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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 20 Dec 2010 15:53:16 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/20/t1292860288zq5cymrrzsh7ue8.htm/, Retrieved Fri, 03 May 2024 16:04:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113001, Retrieved Fri, 03 May 2024 16:04:22 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

140

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMPD  [Exponential Smoothing] [smoothing] [2010-12-07 13:27:21] [8b7e5d4d87654725a776c7f35eb4752f]
- R  D      [Exponential Smoothing] [] [2010-12-20 15:53:16] [a3cd012a7211edfe9ed4466e21aef6a6] [Current]
-    D        [Exponential Smoothing] [] [2010-12-22 13:04:52] [126c9e58bb659a0bfb4675d843c2c69e] 

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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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113001&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113001&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113001&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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0
gamma	0.194972412796345

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.194972412796345 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113001&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]0.194972412796345[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113001&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113001&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	0.194972412796345

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	41.33	41.6101522435898	-0.280152243589754
14	41.29	41.2866768648019	0.0033231351981442
15	41.29	41.2916768648019	-0.00167686480186546
16	41.27	41.2758435314685	-0.00584353146854255
17	41.04	41.0658435314685	-0.0258435314685244
18	40.9	40.9475101981352	-0.0475101981352068
19	40.89	40.7629268648019	0.127073135198138
20	40.72	40.8283435314685	-0.108343531468527
21	40.72	40.7058435314685	0.0141564685314677
22	40.58	40.6666768648019	-0.0866768648018663
23	40.24	40.6100101981352	-0.370010198135191
24	40.07	40.2095935314685	-0.139593531468542
25	40.12	40.0591768648019	0.0608231351981345
26	40.1	40.0766768648019	0.0233231351981473
27	40.1	40.1016768648019	-0.00167686480186546
28	40.08	40.0858435314685	-0.00584353146854966
29	40.06	39.8758435314685	0.184156468531484
30	39.99	39.9675101981352	0.0224898018647934
31	40.05	39.8529268648019	0.197073135198131
32	39.66	39.9883435314685	-0.328343531468526
33	39.66	39.6458435314685	0.0141564685314677
34	39.67	39.6066768648019	0.0633231351981394
35	39.56	39.7000101981352	-0.140010198135194
36	39.64	39.5295935314685	0.110406468531458
37	39.73	39.6291768648019	0.100823135198134
38	39.7	39.6866768648019	0.0133231351981493
39	39.7	39.7016768648019	-0.00167686480186546
40	39.68	39.6858435314685	-0.00584353146854966
41	39.76	39.4758435314685	0.284156468531478
42	40	39.6675101981352	0.332489801864796
43	39.96	39.8629268648019	0.097073135198137
44	40.01	39.8983435314685	0.111656468531471
45	40.01	39.9958435314685	0.0141564685314677
46	40.01	39.9566768648019	0.0533231351981343
47	40	40.0400101981352	-0.0400101981351924
48	39.91	39.9695935314685	-0.0595935314685434
49	39.86	39.8991768648019	-0.0391768648018598
50	39.79	39.8166768648019	-0.0266768648018569
51	39.79	39.7916768648019	-0.00167686480186546
52	39.8	39.7758435314685	0.0241564685314515
53	39.64	39.5958435314685	0.044156468531483
54	39.55	39.5475101981352	0.00248980186479031
55	39.36	39.4129268648019	-0.0529268648018615
56	39.28	39.2983435314685	-0.0183435314685241

