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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_arimaforecasting.wasp
Title produced by softwareARIMA Forecasting
Date of computationMon, 22 Dec 2008 07:22:41 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/22/t1229956044nix7c8bnm883vci.htm/, Retrieved Mon, 13 May 2024 14:53:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36084, Retrieved Mon, 13 May 2024 14:53:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact175

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [] [2008-12-12 12:13:32] [fad8a251ac01c156a8ae23a83577546f]
- RMPD  [(Partial) Autocorrelation Function] [Consumptiegoederen] [2008-12-12 13:39:25] [fad8a251ac01c156a8ae23a83577546f]
-   P     [(Partial) Autocorrelation Function] [auto corr cons] [2008-12-19 10:53:37] [fad8a251ac01c156a8ae23a83577546f]
-   P       [(Partial) Autocorrelation Function] [autocorr cons D] [2008-12-21 18:04:22] [fad8a251ac01c156a8ae23a83577546f]
- RMPD        [ARIMA Backward Selection] [Arima backw sel n...] [2008-12-22 10:23:57] [fad8a251ac01c156a8ae23a83577546f]
- RMPD            [ARIMA Forecasting] [forecast inv] [2008-12-22 14:22:41] [fa8b44cd657c07c6ee11bb2476ca3f8d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
93,0
99,2
112,2
112,1
103,3
108,2
90,4
72,8
111,0
117,9
111,3
110,5
94,8
100,4
132,1
114,6
101,9
130,2
84,0
86,4
122,3
120,9
110,2
112,6
102,0
105,0
130,5
115,5
103,7
130,9
89,1
93,8
123,8
111,9
118,3
116,9
103,6
116,6
141,3
107,0
125,2
136,4
91,6
95,3
132,3
130,6
131,9
118,6
114,3
111,3
126,5
112,1
119,3
142,4
101,1
97,4
129,1
136,9
129,8
123,9

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36084&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36084&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36084&T=0

As an alternative you can also use a QR Code:  
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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Univariate ARIMA Extrapolation Forecast
timeY[t]F[t]95% LB95% UBp-value(H0: Y[t] = F[t])P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[48])
36116.9-------
37103.6-------
38116.6-------
39141.3-------
40107-------
41125.2-------
42136.4-------
4391.6-------
4495.3-------
45132.3-------
46130.6-------
47131.9-------
48118.6-------
49114.3115.7396100.59130.88910.42610.35570.94190.3557
50111.3124.1183108.9669139.26970.04860.8980.83460.7623
51126.5144.4934129.0952159.89170.01110.65780.9995
52112.1114.676597.3676131.98540.38520.09030.80760.3284
53119.3129.7794112.4544147.10440.11790.97730.69780.897
54142.4139.5099121.9505157.06940.37350.9880.63580.9902
55101.196.439878.371114.50860.306600.70020.0081
5697.498.302880.208116.39750.46110.38090.62750.014
57129.1134.8285116.5928153.06410.26910.60710.9594
58136.9133.6813115.2871152.07550.36580.68730.62870.946
59129.8133.956115.5374152.37470.32910.3770.58660.9489
60123.9120.4951102.0055138.98470.35910.1620.57960.5796

