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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 03 Dec 2016 17:40:58 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/03/t1480786877hxztuf55lwhb3s0.htm/, Retrieved Sun, 05 May 2024 14:14:26 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 14:14:26 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
2322
2347
2963
1900
2723
2555
2176
2444
1944
2089
1978
2081
2435
2246
2641
1966
2398
2334
2333
2421
1531
2215
1927
1698
2482
1974
2369
2097
2264
1938
2360
2176
1478
2158
1690
1886
2450
1811
2196
1997
2199
1970
2239
1937
1311
2149
1673
2378
2770
1764
2310
1971
1899
2554
1948
2138
1469
2059
1771
1761




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.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]'Gertrude Mary Cox' @ cox.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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0774605587534282
beta0
gamma0.557931194789423

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0774605587534282 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.557931194789423 \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]0.0774605587534282[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.557931194789423[/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
ParameterValue
alpha0.0774605587534282
beta0
gamma0.557931194789423







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1324352518.34161324786-83.3416132478646
1422462307.79982391967-61.7998239196713
1526412706.67667362939-65.676673629388
1619662029.04488706105-63.0448870610537
1723982443.53362681749-45.5336268174892
1823342384.5871319102-50.5871319102016
1923332109.66585634143223.334143658565
2024212384.9626758326836.0373241673224
2115311895.87637903339-364.876379033388
2222152013.77674943893201.223250561068
2319271919.652513462977.34748653702832
2416982036.46888581029-338.468885810295
2524822314.51773922086167.482260779137
2619742134.49275780919-160.492757809188
2723692523.72933070499-154.729330704992
2820971840.55409172299256.445908277009
2922642288.8040496248-24.8040496247977
3019382228.86217189082-290.862171890816
3123602076.32004489899283.679955101013
3221762259.8870770401-83.8870770401031
3314781555.15566063482-77.1556606348167
3421581986.72217885838171.277821141617
3516901790.48787378271-100.487873782713
3618861720.95489219161165.045107808392
3724502298.42612292022151.573877079784
3818111948.355688765-137.355688764999
3921962342.35098588211-146.350985882114
4019971871.46219798469125.537802015314
4121992164.8087814281334.1912185718684
4219701972.49299411871-2.4929941187138
4322392138.01271263048100.987287369519
4419372118.23654303337-181.236543033366
4513111409.4291337159-98.4291337159007
4621491967.21987187286181.780128127136
4716731631.9176004646641.0823995353394
4823781710.02415034946667.975849650541
4927702319.51885259736450.481147402636
5017641843.8859850808-79.8859850807967
5123102237.7029163998972.2970836001082
5219711923.6955686537847.3044313462199
5318992163.96482882823-264.964828828233
5425541929.59438622463624.405613775371
5519482196.93672243471-248.936722434707