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 41.33 & 41.6101522435898 & -0.280152243589754 \tabularnewline
14 & 41.29 & 41.2866768648019 & 0.0033231351981442 \tabularnewline
15 & 41.29 & 41.2916768648019 & -0.00167686480186546 \tabularnewline
16 & 41.27 & 41.2758435314685 & -0.00584353146854255 \tabularnewline
17 & 41.04 & 41.0658435314685 & -0.0258435314685244 \tabularnewline
18 & 40.9 & 40.9475101981352 & -0.0475101981352068 \tabularnewline
19 & 40.89 & 40.7629268648019 & 0.127073135198138 \tabularnewline
20 & 40.72 & 40.8283435314685 & -0.108343531468527 \tabularnewline
21 & 40.72 & 40.7058435314685 & 0.0141564685314677 \tabularnewline
22 & 40.58 & 40.6666768648019 & -0.0866768648018663 \tabularnewline
23 & 40.24 & 40.6100101981352 & -0.370010198135191 \tabularnewline
24 & 40.07 & 40.2095935314685 & -0.139593531468542 \tabularnewline
25 & 40.12 & 40.0591768648019 & 0.0608231351981345 \tabularnewline
26 & 40.1 & 40.0766768648019 & 0.0233231351981473 \tabularnewline
27 & 40.1 & 40.1016768648019 & -0.00167686480186546 \tabularnewline
28 & 40.08 & 40.0858435314685 & -0.00584353146854966 \tabularnewline
29 & 40.06 & 39.8758435314685 & 0.184156468531484 \tabularnewline
30 & 39.99 & 39.9675101981352 & 0.0224898018647934 \tabularnewline
31 & 40.05 & 39.8529268648019 & 0.197073135198131 \tabularnewline
32 & 39.66 & 39.9883435314685 & -0.328343531468526 \tabularnewline
33 & 39.66 & 39.6458435314685 & 0.0141564685314677 \tabularnewline
34 & 39.67 & 39.6066768648019 & 0.0633231351981394 \tabularnewline
35 & 39.56 & 39.7000101981352 & -0.140010198135194 \tabularnewline
36 & 39.64 & 39.5295935314685 & 0.110406468531458 \tabularnewline
37 & 39.73 & 39.6291768648019 & 0.100823135198134 \tabularnewline
38 & 39.7 & 39.6866768648019 & 0.0133231351981493 \tabularnewline
39 & 39.7 & 39.7016768648019 & -0.00167686480186546 \tabularnewline
40 & 39.68 & 39.6858435314685 & -0.00584353146854966 \tabularnewline
41 & 39.76 & 39.4758435314685 & 0.284156468531478 \tabularnewline
42 & 40 & 39.6675101981352 & 0.332489801864796 \tabularnewline
43 & 39.96 & 39.8629268648019 & 0.097073135198137 \tabularnewline
44 & 40.01 & 39.8983435314685 & 0.111656468531471 \tabularnewline
45 & 40.01 & 39.9958435314685 & 0.0141564685314677 \tabularnewline
46 & 40.01 & 39.9566768648019 & 0.0533231351981343 \tabularnewline
47 & 40 & 40.0400101981352 & -0.0400101981351924 \tabularnewline
48 & 39.91 & 39.9695935314685 & -0.0595935314685434 \tabularnewline
49 & 39.86 & 39.8991768648019 & -0.0391768648018598 \tabularnewline
50 & 39.79 & 39.8166768648019 & -0.0266768648018569 \tabularnewline
51 & 39.79 & 39.7916768648019 & -0.00167686480186546 \tabularnewline
52 & 39.8 & 39.7758435314685 & 0.0241564685314515 \tabularnewline
53 & 39.64 & 39.5958435314685 & 0.044156468531483 \tabularnewline
54 & 39.55 & 39.5475101981352 & 0.00248980186479031 \tabularnewline
55 & 39.36 & 39.4129268648019 & -0.0529268648018615 \tabularnewline