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast \tabularnewline
time & Y[t] & F[t] & 95% LB & 95% UB & p-value(H0: Y[t] = F[t]) & P(F[t]>Y[t-1]) & P(F[t]>Y[t-s]) & P(F[t]>Y[48]) \tabularnewline
36 & 116.9 & - & - & - & - & - & - & - \tabularnewline
37 & 103.6 & - & - & - & - & - & - & - \tabularnewline
38 & 116.6 & - & - & - & - & - & - & - \tabularnewline
39 & 141.3 & - & - & - & - & - & - & - \tabularnewline
40 & 107 & - & - & - & - & - & - & - \tabularnewline
41 & 125.2 & - & - & - & - & - & - & - \tabularnewline
42 & 136.4 & - & - & - & - & - & - & - \tabularnewline
43 & 91.6 & - & - & - & - & - & - & - \tabularnewline
44 & 95.3 & - & - & - & - & - & - & - \tabularnewline
45 & 132.3 & - & - & - & - & - & - & - \tabularnewline
46 & 130.6 & - & - & - & - & - & - & - \tabularnewline
47 & 131.9 & - & - & - & - & - & - & - \tabularnewline
48 & 118.6 & - & - & - & - & - & - & - \tabularnewline
49 & 114.3 & 115.7396 & 100.59 & 130.8891 & 0.4261 & 0.3557 & 0.9419 & 0.3557 \tabularnewline
50 & 111.3 & 124.1183 & 108.9669 & 139.2697 & 0.0486 & 0.898 & 0.8346 & 0.7623 \tabularnewline
51 & 126.5 & 144.4934 & 129.0952 & 159.8917 & 0.011 & 1 & 0.6578 & 0.9995 \tabularnewline
52 & 112.1 & 114.6765 & 97.3676 & 131.9854 & 0.3852 & 0.0903 & 0.8076 & 0.3284 \tabularnewline
53 & 119.3 & 129.7794 & 112.4544 & 147.1044 & 0.1179 & 0.9773 & 0.6978 & 0.897 \tabularnewline
54 & 142.4 & 139.5099 & 121.9505 & 157.0694 & 0.3735 & 0.988 & 0.6358 & 0.9902 \tabularnewline
55 & 101.1 & 96.4398 & 78.371 & 114.5086 & 0.3066 & 0 & 0.7002 & 0.0081 \tabularnewline
56 & 97.4 & 98.3028 & 80.208 & 116.3975 & 0.4611 & 0.3809 & 0.6275 & 0.014 \tabularnewline
57 & 129.1 & 134.8285 & 116.5928 & 153.0641 & 0.269 & 1 & 0.6071 & 0.9594 \tabularnewline
58 & 136.9 & 133.6813 & 115.2871 & 152.0755 & 0.3658 & 0.6873 & 0.6287 & 0.946 \tabularnewline
59 & 129.8 & 133.956 & 115.5374 & 152.3747 & 0.3291 & 0.377 & 0.5866 & 0.9489 \tabularnewline
60 & 123.9 & 120.4951 & 102.0055 & 138.9847 & 0.3591 & 0.162 & 0.5796 & 0.5796 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36084&T=1

[TABLE]
[ROW][C]Univariate ARIMA Extrapolation Forecast[/C][/ROW]
[ROW][C]time[/C][C]Y[t][/C][C]F[t][/C][C]95% LB[/C][C]95% UB[/C][C]p-value(H0: Y[t] = F[t])[/C][C]P(F[t]>Y[t-1])[/C][C]P(F[t]>Y[t-s])[/C][C]P(F[t]>Y[48])[/C][/ROW]
[ROW][C]36[/C][C]116.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]103.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]116.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]141.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]107[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]125.2[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]136.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]91.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]95.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]132.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]130.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]131.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]118.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]114.3[/C][C]115.7396[/C][C]100.59[/C][C]130.8891[/C][C]0.4261[/C][C]0.3557[/C][C]0.9419[/C][C]0.3557[/C][/ROW]
[ROW][C]50[/C][C]111.3[/C][C]124.1183[/C][C]108.9669[/C][C]139.2697[/C][C]0.0486[/C][C]0.898[/C][C]0.8346[/C][C]0.7623[/C][/ROW]
[ROW][C]51[/C][C]126.5[/C][C]144.4934[/C][C]129.0952[/C][C]159.8917[/C][C]0.011[/C][C]1[/C][C]0.6578[/C][C]0.9995[/C][/ROW]
[ROW][C]52[/C][C]112.1[/C][C]114.6765[/C][C]97.3676[/C][C]131.9854[/C][C]0.3852[/C][C]0.0903[/C][C]0.8076[/C][C]0.3284[/C][/ROW]
[ROW][C]53[/C][C]119.3[/C][C]129.7794[/C][C]112.4544[/C][C]147.1044[/C][C]0.1179[/C][C]0.9773[/C][C]0.6978[/C][C]0.897[/C][/ROW]
[ROW][C]54[/C][C]142.4[/C][C]139.5099[/C][C]121.9505[/C][C]157.0694[/C][C]0.3735[/C][C]0.988[/C][C]0.6358[/C][C]0.9902[/C][/ROW]
[ROW][C]55[/C][C]101.1[/C][C]96.4398[/C][C]78.371[/C][C]114.5086[/C][C]0.3066[/C][C]0[/C][C]0.7002[/C][C]0.0081[/C][/ROW]
[ROW][C]56[/C][C]97.4[/C][C]98.3028[/C][C]80.208[/C][C]116.3975[/C][C]0.4611[/C][C]0.3809[/C][C]0.6275[/C][C]0.014[/C][/ROW]
[ROW][C]57[/C][C]129.1[/C][C]134.8285[/C][C]116.5928[/C][C]153.0641[/C][C]0.269[/C][C]1[/C][C]0.6071[/C][C]0.9594[/C][/ROW]
[ROW][C]58[/C][C]136.9[/C][C]133.6813[/C][C]115.2871[/C][C]152.0755[/C][C]0.3658[/C][C]0.6873[/C][C]0.6287[/C][C]0.946[/C][/ROW]
[ROW][C]59[/C][C]129.8[/C][C]133.956[/C][C]115.5374[/C][C]152.3747[/C][C]0.3291[/C][C]0.377[/C][C]0.5866[/C][C]0.9489[/C][/ROW]
[ROW][C]60[/C][C]123.9[/C][C]120.4951[/C][C]102.0055[/C][C]138.9847[/C][C]0.3591[/C][C]0.162[/C][C]0.5796[/C][C]0.5796[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36084&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36084&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Univariate ARIMA Extrapolation Forecast
timeY[t]F[t]95% LB95% UBp-value(H0: Y[t] = F[t])P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[48])
36116.9-------
37103.6-------
38116.6-------
39141.3-------
40107-------
41125.2-------
42136.4-------
4391.6-------
4495.3-------
45132.3-------
46130.6-------
47131.9-------
48118.6-------
49114.3115.7396100.59130.88910.42610.35570.94190.3557
50111.3124.1183108.9669139.26970.04860.8980.83460.7623
51126.5144.4934129.0952159.89170.01110.65780.9995
52112.1114.676597.3676131.98540.38520.09030.80760.3284
53119.3129.7794112.4544147.10440.11790.97730.69780.897
54142.4139.5099121.9505157.06940.37350.9880.63580.9902
55101.196.439878.371114.50860.306600.70020.0081
5697.498.302880.208116.39750.46110.38090.62750.014
57129.1134.8285116.5928153.06410.26910.60710.9594
58136.9133.6813115.2871152.07550.36580.68730.62870.946
59129.8133.956115.5374152.37470.32910.3770.58660.9489
60123.9120.4951102.0055138.98470.35910.1620.57960.5796






