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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 computationSun, 20 Dec 2009 03:24:37 -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/2009/Dec/20/t1261304735t9efpnfc7vrb0w1.htm/, Retrieved Sun, 10 Nov 2024 19:42:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69818, Retrieved Sun, 10 Nov 2024 19:42:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact204

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Forecasting] [] [2009-12-06 10:44:58] [1e83ffa964db6f7ea6ccc4e7b5acbbff]
-   PD  [ARIMA Forecasting] [ws 10 deel 2 prblm] [2009-12-09 19:29:01] [134dc66689e3d457a82860db6471d419]
-   P     [ARIMA Forecasting] [ws 10 deel 2 arim...] [2009-12-12 09:45:03] [134dc66689e3d457a82860db6471d419]
-    D      [ARIMA Forecasting] [WS 10 ] [2009-12-12 11:53:20] [3425351e86519d261a643e224a0c8ee1]
-   PD        [ARIMA Forecasting] [] [2009-12-19 16:24:22] [3425351e86519d261a643e224a0c8ee1]
-   P             [ARIMA Forecasting] [] [2009-12-20 10:24:37] [17416e80e7873ecccac25c455c5f767e] [Current]
-   PD              [ARIMA Forecasting] [ARIMA forecasting] [2009-12-21 15:59:35] [76ab39dc7a55316678260825bd5ad46c]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
91.98
91.72
90.27
91.89
92.07
92.92
93.34
93.6
92.41
93.6
93.77
93.6
93.6
93.51
92.66
94.2
94.37
94.45
94.62
94.37
93.43
94.79
94.88
94.79
94.62
94.71
93.77
95.73
95.99
95.82
95.47
95.82
94.71
96.33
96.5
96.16
96.33
96.33
95.05
96.84
96.92
97.44
97.78
97.69
96.67
98.29
98.2
98.71
98.54
98.2
96.92
99.06
99.65
99.82
99.99
100.33
99.31
101.1
101.1
100.93
100.85
100.93
99.6
101.88
101.81
102.38
102.74
102.82
101.72
103.47
102.98
102.68
102.9
103.03
101.29
103.69
103.68
104.2
104.08
104.16
103.05
104.66
104.46
104.95
105.85
106.23
104.86
107.44
108.23
108.45
109.39
110.15
109.13
110.28
110.17
109.99
109.26
109.11
107.06
109.53
108.92
109.24
109.12
109
107.23
109.49
109.04
109.02
109.23

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'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69818&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69818&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69818&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'Gwilym Jenkins' @ 72.249.127.135






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[94])
82104.66-------
83104.46-------
84104.95-------
85105.85-------
86106.23-------
87104.86-------
88107.44-------
89108.23-------
90108.45-------
91109.39-------
92110.15-------
93109.13-------
94110.28-------
95110.17110.0421109.3959110.68820.3490.235210.2352
96109.99110.1598109.2005111.11910.36430.491710.403
97109.26110.552109.3586111.74540.01690.82210.6725
98109.11110.7148109.3264112.10330.01170.9810.7303
99107.06109.2984107.7391110.85770.00240.593610.1086
100109.53111.6516109.9383113.36480.0076110.9417
101108.92112.0281110.1737113.88265e-040.995910.9677
102109.24112.3774110.3918114.3630.0010.99970.99990.9808
103109.12112.8112110.7026114.91993e-040.99950.99930.9907
104109113.1834110.9586115.40831e-040.99980.99620.9947
105107.23112.1261109.7907114.461400.99570.9940.9394
106109.49113.5746111.1338116.01535e-0410.99590.9959
107109.04113.3657110.7393115.99226e-040.99810.99150.9894
108109.02113.4839110.6752116.29269e-040.9990.99260.9873
109109.23113.876110.8961116.8560.00110.99930.99880.991