5621382004.79081875951133.209181240486
5714691362.96264512505106.037354874953
5820592080.81897079172-21.8189707917154
5917711657.32677449391113.673225506092
6017612063.72679265097-302.726792650968

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2435 & 2518.34161324786 & -83.3416132478646 \tabularnewline
14 & 2246 & 2307.79982391967 & -61.7998239196713 \tabularnewline
15 & 2641 & 2706.67667362939 & -65.676673629388 \tabularnewline
16 & 1966 & 2029.04488706105 & -63.0448870610537 \tabularnewline
17 & 2398 & 2443.53362681749 & -45.5336268174892 \tabularnewline
18 & 2334 & 2384.5871319102 & -50.5871319102016 \tabularnewline
19 & 2333 & 2109.66585634143 & 223.334143658565 \tabularnewline
20 & 2421 & 2384.96267583268 & 36.0373241673224 \tabularnewline
21 & 1531 & 1895.87637903339 & -364.876379033388 \tabularnewline
22 & 2215 & 2013.77674943893 & 201.223250561068 \tabularnewline
23 & 1927 & 1919.65251346297 & 7.34748653702832 \tabularnewline
24 & 1698 & 2036.46888581029 & -338.468885810295 \tabularnewline
25 & 2482 & 2314.51773922086 & 167.482260779137 \tabularnewline
26 & 1974 & 2134.49275780919 & -160.492757809188 \tabularnewline
27 & 2369 & 2523.72933070499 & -154.729330704992 \tabularnewline
28 & 2097 & 1840.55409172299 & 256.445908277009 \tabularnewline
29 & 2264 & 2288.8040496248 & -24.8040496247977 \tabularnewline
30 & 1938 & 2228.86217189082 & -290.862171890816 \tabularnewline
31 & 2360 & 2076.32004489899 & 283.679955101013 \tabularnewline
32 & 2176 & 2259.8870770401 & -83.8870770401031 \tabularnewline
33 & 1478 & 1555.15566063482 & -77.1556606348167 \tabularnewline
34 & 2158 & 1986.72217885838 & 171.277821141617 \tabularnewline
35 & 1690 & 1790.48787378271 & -100.487873782713 \tabularnewline
36 & 1886 & 1720.95489219161 & 165.045107808392 \tabularnewline
37 & 2450 & 2298.42612292022 & 151.573877079784 \tabularnewline
38 & 1811 & 1948.355688765 & -137.355688764999 \tabularnewline
39 & 2196 & 2342.35098588211 & -146.350985882114 \tabularnewline
40 & 1997 & 1871.46219798469 & 125.537802015314 \tabularnewline
41 & 2199 & 2164.80878142813 & 34.1912185718684 \tabularnewline
42 & 1970 & 1972.49299411871 & -2.4929941187138 \tabularnewline
43 & 2239 & 2138.01271263048 & 100.987287369519 \tabularnewline
44 & 1937 & 2118.23654303337 & -181.236543033366 \tabularnewline
45 & 1311 & 1409.4291337159 & -98.4291337159007 \tabularnewline
46 & 2149 & 1967.21987187286 & 181.780128127136 \tabularnewline
47 & 1673 & 1631.91760046466 & 41.0823995353394 \tabularnewline
48 & 2378 & 1710.02415034946 & 667.975849650541 \tabularnewline
49 & 2770 & 2319.51885259736 & 450.481147402636 \tabularnewline
50 & 1764 & 1843.8859850808 & -79.8859850807967 \tabularnewline
51 & 2310 & 2237.70291639989 & 72.2970836001082 \tabularnewline
52 & 1971 & 1923.69556865378 & 47.3044313462199 \tabularnewline
53 & 1899 & 2163.96482882823 & -264.964828828233 \tabularnewline
54 & 2554 & 1929.59438622463 & 624.405613775371 \tabularnewline
55 & 1948 & 2196.93672243471 & -248.936722434707 \tabularnewline
56 & 2138 & 2004.79081875951 & 133.209181240486 \tabularnewline
57 & 1469 & 1362.96264512505 & 106.037354874953 \tabularnewline