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
490.0668-0.01240.0012.07240.17270.4156
500.0623-0.10330.0086164.309213.69243.7003
510.0544-0.12450.0104323.763226.98035.1943
520.077-0.02250.00196.63840.55320.7438
530.0681-0.08070.0067109.81839.15153.0251
540.06420.02070.00178.35250.6960.8343
550.09560.04830.00421.71711.80981.3453
560.0939-0.00928e-040.8150.06790.2606
570.069-0.04250.003532.81552.73461.6537
580.07020.02410.00210.36020.86330.9292
590.0702-0.0310.002617.27271.43941.1997
600.07830.02830.002411.59310.96610.9829

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
49 & 0.0668 & -0.0124 & 0.001 & 2.0724 & 0.1727 & 0.4156 \tabularnewline
50 & 0.0623 & -0.1033 & 0.0086 & 164.3092 & 13.6924 & 3.7003 \tabularnewline
51 & 0.0544 & -0.1245 & 0.0104 & 323.7632 & 26.9803 & 5.1943 \tabularnewline
52 & 0.077 & -0.0225 & 0.0019 & 6.6384 & 0.5532 & 0.7438 \tabularnewline
53 & 0.0681 & -0.0807 & 0.0067 & 109.8183 & 9.1515 & 3.0251 \tabularnewline
54 & 0.0642 & 0.0207 & 0.0017 & 8.3525 & 0.696 & 0.8343 \tabularnewline
55 & 0.0956 & 0.0483 & 0.004 & 21.7171 & 1.8098 & 1.3453 \tabularnewline
56 & 0.0939 & -0.0092 & 8e-04 & 0.815 & 0.0679 & 0.2606 \tabularnewline
57 & 0.069 & -0.0425 & 0.0035 & 32.8155 & 2.7346 & 1.6537 \tabularnewline
58 & 0.0702 & 0.0241 & 0.002 & 10.3602 & 0.8633 & 0.9292 \tabularnewline
59 & 0.0702 & -0.031 & 0.0026 & 17.2727 & 1.4394 & 1.1997 \tabularnewline
60 & 0.0783 & 0.0283 & 0.0024 & 11.5931 & 0.9661 & 0.9829 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36084&T=2