56 & 39.28 & 39.2983435314685 & -0.0183435314685241 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113001&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]41.33[/C][C]41.6101522435898[/C][C]-0.280152243589754[/C][/ROW]
[ROW][C]14[/C][C]41.29[/C][C]41.2866768648019[/C][C]0.0033231351981442[/C][/ROW]
[ROW][C]15[/C][C]41.29[/C][C]41.2916768648019[/C][C]-0.00167686480186546[/C][/ROW]
[ROW][C]16[/C][C]41.27[/C][C]41.2758435314685[/C][C]-0.00584353146854255[/C][/ROW]
[ROW][C]17[/C][C]41.04[/C][C]41.0658435314685[/C][C]-0.0258435314685244[/C][/ROW]
[ROW][C]18[/C][C]40.9[/C][C]40.9475101981352[/C][C]-0.0475101981352068[/C][/ROW]
[ROW][C]19[/C][C]40.89[/C][C]40.7629268648019[/C][C]0.127073135198138[/C][/ROW]
[ROW][C]20[/C][C]40.72[/C][C]40.8283435314685[/C][C]-0.108343531468527[/C][/ROW]
[ROW][C]21[/C][C]40.72[/C][C]40.7058435314685[/C][C]0.0141564685314677[/C][/ROW]
[ROW][C]22[/C][C]40.58[/C][C]40.6666768648019[/C][C]-0.0866768648018663[/C][/ROW]
[ROW][C]23[/C][C]40.24[/C][C]40.6100101981352[/C][C]-0.370010198135191[/C][/ROW]
[ROW][C]24[/C][C]40.07[/C][C]40.2095935314685[/C][C]-0.139593531468542[/C][/ROW]
[ROW][C]25[/C][C]40.12[/C][C]40.0591768648019[/C][C]0.0608231351981345[/C][/ROW]
[ROW][C]26[/C][C]40.1[/C][C]40.0766768648019[/C][C]0.0233231351981473[/C][/ROW]
[ROW][C]27[/C][C]40.1[/C][C]40.1016768648019[/C][C]-0.00167686480186546[/C][/ROW]
[ROW][C]28[/C][C]40.08[/C][C]40.0858435314685[/C][C]-0.00584353146854966[/C][/ROW]
[ROW][C]29[/C][C]40.06[/C][C]39.8758435314685[/C][C]0.184156468531484[/C][/ROW]
[ROW][C]30[/C][C]39.99[/C][C]39.9675101981352[/C][C]0.0224898018647934[/C][/ROW]
[ROW][C]31[/C][C]40.05[/C][C]39.8529268648019[/C][C]0.197073135198131[/C][/ROW]
[ROW][C]32[/C][C]39.66[/C][C]39.9883435314685[/C][C]-0.328343531468526[/C][/ROW]
[ROW][C]33[/C][C]39.66[/C][C]39.6458435314685[/C][C]0.0141564685314677[/C][/ROW]
[ROW][C]34[/C][C]39.67[/C][C]39.6066768648019[/C][C]0.0633231351981394[/C][/ROW]
[ROW][C]35[/C][C]39.56[/C][C]39.7000101981352[/C][C]-0.140010198135194[/C][/ROW]
[ROW][C]36[/C][C]39.64[/C][C]39.5295935314685[/C][C]0.110406468531458[/C][/ROW]
[ROW][C]37[/C][C]39.73[/C][C]39.6291768648019[/C][C]0.100823135198134[/C][/ROW]
[ROW][C]38[/C][C]39.7[/C][C]39.6866768648019[/C][C]0.0133231351981493[/C][/ROW]
[ROW][C]39[/C][C]39.7[/C][C]39.7016768648019[/C][C]-0.00167686480186546[/C][/ROW]
[ROW][C]40[/C][C]39.68[/C][C]39.6858435314685[/C][C]-0.00584353146854966[/C][/ROW]
[ROW][C]41[/C][C]39.76[/C][C]39.4758435314685[/C][C]0.284156468531478[/C][/ROW]
[ROW][C]42[/C][C]40[/C][C]39.6675101981352[/C][C]0.332489801864796[/C][/ROW]
[ROW][C]43[/C][C]39.96[/C][C]39.8629268648019[/C][C]0.097073135198137[/C][/ROW]
[ROW][C]44[/C][C]40.01[/C][C]39.8983435314685[/C][C]0.111656468531471[/C][/ROW]
[ROW][C]45[/C][C]40.01[/C][C]39.9958435314685[/C][C]0.0141564685314677[/C][/ROW]
[ROW][C]46[/C][C]40.01[/C][C]39.9566768648019[/C][C]0.0533231351981343[/C][/ROW]