58 & 2059 & 2080.81897079172 & -21.8189707917154 \tabularnewline
59 & 1771 & 1657.32677449391 & 113.673225506092 \tabularnewline
60 & 1761 & 2063.72679265097 & -302.726792650968 \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]2435[/C][C]2518.34161324786[/C][C]-83.3416132478646[/C][/ROW]
[ROW][C]14[/C][C]2246[/C][C]2307.79982391967[/C][C]-61.7998239196713[/C][/ROW]
[ROW][C]15[/C][C]2641[/C][C]2706.67667362939[/C][C]-65.676673629388[/C][/ROW]
[ROW][C]16[/C][C]1966[/C][C]2029.04488706105[/C][C]-63.0448870610537[/C][/ROW]
[ROW][C]17[/C][C]2398[/C][C]2443.53362681749[/C][C]-45.5336268174892[/C][/ROW]
[ROW][C]18[/C][C]2334[/C][C]2384.5871319102[/C][C]-50.5871319102016[/C][/ROW]
[ROW][C]19[/C][C]2333[/C][C]2109.66585634143[/C][C]223.334143658565[/C][/ROW]
[ROW][C]20[/C][C]2421[/C][C]2384.96267583268[/C][C]36.0373241673224[/C][/ROW]
[ROW][C]21[/C][C]1531[/C][C]1895.87637903339[/C][C]-364.876379033388[/C][/ROW]
[ROW][C]22[/C][C]2215[/C][C]2013.77674943893[/C][C]201.223250561068[/C][/ROW]
[ROW][C]23[/C][C]1927[/C][C]1919.65251346297[/C][C]7.34748653702832[/C][/ROW]
[ROW][C]24[/C][C]1698[/C][C]2036.46888581029[/C][C]-338.468885810295[/C][/ROW]
[ROW][C]25[/C][C]2482[/C][C]2314.51773922086[/C][C]167.482260779137[/C][/ROW]
[ROW][C]26[/C][C]1974[/C][C]2134.49275780919[/C][C]-160.492757809188[/C][/ROW]
[ROW][C]27[/C][C]2369[/C][C]2523.72933070499[/C][C]-154.729330704992[/C][/ROW]
[ROW][C]28[/C][C]2097[/C][C]1840.55409172299[/C][C]256.445908277009[/C][/ROW]
[ROW][C]29[/C][C]2264[/C][C]2288.8040496248[/C][C]-24.8040496247977[/C][/ROW]
[ROW][C]30[/C][C]1938[/C][C]2228.86217189082[/C][C]-290.862171890816[/C][/ROW]
[ROW][C]31[/C][C]2360[/C][C]2076.32004489899[/C][C]283.679955101013[/C][/ROW]
[ROW][C]32[/C][C]2176[/C][C]2259.8870770401[/C][C]-83.8870770401031[/C][/ROW]
[ROW][C]33[/C][C]1478[/C][C]1555.15566063482[/C][C]-77.1556606348167[/C][/ROW]
[ROW][C]34[/C][C]2158[/C][C]1986.72217885838[/C][C]171.277821141617[/C][/ROW]
[ROW][C]35[/C][C]1690[/C][C]1790.48787378271[/C][C]-100.487873782713[/C][/ROW]
[ROW][C]36[/C][C]1886[/C][C]1720.95489219161[/C][C]165.045107808392[/C][/ROW]
[ROW][C]37[/C][C]2450[/C][C]2298.42612292022[/C][C]151.573877079784[/C][/ROW]
[ROW][C]38[/C][C]1811[/C][C]1948.355688765[/C][C]-137.355688764999[/C][/ROW]
[ROW][C]39[/C][C]2196[/C][C]2342.35098588211[/C][C]-146.350985882114[/C][/ROW]
[ROW][C]40[/C][C]1997[/C][C]1871.46219798469[/C][C]125.537802015314[/C][/ROW]
[ROW][C]41[/C][C]2199[/C][C]2164.80878142813[/C][C]34.1912185718684[/C][/ROW]
[ROW][C]42[/C][C]1970[/C][C]1972.49299411871[/C][C]-2.4929941187138[/C][/ROW]
[ROW][C]43[/C][C]2239[/C][C]2138.01271263048[/C][C]100.987287369519[/C][/ROW]
[ROW][C]44[/C][C]1937[/C][C]2118.23654303337[/C][C]-181.236543033366[/C][/ROW]
[ROW][C]45[/C][C]1311[/C][C]1409.4291337159[/C][C]-98.4291337159007[/C][/ROW]
[ROW][C]46[/C][C]2149[/C][C]1967.21987187286[/C][C]181.780128127136[/C][/ROW]
[ROW][C]47[/C][C]1673[/C][C]1631.91760046466[/C][C]41.0823995353394[/C][/ROW]
[ROW][C]48[/C][C]2378[/C][C]1710.02415034946[/C][C]667.975849650541[/C][/ROW]
[ROW][C]49[/C][C]2770[/C][C]2319.51885259736[/C][C]450.481147402636[/C][/ROW]