[TABLE]
[ROW][C]Univariate ARIMA Extrapolation Forecast Performance[/C][/ROW]
[ROW][C]time[/C][C]% S.E.[/C][C]PE[/C][C]MAPE[/C][C]Sq.E[/C][C]MSE[/C][C]RMSE[/C][/ROW]
[ROW][C]49[/C][C]0.0668[/C][C]-0.0124[/C][C]0.001[/C][C]2.0724[/C][C]0.1727[/C][C]0.4156[/C][/ROW]
[ROW][C]50[/C][C]0.0623[/C][C]-0.1033[/C][C]0.0086[/C][C]164.3092[/C][C]13.6924[/C][C]3.7003[/C][/ROW]
[ROW][C]51[/C][C]0.0544[/C][C]-0.1245[/C][C]0.0104[/C][C]323.7632[/C][C]26.9803[/C][C]5.1943[/C][/ROW]
[ROW][C]52[/C][C]0.077[/C][C]-0.0225[/C][C]0.0019[/C][C]6.6384[/C][C]0.5532[/C][C]0.7438[/C][/ROW]
[ROW][C]53[/C][C]0.0681[/C][C]-0.0807[/C][C]0.0067[/C][C]109.8183[/C][C]9.1515[/C][C]3.0251[/C][/ROW]
[ROW][C]54[/C][C]0.0642[/C][C]0.0207[/C][C]0.0017[/C][C]8.3525[/C][C]0.696[/C][C]0.8343[/C][/ROW]
[ROW][C]55[/C][C]0.0956[/C][C]0.0483[/C][C]0.004[/C][C]21.7171[/C][C]1.8098[/C][C]1.3453[/C][/ROW]
[ROW][C]56[/C][C]0.0939[/C][C]-0.0092[/C][C]8e-04[/C][C]0.815[/C][C]0.0679[/C][C]0.2606[/C][/ROW]
[ROW][C]57[/C][C]0.069[/C][C]-0.0425[/C][C]0.0035[/C][C]32.8155[/C][C]2.7346[/C][C]1.6537[/C][/ROW]
[ROW][C]58[/C][C]0.0702[/C][C]0.0241[/C][C]0.002[/C][C]10.3602[/C][C]0.8633[/C][C]0.9292[/C][/ROW]
[ROW][C]59[/C][C]0.0702[/C][C]-0.031[/C][C]0.0026[/C][C]17.2727[/C][C]1.4394[/C][C]1.1997[/C][/ROW]
[ROW][C]60[/C][C]0.0783[/C][C]0.0283[/C][C]0.0024[/C][C]11.5931[/C][C]0.9661[/C][C]0.9829[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36084&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36084&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
490.0668-0.01240.0012.07240.17270.4156
500.0623-0.10330.0086164.309213.69243.7003
510.0544-0.12450.0104323.763226.98035.1943
520.077-0.02250.00196.63840.55320.7438
530.0681-0.08070.0067109.81839.15153.0251
540.06420.02070.00178.35250.6960.8343
550.09560.04830.00421.71711.80981.3453
560.0939-0.00928e-040.8150.06790.2606
570.069-0.04250.003532.81552.73461.6537
580.07020.02410.00210.36020.86330.9292
590.0702-0.0310.002617.27271.43941.1997
600.07830.02830.002411.59310.96610.9829