[ROW][C]47[/C][C]40[/C][C]40.0400101981352[/C][C]-0.0400101981351924[/C][/ROW]
[ROW][C]48[/C][C]39.91[/C][C]39.9695935314685[/C][C]-0.0595935314685434[/C][/ROW]
[ROW][C]49[/C][C]39.86[/C][C]39.8991768648019[/C][C]-0.0391768648018598[/C][/ROW]
[ROW][C]50[/C][C]39.79[/C][C]39.8166768648019[/C][C]-0.0266768648018569[/C][/ROW]
[ROW][C]51[/C][C]39.79[/C][C]39.7916768648019[/C][C]-0.00167686480186546[/C][/ROW]
[ROW][C]52[/C][C]39.8[/C][C]39.7758435314685[/C][C]0.0241564685314515[/C][/ROW]
[ROW][C]53[/C][C]39.64[/C][C]39.5958435314685[/C][C]0.044156468531483[/C][/ROW]
[ROW][C]54[/C][C]39.55[/C][C]39.5475101981352[/C][C]0.00248980186479031[/C][/ROW]
[ROW][C]55[/C][C]39.36[/C][C]39.4129268648019[/C][C]-0.0529268648018615[/C][/ROW]
[ROW][C]56[/C][C]39.28[/C][C]39.2983435314685[/C][C]-0.0183435314685241[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113001&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113001&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	41.33	41.6101522435898	-0.280152243589754
14	41.29	41.2866768648019	0.0033231351981442
15	41.29	41.2916768648019	-0.00167686480186546
16	41.27	41.2758435314685	-0.00584353146854255
17	41.04	41.0658435314685	-0.0258435314685244
18	40.9	40.9475101981352	-0.0475101981352068
19	40.89	40.7629268648019	0.127073135198138
20	40.72	40.8283435314685	-0.108343531468527
21	40.72	40.7058435314685	0.0141564685314677
22	40.58	40.6666768648019	-0.0866768648018663
23	40.24	40.6100101981352	-0.370010198135191
24	40.07	40.2095935314685	-0.139593531468542
25	40.12	40.0591768648019	0.0608231351981345
26	40.1	40.0766768648019	0.0233231351981473
27	40.1	40.1016768648019	-0.00167686480186546
28	40.08	40.0858435314685	-0.00584353146854966
29	40.06	39.8758435314685	0.184156468531484
30	39.99	39.9675101981352	0.0224898018647934
31	40.05	39.8529268648019	0.197073135198131
32	39.66	39.9883435314685	-0.328343531468526
33	39.66	39.6458435314685	0.0141564685314677
34	39.67	39.6066768648019	0.0633231351981394
35	39.56	39.7000101981352	-0.140010198135194
36	39.64	39.5295935314685	0.110406468531458
37	39.73	39.6291768648019	0.100823135198134
38	39.7	39.6866768648019	0.0133231351981493
39	39.7	39.7016768648019	-0.00167686480186546
40	39.68	39.6858435314685	-0.00584353146854966
41	39.76	39.4758435314685	0.284156468531478
42	40	39.6675101981352	0.332489801864796
43	39.96	39.8629268648019	0.097073135198137
44	40.01	39.8983435314685	0.111656468531471
45	40.01	39.9958435314685	0.0141564685314677
46	40.01	39.9566768648019	0.0533231351981343
47	40	40.0400101981352	-0.0400101981351924
48	39.91	39.9695935314685	-0.0595935314685434
49	39.86	39.8991768648019	-0.0391768648018598
50	39.79	39.8166768648019	-0.0266768648018569
51	39.79	39.7916768648019	-0.00167686480186546
52	39.8	39.7758435314685	0.0241564685314515
53	39.64	39.5958435314685	0.044156468531483
54	39.55	39.5475101981352	0.00248980186479031
55	39.36	39.4129268648019	-0.0529268648018615
56	39.28	39.2983435314685	-0.0183435314685241