[ROW][C]50[/C][C]1764[/C][C]1843.8859850808[/C][C]-79.8859850807967[/C][/ROW]
[ROW][C]51[/C][C]2310[/C][C]2237.70291639989[/C][C]72.2970836001082[/C][/ROW]
[ROW][C]52[/C][C]1971[/C][C]1923.69556865378[/C][C]47.3044313462199[/C][/ROW]
[ROW][C]53[/C][C]1899[/C][C]2163.96482882823[/C][C]-264.964828828233[/C][/ROW]
[ROW][C]54[/C][C]2554[/C][C]1929.59438622463[/C][C]624.405613775371[/C][/ROW]
[ROW][C]55[/C][C]1948[/C][C]2196.93672243471[/C][C]-248.936722434707[/C][/ROW]
[ROW][C]56[/C][C]2138[/C][C]2004.79081875951[/C][C]133.209181240486[/C][/ROW]
[ROW][C]57[/C][C]1469[/C][C]1362.96264512505[/C][C]106.037354874953[/C][/ROW]
[ROW][C]58[/C][C]2059[/C][C]2080.81897079172[/C][C]-21.8189707917154[/C][/ROW]
[ROW][C]59[/C][C]1771[/C][C]1657.32677449391[/C][C]113.673225506092[/C][/ROW]
[ROW][C]60[/C][C]1761[/C][C]2063.72679265097[/C][C]-302.726792650968[/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
tObservedFittedResiduals
1324352518.34161324786-83.3416132478646
1422462307.79982391967-61.7998239196713
1526412706.67667362939-65.676673629388
1619662029.04488706105-63.0448870610537
1723982443.53362681749-45.5336268174892
1823342384.5871319102-50.5871319102016
1923332109.66585634143223.334143658565
2024212384.9626758326836.0373241673224
2115311895.87637903339-364.876379033388
2222152013.77674943893201.223250561068
2319271919.652513462977.34748653702832
2416982036.46888581029-338.468885810295
2524822314.51773922086167.482260779137
2619742134.49275780919-160.492757809188
2723692523.72933070499-154.729330704992
2820971840.55409172299256.445908277009
2922642288.8040496248-24.8040496247977
3019382228.86217189082-290.862171890816
3123602076.32004489899283.679955101013
3221762259.8870770401-83.8870770401031
3314781555.15566063482-77.1556606348167
3421581986.72217885838171.277821141617
3516901790.48787378271-100.487873782713
3618861720.95489219161165.045107808392
3724502298.42612292022151.573877079784
3818111948.355688765-137.355688764999
3921962342.35098588211-146.350985882114
4019971871.46219798469125.537802015314
4121992164.8087814281334.1912185718684
4219701972.49299411871-2.4929941187138
4322392138.01271263048100.987287369519
4419372118.23654303337-181.236543033366
4513111409.4291337159-98.4291337159007
4621491967.21987187286181.780128127136
4716731631.9176004646641.0823995353394
4823781710.02415034946667.975849650541
4927702319.51885259736450.481147402636
5017641843.8859850808-79.8859850807967
5123102237.7029163998972.2970836001082
5219711923.6955686537847.3044313462199
5318992163.96482882823-264.964828828233
5425541929.59438622463624.405613775371
5519482196.93672243471-248.936722434707
5621382004.79081875951133.209181240486
5714691362.96264512505106.037354874953
5820592080.81897079172-21.8189707917154
5917711657.32677449391113.673225506092
6017612063.72679265097-302.726792650968







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
612486.082859306292059.987148709942912.17856990263
621702.568330018131275.196214642592129.94044539366
632180.903959275271752.259239941742609.5486786088
641848.432382704241418.518826481042278.34593892743
651924.308201138631493.129541837832355.48686043943
662168.233084613141735.793023277022600.67314594927
