	-37	-25.455822762085	-11.544177237915
32	-30	-38.730973461569	8.73097346156902
33	-32	-40.1053536682378	8.1053536682378
34	-30	-42.4179241978911	12.4179241978911
35	-21	-31.0040057622917	10.0040057622917
36	-19	-22.491832656122	3.49183265612195
37	-9	-12.793474249745	3.79347424974502
38	-8	-9.58278279346753	1.58278279346753
39	-6	-5.78600149383874	-0.213998506161261
40	-4	1.45355764362049	-5.45355764362049
41	-1	-5.31511291020716	4.31511291020716
42	-2	-4.53395147649685	2.53395147649685
43	-1	7.21867972662685	-8.21867972662685
44	-4	3.2999754298959	-7.2999754298959
45	-8	-9.21963421607926	1.21963421607926
46	-6	-14.8774853915441	8.87748539154407
47	-11	-5.98489596670296	-5.01510403329704
48	-11	-10.5130700362578	-0.486929963742188
49	-3	-4.01871490788864	1.01871490788864
50	-6	-3.81372300664488	-2.18627699335512
51	2	-3.88245734428076	5.88245734428076
52	2	6.56886696526081	-4.56886696526081
53	4	2.5395595732683	1.4604404267317
54	8	0.371634517879166	7.62836548212083
55	6	13.4512902126296	-7.45129021262961
56	8	10.2862805143649	-2.28628051436489
57	5	3.79344779186783	1.20655220813217
58	3	0.109144492822566	2.89085550717743
59	5	1.09672680684589	3.90327319315411
60	3	4.81342908784275	-1.81342908784275

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	10.9318332091124	-0.992087643406805	22.8557540616315
62	9.85317449128932	-5.55069923049341	25.2570482130721
63	13.6813596939417	-4.88471555898926	32.2474349468727
64	17.2525130504864	-4.31574083871496	38.8207669396877
65	18.406397498176	-6.0783082501191	42.8911032464711
66	16.7574257388553	-10.5991654760867	44.1140169537974
67	20.3143294154384	-9.89471875130952	50.5233775821863
68	24.2574925038351	-8.80096410938656	57.3159491170568
69	20.6440106014692	-15.27197725593	56.5599984588684
70	16.680931047911	-22.1085867998782	55.4704488957003
71	15.794616689908	-25.890120328225	57.4793537080409
72	15.1020437210649	-29.5037878858336	59.7078753279634

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 10.9318332091124 & -0.992087643406805 & 22.8557540616315 \tabularnewline
62 & 9.85317449128932 & -5.55069923049341 & 25.2570482130721 \tabularnewline
63 & 13.6813596939417 & -4.88471555898926 & 32.2474349468727 \tabularnewline
64 & 17.2525130504864 & -4.31574083871496 & 38.8207669396877 \tabularnewline
65 & 18.406397498176 & -6.0783082501191 & 42.8911032464711 \tabularnewline
66 & 16.7574257388553 & -10.5991654760867 & 44.1140169537974 \tabularnewline
67 & 20.3143294154384 & -9.89471875130952 & 50.5233775821863 \tabularnewline
68 & 24.2574925038351 & -8.80096410938656 & 57.3159491170568 \tabularnewline
69 & 20.6440106014692 & -15.27197725593 & 56.5599984588684 \tabularnewline
70 & 16.680931047911 & -22.1085867998782 & 55.4704488957003 \tabularnewline
71 & 15.794616689908 & -25.890120328225 & 57.4793537080409 \tabularnewline
72 & 15.1020437210649 & -29.5037878858336 & 59.7078753279634 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]61[/C][C]10.9318332091124[/C][C]-0.992087643406805[/C][C]22.8557540616315[/C][/ROW]
[ROW][C]62[/C][C]9.85317449128932[/C][C]-5.55069923049341[/C][C]25.2570482130721[/C][/ROW]
[ROW][C]63[/C][C]13.6813596939417[/C][C]-4.88471555898926[/C][C]32.2474349468727[/C][/ROW]
[ROW][C]64[/C][C]17.2525130504864[/C][C]-4.31574083871496[/C][C]38.8207669396877[/C][/ROW]
[ROW][C]65[/C][C]18.406397498176[/C][C]-6.0783082501191[/C][C]42.8911032464711[/C][/ROW]
[ROW][C]66[/C][C]16.7574257388553[/C][C]-10.5991654760867[/C][C]44.1140169537974[/C][/ROW]
[ROW][C]67[/C][C]20.3143294154384[/C][C]-9.89471875130952[/C][C]50.5233775821863[/C][/ROW]
[ROW][C]68[/C][C]24.2574925038351[/C][C]-8.80096410938656[/C][C]57.3159491170568[/C][/ROW]
[ROW][C]69[/C][C]20.6440106014692[/C][C]-15.27197725593[/C][C]56.5599984588684[/C][/ROW]
[ROW][C]70[/C][C]16.680931047911[/C][C]-22.1085867998782[/C][C]55.4704488957003[/C][/ROW]
[ROW][C]71[/C][C]15.794616689908[/C][C]-25.890120328225[/C][C]57.4793537080409[/C][/ROW]
[ROW][C]72[/C][C]15.1020437210649[/C][C]-29.5037878858336[/C][C]59.7078753279634[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
61	10.9318332091124	-0.992087643406805	22.8557540616315
62	9.85317449128932	-5.55069923049341	25.2570482130721
63	13.6813596939417	-4.88471555898926	32.2474349468727
64	17.2525130504864	-4.31574083871496	38.8207669396877
65	18.406397498176	-6.0783082501191	42.8911032464711
66	16.7574257388553	-10.5991654760867	44.1140169537974
67	20.3143294154384	-9.89471875130952	50.5233775821863
68	24.2574925038351	-8.80096410938656	57.3159491170568
69	20.6440106014692	-15.27197725593	56.5599984588684
70	16.680931047911	-22.1085867998782	55.4704488957003
71	15.794616689908	-25.890120328225	57.4793537080409
72	15.1020437210649	-29.5037878858336	59.7078753279634

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 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code