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
57	39.2658435314685	39.0097350318951	39.521952031042
58	39.2125203962704	38.8503282827346	39.5747125098062
59	39.2425305944056	38.7989376608941	39.6861235279171
60	39.2121241258741	38.6999071267272	39.7243411250211
61	39.201300990676	38.6286249760142	39.7739770053378
62	39.1579778554778	38.530642712733	39.7853129982227
63	39.1596547202797	38.4820553217584	39.837254118801
64	39.1454982517483	38.4211140246766	39.8698824788199
65	38.9413417832168	38.1730162844963	39.7096672819372
66	38.848851981352	38.0389657945715	39.6587381681324
67	38.7117788461538	37.8623630474477	39.56119464486
68	38.6501223776224	37.7629365105994	39.5373082446454

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
57 & 39.2658435314685 & 39.0097350318951 & 39.521952031042 \tabularnewline
58 & 39.2125203962704 & 38.8503282827346 & 39.5747125098062 \tabularnewline
59 & 39.2425305944056 & 38.7989376608941 & 39.6861235279171 \tabularnewline
60 & 39.2121241258741 & 38.6999071267272 & 39.7243411250211 \tabularnewline
61 & 39.201300990676 & 38.6286249760142 & 39.7739770053378 \tabularnewline
62 & 39.1579778554778 & 38.530642712733 & 39.7853129982227 \tabularnewline
63 & 39.1596547202797 & 38.4820553217584 & 39.837254118801 \tabularnewline
64 & 39.1454982517483 & 38.4211140246766 & 39.8698824788199 \tabularnewline
65 & 38.9413417832168 & 38.1730162844963 & 39.7096672819372 \tabularnewline
66 & 38.848851981352 & 38.0389657945715 & 39.6587381681324 \tabularnewline
67 & 38.7117788461538 & 37.8623630474477 & 39.56119464486 \tabularnewline
68 & 38.6501223776224 & 37.7629365105994 & 39.5373082446454 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113001&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]57[/C][C]39.2658435314685[/C][C]39.0097350318951[/C][C]39.521952031042[/C][/ROW]
[ROW][C]58[/C][C]39.2125203962704[/C][C]38.8503282827346[/C][C]39.5747125098062[/C][/ROW]
[ROW][C]59[/C][C]39.2425305944056[/C][C]38.7989376608941[/C][C]39.6861235279171[/C][/ROW]
[ROW][C]60[/C][C]39.2121241258741[/C][C]38.6999071267272[/C][C]39.7243411250211[/C][/ROW]
[ROW][C]61[/C][C]39.201300990676[/C][C]38.6286249760142[/C][C]39.7739770053378[/C][/ROW]
[ROW][C]62[/C][C]39.1579778554778[/C][C]38.530642712733[/C][C]39.7853129982227[/C][/ROW]
[ROW][C]63[/C][C]39.1596547202797[/C][C]38.4820553217584[/C][C]39.837254118801[/C][/ROW]
[ROW][C]64[/C][C]39.1454982517483[/C][C]38.4211140246766[/C][C]39.8698824788199[/C][/ROW]
[ROW][C]65[/C][C]38.9413417832168[/C][C]38.1730162844963[/C][C]39.7096672819372[/C][/ROW]
[ROW][C]66[/C][C]38.848851981352[/C][C]38.0389657945715[/C][C]39.6587381681324[/C][/ROW]
[ROW][C]67[/C][C]38.7117788461538[/C][C]37.8623630474477[/C][C]39.56119464486[/C][/ROW]
[ROW][C]68[/C][C]38.6501223776224[/C][C]37.7629365105994[/C][C]39.5373082446454[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113001&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113001&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
57	39.2658435314685	39.0097350318951	39.521952031042
58	39.2125203962704	38.8503282827346	39.5747125098062
59	39.2425305944056	38.7989376608941	39.6861235279171
60	39.2121241258741	38.6999071267272	39.7243411250211
61	39.201300990676	38.6286249760142	39.7739770053378
62	39.1579778554778	38.530642712733	39.7853129982227
63	39.1596547202797	38.4820553217584	39.837254118801
64	39.1454982517483	38.4211140246766	39.8698824788199
65	38.9413417832168	38.1730162844963	39.7096672819372
66	38.848851981352	38.0389657945715	39.6587381681324
67	38.7117788461538	37.8623630474477	39.56119464486
68	38.6501223776224	37.7629365105994	39.5373082446454

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