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;
R code (references can be found in the software module):
par1 <- as.numeric(par1) #cut off periods
par2 <- as.numeric(par2) #lambda
par3 <- as.numeric(par3) #degree of non-seasonal differencing
par4 <- as.numeric(par4) #degree of seasonal differencing
par5 <- as.numeric(par5) #seasonal period
par6 <- as.numeric(par6) #p
par7 <- as.numeric(par7) #q
par8 <- as.numeric(par8) #P
par9 <- as.numeric(par9) #Q
if (par10 == 'TRUE') par10 <- TRUE
if (par10 == 'FALSE') par10 <- FALSE
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
lx <- length(x)
first <- lx - 2*par1
nx <- lx - par1
nx1 <- nx + 1
fx <- lx - nx
if (fx < 1) {
fx <- par5
nx1 <- lx + fx - 1
first <- lx - 2*fx
}
first <- 1
if (fx < 3) fx <- round(lx/10,0)
(arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method='ML'))
(forecast <- predict(arima.out,fx))
(lb <- forecast$pred - 1.96 * forecast$se)
(ub <- forecast$pred + 1.96 * forecast$se)
if (par2 == 0) {
x <- exp(x)
forecast$pred <- exp(forecast$pred)
lb <- exp(lb)
ub <- exp(ub)
}
if (par2 != 0) {
x <- x^(1/par2)
forecast$pred <- forecast$pred^(1/par2)
lb <- lb^(1/par2)
ub <- ub^(1/par2)
}
if (par2 < 0) {
olb <- lb
lb <- ub
ub <- olb
}
(actandfor <- c(x[1:nx], forecast$pred))
(perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
bitmap(file='test1.png')
opar <- par(mar=c(4,4,2,2),las=1)
ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
plot(x,ylim=ylim,type='n',xlim=c(first,lx))
usr <- par('usr')
rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
abline(h= (-3:3)*2 , col ='gray', lty =3)
polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
lines(nx1:lx, lb , lty=2)
lines(nx1:lx, ub , lty=2)
lines(x, lwd=2)
lines(nx1:lx, forecast$pred , lwd=2 , col ='white')
box()
par(opar)
dev.off()
prob.dec <- array(NA, dim=fx)
prob.sdec <- array(NA, dim=fx)
prob.ldec <- array(NA, dim=fx)
prob.pval <- array(NA, dim=fx)
perf.pe <- array(0, dim=fx)
perf.mape <- array(0, dim=fx)
perf.se <- array(0, dim=fx)
perf.mse <- array(0, dim=fx)
perf.rmse <- array(0, dim=fx)
for (i in 1:fx) {
locSD <- (ub[i] - forecast$pred[i]) / 1.96
perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$pred[i]
perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
perf.se[i] = (x[nx+i] - forecast$pred[i])^2
perf.mse[i] = perf.mse[i] + perf.se[i]
prob.dec[i] = pnorm((x[nx+i-1] - forecast$pred[i]) / locSD)
prob.sdec[i] = pnorm((x[nx+i-par5] - forecast$pred[i]) / locSD)
prob.ldec[i] = pnorm((x[nx] - forecast$pred[i]) / locSD)
prob.pval[i] = pnorm(abs(x[nx+i] - forecast$pred[i]) / locSD)
}
perf.mape = perf.mape / fx
perf.mse = perf.mse / fx
perf.rmse = sqrt(perf.mse)
bitmap(file='test2.png')
plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub)))
dum <- forecast$pred
dum[1:12] <- x[(nx+1):lx]
lines(dum, lty=1)
lines(ub,lty=3)
lines(lb,lty=3)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'time',1,header=TRUE)
a<-table.element(a,'Y[t]',1,header=TRUE)
a<-table.element(a,'F[t]',1,header=TRUE)
a<-table.element(a,'95% LB',1,header=TRUE)
a<-table.element(a,'95% UB',1,header=TRUE)
a<-table.element(a,'p-value
(H0: Y[t] = F[t])',1,header=TRUE)
a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE)
a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE)
mylab <- paste('P(F[t]>Y[',nx,sep='')
mylab <- paste(mylab,'])',sep='')
a<-table.element(a,mylab,1,header=TRUE)
a<-table.row.end(a)
for (i in (nx-par5):nx) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.row.end(a)
}
for (i in 1:fx) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,round(x[nx+i],4))
a<-table.element(a,round(forecast$pred[i],4))
a<-table.element(a,round(lb[i],4))
a<-table.element(a,round(ub[i],4))
a<-table.element(a,round((1-prob.pval[i]),4))
a<-table.element(a,round((1-prob.dec[i]),4))
a<-table.element(a,round((1-prob.sdec[i]),4))
a<-table.element(a,round((1-prob.ldec[i]),4))
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,'Univariate ARIMA Extrapolation Forecast Performance',7,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'time',1,header=TRUE)
a<-table.element(a,'% S.E.',1,header=TRUE)
a<-table.element(a,'PE',1,header=TRUE)
a<-table.element(a,'MAPE',1,header=TRUE)
a<-table.element(a,'Sq.E',1,header=TRUE)
a<-table.element(a,'MSE',1,header=TRUE)
a<-table.element(a,'RMSE',1,header=TRUE)
a<-table.row.end(a)
for (i in 1:fx) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,round(perc.se[i],4))
a<-table.element(a,round(perf.pe[i],4))
a<-table.element(a,round(perf.mape[i],4))
a<-table.element(a,round(perf.se[i],4))
a<-table.element(a,round(perf.mse[i],4))
a<-table.element(a,round(perf.rmse[i],4))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')