671937.687493968551503.989699346132371.38528859097
681961.520035993011526.568145006992396.47192697902
691295.38769801018859.1853162144551731.59007980591
701939.22092985821501.771631886172376.67022783023
711587.15851023841148.465840242442025.85118023436
721770.426612472551330.494084554752210.35914039034

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 2486.08285930629 & 2059.98714870994 & 2912.17856990263 \tabularnewline
62 & 1702.56833001813 & 1275.19621464259 & 2129.94044539366 \tabularnewline
63 & 2180.90395927527 & 1752.25923994174 & 2609.5486786088 \tabularnewline
64 & 1848.43238270424 & 1418.51882648104 & 2278.34593892743 \tabularnewline
65 & 1924.30820113863 & 1493.12954183783 & 2355.48686043943 \tabularnewline
66 & 2168.23308461314 & 1735.79302327702 & 2600.67314594927 \tabularnewline
67 & 1937.68749396855 & 1503.98969934613 & 2371.38528859097 \tabularnewline
68 & 1961.52003599301 & 1526.56814500699 & 2396.47192697902 \tabularnewline
69 & 1295.38769801018 & 859.185316214455 & 1731.59007980591 \tabularnewline
70 & 1939.2209298582 & 1501.77163188617 & 2376.67022783023 \tabularnewline
71 & 1587.1585102384 & 1148.46584024244 & 2025.85118023436 \tabularnewline
72 & 1770.42661247255 & 1330.49408455475 & 2210.35914039034 \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]2486.08285930629[/C][C]2059.98714870994[/C][C]2912.17856990263[/C][/ROW]
[ROW][C]62[/C][C]1702.56833001813[/C][C]1275.19621464259[/C][C]2129.94044539366[/C][/ROW]
[ROW][C]63[/C][C]2180.90395927527[/C][C]1752.25923994174[/C][C]2609.5486786088[/C][/ROW]
[ROW][C]64[/C][C]1848.43238270424[/C][C]1418.51882648104[/C][C]2278.34593892743[/C][/ROW]
[ROW][C]65[/C][C]1924.30820113863[/C][C]1493.12954183783[/C][C]2355.48686043943[/C][/ROW]
[ROW][C]66[/C][C]2168.23308461314[/C][C]1735.79302327702[/C][C]2600.67314594927[/C][/ROW]
[ROW][C]67[/C][C]1937.68749396855[/C][C]1503.98969934613[/C][C]2371.38528859097[/C][/ROW]
[ROW][C]68[/C][C]1961.52003599301[/C][C]1526.56814500699[/C][C]2396.47192697902[/C][/ROW]
[ROW][C]69[/C][C]1295.38769801018[/C][C]859.185316214455[/C][C]1731.59007980591[/C][/ROW]
[ROW][C]70[/C][C]1939.2209298582[/C][C]1501.77163188617[/C][C]2376.67022783023[/C][/ROW]
[ROW][C]71[/C][C]1587.1585102384[/C][C]1148.46584024244[/C][C]2025.85118023436[/C][/ROW]
[ROW][C]72[/C][C]1770.42661247255[/C][C]1330.49408455475[/C][C]2210.35914039034[/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
tForecast95% Lower Bound95% Upper Bound
612486.082859306292059.987148709942912.17856990263
621702.568330018131275.196214642592129.94044539366
632180.903959275271752.259239941742609.5486786088
641848.432382704241418.518826481042278.34593892743
651924.308201138631493.129541837832355.48686043943
662168.233084613141735.793023277022600.67314594927
671937.687493968551503.989699346132371.38528859097
681961.520035993011526.568145006992396.47192697902
691295.38769801018859.1853162144551731.59007980591
701939.22092985821501.771631886172376.67022783023
711587.15851023841148.465840242442025.85118023436
721770.426612472551330.494084554752210.35914039034



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')