Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Thu, 24 Nov 2016 15:51:01 +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/24/t14800026921j25srsyjfreydp.htm/, Retrieved Tue, 07 May 2024 06:45:12 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 07 May 2024 06:45:12 +0200

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

Dataseries X:

Download CSV

Histogram

Boxplots

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	'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.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	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.88772723733376
beta	0.0985238704021833
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.88772723733376 \tabularnewline
beta & 0.0985238704021833 \tabularnewline
gamma & 1 \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]0.88772723733376[/C][/ROW]
[ROW][C]beta[/C][C]0.0985238704021833[/C][/ROW]
[ROW][C]gamma[/C][C]1[/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	0.88772723733376
beta	0.0985238704021833
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	81	70.8202457264958	10.1797542735042
14	84	83.7169871057179	0.283012894282081
15	84	84.9778745670096	-0.977874567009621
16	80	81.2005773708562	-1.20057737085617
17	76	77.4539088770941	-1.45390887709409
18	87	88.5635221902699	-1.56352219026995
19	83	81.8974128298321	1.10258717016789
20	78	79.694516201891	-1.69451620189096
21	87	89.4020150677427	-2.40201506774272
22	85	87.1463621016082	-2.1463621016082
23	81	86.9716000874687	-5.97160008746873
24	78	76.9621134399601	1.03788656003987
25	87	90.4921574479012	-3.49215744790118
26	89	88.5246155017519	0.475384498248062
27	88	88.2153180164815	-0.215318016481476
28	84	83.5572594083402	0.442740591659842
29	82	79.8519950354653	2.14800496453473
30	91	93.072878769783	-2.07287876978297
31	93	85.1354416407327	7.86455835926732
32	90	88.094220679622	1.90577932037797
33	100	100.70618548892	-0.706185488920198
34	98	99.9208090875611	-1.92080908756111
35	95	99.4726735745444	-4.47267357454444
36	89	91.6677658289789	-2.66776582897893
37	99	101.162462334972	-2.16246233497159
38	100	100.699933688689	-0.699933688689214
39	99	99.0460909330859	-0.0460909330859351
40	94	94.4033066442324	-0.403306644232359
41	86	89.8556053514759	-3.85560535147587
42	90	96.4651082151326	-6.46510821513262
43	86	84.5521961103863	1.44780388961368
44	82	79.3923378078708	2.60766219212918
45	86	90.6422179227536	-4.64221792275359
46	84	84.1901819026899	-0.190181902689901
47	82	83.1070638046341	-1.10706380463411
48	80	76.9021029519331	3.09789704806694
49	86	90.4857069758429	-4.48570697584294
50	80	86.8356162620417	-6.83561626204168
51	79	77.98237199374	1.01762800626001
52	78	72.5108120099891	5.48918799001089
53	73	71.5888484816646	1.41115151833539
54	80	81.8238704625652	-1.82387046256518
55	79	74.5685011523865	4.43149884761348
56	74	72.0975166448405	1.90248335515946
57	82	81.7556956669781	0.244304333021859
58	81	80.4170569594542	0.582943040545842
59	76	80.2605973977128	-4.26059739771284
60	69	71.7957214083334	-2.79572140833345

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 81 & 70.8202457264958 & 10.1797542735042 \tabularnewline
14 & 84 & 83.7169871057179 & 0.283012894282081 \tabularnewline
15 & 84 & 84.9778745670096 & -0.977874567009621 \tabularnewline
16 & 80 & 81.2005773708562 & -1.20057737085617 \tabularnewline
17 & 76 & 77.4539088770941 & -1.45390887709409 \tabularnewline
18 & 87 & 88.5635221902699 & -1.56352219026995 \tabularnewline
19 & 83 & 81.8974128298321 & 1.10258717016789 \tabularnewline
20 & 78 & 79.694516201891 & -1.69451620189096 \tabularnewline
21 & 87 & 89.4020150677427 & -2.40201506774272 \tabularnewline
22 & 85 & 87.1463621016082 & -2.1463621016082 \tabularnewline
23 & 81 & 86.9716000874687 & -5.97160008746873 \tabularnewline
24 & 78 & 76.9621134399601 & 1.03788656003987 \tabularnewline
25 & 87 & 90.4921574479012 & -3.49215744790118 \tabularnewline
26 & 89 & 88.5246155017519 & 0.475384498248062 \tabularnewline
27 & 88 & 88.2153180164815 & -0.215318016481476 \tabularnewline
28 & 84 & 83.5572594083402 & 0.442740591659842 \tabularnewline
29 & 82 & 79.8519950354653 & 2.14800496453473 \tabularnewline
30 & 91 & 93.072878769783 & -2.07287876978297 \tabularnewline
31 & 93 & 85.1354416407327 & 7.86455835926732 \tabularnewline
32 & 90 & 88.094220679622 & 1.90577932037797 \tabularnewline
33 & 100 & 100.70618548892 & -0.706185488920198 \tabularnewline
34 & 98 & 99.9208090875611 & -1.92080908756111 \tabularnewline
35 & 95 & 99.4726735745444 & -4.47267357454444 \tabularnewline
36 & 89 & 91.6677658289789 & -2.66776582897893 \tabularnewline
37 & 99 & 101.162462334972 & -2.16246233497159 \tabularnewline
38 & 100 & 100.699933688689 & -0.699933688689214 \tabularnewline
39 & 99 & 99.0460909330859 & -0.0460909330859351 \tabularnewline
40 & 94 & 94.4033066442324 & -0.403306644232359 \tabularnewline
41 & 86 & 89.8556053514759 & -3.85560535147587 \tabularnewline
42 & 90 & 96.4651082151326 & -6.46510821513262 \tabularnewline
43 & 86 & 84.5521961103863 & 1.44780388961368 \tabularnewline
44 & 82 & 79.3923378078708 & 2.60766219212918 \tabularnewline
45 & 86 & 90.6422179227536 & -4.64221792275359 \tabularnewline
46 & 84 & 84.1901819026899 & -0.190181902689901 \tabularnewline
47 & 82 & 83.1070638046341 & -1.10706380463411 \tabularnewline
48 & 80 & 76.9021029519331 & 3.09789704806694 \tabularnewline
49 & 86 & 90.4857069758429 & -4.48570697584294 \tabularnewline
50 & 80 & 86.8356162620417 & -6.83561626204168 \tabularnewline
51 & 79 & 77.98237199374 & 1.01762800626001 \tabularnewline
52 & 78 & 72.5108120099891 & 5.48918799001089 \tabularnewline
53 & 73 & 71.5888484816646 & 1.41115151833539 \tabularnewline
54 & 80 & 81.8238704625652 & -1.82387046256518 \tabularnewline
55 & 79 & 74.5685011523865 & 4.43149884761348 \tabularnewline
56 & 74 & 72.0975166448405 & 1.90248335515946 \tabularnewline
57 & 82 & 81.7556956669781 & 0.244304333021859 \tabularnewline
58 & 81 & 80.4170569594542 & 0.582943040545842 \tabularnewline
59 & 76 & 80.2605973977128 & -4.26059739771284 \tabularnewline
60 & 69 & 71.7957214083334 & -2.79572140833345 \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]81[/C][C]70.8202457264958[/C][C]10.1797542735042[/C][/ROW]
[ROW][C]14[/C][C]84[/C][C]83.7169871057179[/C][C]0.283012894282081[/C][/ROW]
[ROW][C]15[/C][C]84[/C][C]84.9778745670096[/C][C]-0.977874567009621[/C][/ROW]
[ROW][C]16[/C][C]80[/C][C]81.2005773708562[/C][C]-1.20057737085617[/C][/ROW]
[ROW][C]17[/C][C]76[/C][C]77.4539088770941[/C][C]-1.45390887709409[/C][/ROW]
[ROW][C]18[/C][C]87[/C][C]88.5635221902699[/C][C]-1.56352219026995[/C][/ROW]
[ROW][C]19[/C][C]83[/C][C]81.8974128298321[/C][C]1.10258717016789[/C][/ROW]
[ROW][C]20[/C][C]78[/C][C]79.694516201891[/C][C]-1.69451620189096[/C][/ROW]
[ROW][C]21[/C][C]87[/C][C]89.4020150677427[/C][C]-2.40201506774272[/C][/ROW]
[ROW][C]22[/C][C]85[/C][C]87.1463621016082[/C][C]-2.1463621016082[/C][/ROW]
[ROW][C]23[/C][C]81[/C][C]86.9716000874687[/C][C]-5.97160008746873[/C][/ROW]
[ROW][C]24[/C][C]78[/C][C]76.9621134399601[/C][C]1.03788656003987[/C][/ROW]
[ROW][C]25[/C][C]87[/C][C]90.4921574479012[/C][C]-3.49215744790118[/C][/ROW]
[ROW][C]26[/C][C]89[/C][C]88.5246155017519[/C][C]0.475384498248062[/C][/ROW]
[ROW][C]27[/C][C]88[/C][C]88.2153180164815[/C][C]-0.215318016481476[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]83.5572594083402[/C][C]0.442740591659842[/C][/ROW]
[ROW][C]29[/C][C]82[/C][C]79.8519950354653[/C][C]2.14800496453473[/C][/ROW]
[ROW][C]30[/C][C]91[/C][C]93.072878769783[/C][C]-2.07287876978297[/C][/ROW]
[ROW][C]31[/C][C]93[/C][C]85.1354416407327[/C][C]7.86455835926732[/C][/ROW]
[ROW][C]32[/C][C]90[/C][C]88.094220679622[/C][C]1.90577932037797[/C][/ROW]
[ROW][C]33[/C][C]100[/C][C]100.70618548892[/C][C]-0.706185488920198[/C][/ROW]
[ROW][C]34[/C][C]98[/C][C]99.9208090875611[/C][C]-1.92080908756111[/C][/ROW]
[ROW][C]35[/C][C]95[/C][C]99.4726735745444[/C][C]-4.47267357454444[/C][/ROW]
[ROW][C]36[/C][C]89[/C][C]91.6677658289789[/C][C]-2.66776582897893[/C][/ROW]
[ROW][C]37[/C][C]99[/C][C]101.162462334972[/C][C]-2.16246233497159[/C][/ROW]
[ROW][C]38[/C][C]100[/C][C]100.699933688689[/C][C]-0.699933688689214[/C][/ROW]
[ROW][C]39[/C][C]99[/C][C]99.0460909330859[/C][C]-0.0460909330859351[/C][/ROW]
[ROW][C]40[/C][C]94[/C][C]94.4033066442324[/C][C]-0.403306644232359[/C][/ROW]
[ROW][C]41[/C][C]86[/C][C]89.8556053514759[/C][C]-3.85560535147587[/C][/ROW]
[ROW][C]42[/C][C]90[/C][C]96.4651082151326[/C][C]-6.46510821513262[/C][/ROW]
[ROW][C]43[/C][C]86[/C][C]84.5521961103863[/C][C]1.44780388961368[/C][/ROW]
[ROW][C]44[/C][C]82[/C][C]79.3923378078708[/C][C]2.60766219212918[/C][/ROW]
[ROW][C]45[/C][C]86[/C][C]90.6422179227536[/C][C]-4.64221792275359[/C][/ROW]
[ROW][C]46[/C][C]84[/C][C]84.1901819026899[/C][C]-0.190181902689901[/C][/ROW]
[ROW][C]47[/C][C]82[/C][C]83.1070638046341[/C][C]-1.10706380463411[/C][/ROW]
[ROW][C]48[/C][C]80[/C][C]76.9021029519331[/C][C]3.09789704806694[/C][/ROW]
[ROW][C]49[/C][C]86[/C][C]90.4857069758429[/C][C]-4.48570697584294[/C][/ROW]
[ROW][C]50[/C][C]80[/C][C]86.8356162620417[/C][C]-6.83561626204168[/C][/ROW]
[ROW][C]51[/C][C]79[/C][C]77.98237199374[/C][C]1.01762800626001[/C][/ROW]
[ROW][C]52[/C][C]78[/C][C]72.5108120099891[/C][C]5.48918799001089[/C][/ROW]
[ROW][C]53[/C][C]73[/C][C]71.5888484816646[/C][C]1.41115151833539[/C][/ROW]
[ROW][C]54[/C][C]80[/C][C]81.8238704625652[/C][C]-1.82387046256518[/C][/ROW]
[ROW][C]55[/C][C]79[/C][C]74.5685011523865[/C][C]4.43149884761348[/C][/ROW]
[ROW][C]56[/C][C]74[/C][C]72.0975166448405[/C][C]1.90248335515946[/C][/ROW]
[ROW][C]57[/C][C]82[/C][C]81.7556956669781[/C][C]0.244304333021859[/C][/ROW]
[ROW][C]58[/C][C]81[/C][C]80.4170569594542[/C][C]0.582943040545842[/C][/ROW]
[ROW][C]59[/C][C]76[/C][C]80.2605973977128[/C][C]-4.26059739771284[/C][/ROW]
[ROW][C]60[/C][C]69[/C][C]71.7957214083334[/C][C]-2.79572140833345[/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	81	70.8202457264958	10.1797542735042
14	84	83.7169871057179	0.283012894282081
15	84	84.9778745670096	-0.977874567009621
16	80	81.2005773708562	-1.20057737085617
17	76	77.4539088770941	-1.45390887709409
18	87	88.5635221902699	-1.56352219026995
19	83	81.8974128298321	1.10258717016789
20	78	79.694516201891	-1.69451620189096
21	87	89.4020150677427	-2.40201506774272
22	85	87.1463621016082	-2.1463621016082
23	81	86.9716000874687	-5.97160008746873
24	78	76.9621134399601	1.03788656003987
25	87	90.4921574479012	-3.49215744790118
26	89	88.5246155017519	0.475384498248062
27	88	88.2153180164815	-0.215318016481476
28	84	83.5572594083402	0.442740591659842
29	82	79.8519950354653	2.14800496453473
30	91	93.072878769783	-2.07287876978297
31	93	85.1354416407327	7.86455835926732
32	90	88.094220679622	1.90577932037797
33	100	100.70618548892	-0.706185488920198
34	98	99.9208090875611	-1.92080908756111
35	95	99.4726735745444	-4.47267357454444
36	89	91.6677658289789	-2.66776582897893
37	99	101.162462334972	-2.16246233497159
38	100	100.699933688689	-0.699933688689214
39	99	99.0460909330859	-0.0460909330859351
40	94	94.4033066442324	-0.403306644232359
41	86	89.8556053514759	-3.85560535147587
42	90	96.4651082151326	-6.46510821513262
43	86	84.5521961103863	1.44780388961368
44	82	79.3923378078708	2.60766219212918
45	86	90.6422179227536	-4.64221792275359
46	84	84.1901819026899	-0.190181902689901
47	82	83.1070638046341	-1.10706380463411
48	80	76.9021029519331	3.09789704806694
49	86	90.4857069758429	-4.48570697584294
50	80	86.8356162620417	-6.83561626204168
51	79	77.98237199374	1.01762800626001
52	78	72.5108120099891	5.48918799001089
53	73	71.5888484816646	1.41115151833539
54	80	81.8238704625652	-1.82387046256518
55	79	74.5685011523865	4.43149884761348
56	74	72.0975166448405	1.90248335515946
57	82	81.7556956669781	0.244304333021859
58	81	80.4170569594542	0.582943040545842
59	76	80.2605973977128	-4.26059739771284
60	69	71.7957214083334	-2.79572140833345

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	78.8479580204774	72.3073434976876	85.3885725432673
62	78.8604415070948	69.724641226418	87.9962417877716
63	77.4992450346586	66.0200962807561	88.9783937885611
64	72.079518861609	58.3551549208679	85.8038828023502
65	65.7998796047598	49.8662901044537	81.7334691050658
66	74.2686348834306	56.1305897385418	92.4066800283194
67	69.3438483938984	48.9884833339451	89.6992134538516
68	62.2765486558159	39.6803014296314	84.8727958820004
69	69.5148639858099	44.6473814668366	94.3823465047833
70	67.4311930869651	40.2576898107493	94.6046963631808
71	65.5962794076218	36.0790358316235	95.1135229836201
72	60.8335971601701	28.9329490460155	92.7342452743247

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 78.8479580204774 & 72.3073434976876 & 85.3885725432673 \tabularnewline
62 & 78.8604415070948 & 69.724641226418 & 87.9962417877716 \tabularnewline
63 & 77.4992450346586 & 66.0200962807561 & 88.9783937885611 \tabularnewline
64 & 72.079518861609 & 58.3551549208679 & 85.8038828023502 \tabularnewline
65 & 65.7998796047598 & 49.8662901044537 & 81.7334691050658 \tabularnewline
66 & 74.2686348834306 & 56.1305897385418 & 92.4066800283194 \tabularnewline
67 & 69.3438483938984 & 48.9884833339451 & 89.6992134538516 \tabularnewline
68 & 62.2765486558159 & 39.6803014296314 & 84.8727958820004 \tabularnewline
69 & 69.5148639858099 & 44.6473814668366 & 94.3823465047833 \tabularnewline
70 & 67.4311930869651 & 40.2576898107493 & 94.6046963631808 \tabularnewline
71 & 65.5962794076218 & 36.0790358316235 & 95.1135229836201 \tabularnewline
72 & 60.8335971601701 & 28.9329490460155 & 92.7342452743247 \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]78.8479580204774[/C][C]72.3073434976876[/C][C]85.3885725432673[/C][/ROW]
[ROW][C]62[/C][C]78.8604415070948[/C][C]69.724641226418[/C][C]87.9962417877716[/C][/ROW]
[ROW][C]63[/C][C]77.4992450346586[/C][C]66.0200962807561[/C][C]88.9783937885611[/C][/ROW]
[ROW][C]64[/C][C]72.079518861609[/C][C]58.3551549208679[/C][C]85.8038828023502[/C][/ROW]
[ROW][C]65[/C][C]65.7998796047598[/C][C]49.8662901044537[/C][C]81.7334691050658[/C][/ROW]
[ROW][C]66[/C][C]74.2686348834306[/C][C]56.1305897385418[/C][C]92.4066800283194[/C][/ROW]
[ROW][C]67[/C][C]69.3438483938984[/C][C]48.9884833339451[/C][C]89.6992134538516[/C][/ROW]
[ROW][C]68[/C][C]62.2765486558159[/C][C]39.6803014296314[/C][C]84.8727958820004[/C][/ROW]
[ROW][C]69[/C][C]69.5148639858099[/C][C]44.6473814668366[/C][C]94.3823465047833[/C][/ROW]
[ROW][C]70[/C][C]67.4311930869651[/C][C]40.2576898107493[/C][C]94.6046963631808[/C][/ROW]
[ROW][C]71[/C][C]65.5962794076218[/C][C]36.0790358316235[/C][C]95.1135229836201[/C][/ROW]
[ROW][C]72[/C][C]60.8335971601701[/C][C]28.9329490460155[/C][C]92.7342452743247[/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	78.8479580204774	72.3073434976876	85.3885725432673
62	78.8604415070948	69.724641226418	87.9962417877716
63	77.4992450346586	66.0200962807561	88.9783937885611
64	72.079518861609	58.3551549208679	85.8038828023502
65	65.7998796047598	49.8662901044537	81.7334691050658
66	74.2686348834306	56.1305897385418	92.4066800283194
67	69.3438483938984	48.9884833339451	89.6992134538516
68	62.2765486558159	39.6803014296314	84.8727958820004
69	69.5148639858099	44.6473814668366	94.3823465047833
70	67.4311930869651	40.2576898107493	94.6046963631808
71	65.5962794076218	36.0790358316235	95.1135229836201
72	60.8335971601701	28.9329490460155	92.7342452743247

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