\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[94]) \tabularnewline
82 & 104.66 & - & - & - & - & - & - & - \tabularnewline
83 & 104.46 & - & - & - & - & - & - & - \tabularnewline
84 & 104.95 & - & - & - & - & - & - & - \tabularnewline
85 & 105.85 & - & - & - & - & - & - & - \tabularnewline
86 & 106.23 & - & - & - & - & - & - & - \tabularnewline
87 & 104.86 & - & - & - & - & - & - & - \tabularnewline
88 & 107.44 & - & - & - & - & - & - & - \tabularnewline
89 & 108.23 & - & - & - & - & - & - & - \tabularnewline
90 & 108.45 & - & - & - & - & - & - & - \tabularnewline
91 & 109.39 & - & - & - & - & - & - & - \tabularnewline
92 & 110.15 & - & - & - & - & - & - & - \tabularnewline
93 & 109.13 & - & - & - & - & - & - & - \tabularnewline
94 & 110.28 & - & - & - & - & - & - & - \tabularnewline
95 & 110.17 & 110.0421 & 109.3959 & 110.6882 & 0.349 & 0.2352 & 1 & 0.2352 \tabularnewline
96 & 109.99 & 110.1598 & 109.2005 & 111.1191 & 0.3643 & 0.4917 & 1 & 0.403 \tabularnewline
97 & 109.26 & 110.552 & 109.3586 & 111.7454 & 0.0169 & 0.822 & 1 & 0.6725 \tabularnewline
98 & 109.11 & 110.7148 & 109.3264 & 112.1033 & 0.0117 & 0.98 & 1 & 0.7303 \tabularnewline
99 & 107.06 & 109.2984 & 107.7391 & 110.8577 & 0.0024 & 0.5936 & 1 & 0.1086 \tabularnewline
100 & 109.53 & 111.6516 & 109.9383 & 113.3648 & 0.0076 & 1 & 1 & 0.9417 \tabularnewline
101 & 108.92 & 112.0281 & 110.1737 & 113.8826 & 5e-04 & 0.9959 & 1 & 0.9677 \tabularnewline
102 & 109.24 & 112.3774 & 110.3918 & 114.363 & 0.001 & 0.9997 & 0.9999 & 0.9808 \tabularnewline
103 & 109.12 & 112.8112 & 110.7026 & 114.9199 & 3e-04 & 0.9995 & 0.9993 & 0.9907 \tabularnewline
104 & 109 & 113.1834 & 110.9586 & 115.4083 & 1e-04 & 0.9998 & 0.9962 & 0.9947 \tabularnewline
105 & 107.23 & 112.1261 & 109.7907 & 114.4614 & 0 & 0.9957 & 0.994 & 0.9394 \tabularnewline
106 & 109.49 & 113.5746 & 111.1338 & 116.0153 & 5e-04 & 1 & 0.9959 & 0.9959 \tabularnewline
107 & 109.04 & 113.3657 & 110.7393 & 115.9922 & 6e-04 & 0.9981 & 0.9915 & 0.9894 \tabularnewline
108 & 109.02 & 113.4839 & 110.6752 & 116.2926 & 9e-04 & 0.999 & 0.9926 & 0.9873 \tabularnewline
109 & 109.23 & 113.876 & 110.8961 & 116.856 & 0.0011 & 0.9993 & 0.9988 & 0.991 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69818&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[94])[/C][/ROW]
[ROW][C]82[/C][C]104.66[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]83[/C][C]104.46[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]84[/C][C]104.95[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]85[/C][C]105.85[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]86[/C][C]106.23[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]87[/C][C]104.86[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]88[/C][C]107.44[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]89[/C][C]108.23[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]90[/C][C]108.45[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]91[/C][C]109.39[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]92[/C][C]110.15[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]93[/C][C]109.13[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]94[/C][C]110.28[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]95[/C][C]110.17[/C][C]110.0421[/C][C]109.3959[/C][C]110.6882[/C][C]0.349[/C][C]0.2352[/C][C]1[/C][C]0.2352[/C][/ROW]
[ROW][C]96[/C][C]109.99[/C][C]110.1598[/C][C]109.2005[/C][C]111.1191[/C][C]0.3643[/C][C]0.4917[/C][C]1[/C][C]0.403[/C][/ROW]
[ROW][C]97[/C][C]109.26[/C][C]110.552[/C][C]109.3586[/C][C]111.7454[/C][C]0.0169[/C][C]0.822[/C][C]1[/C][C]0.6725[/C][/ROW]
[ROW][C]98[/C][C]109.11[/C][C]110.7148[/C][C]109.3264[/C][C]112.1033[/C][C]0.0117[/C][C]0.98[/C][C]1[/C][C]0.7303[/C][/ROW]
[ROW][C]99[/C][C]107.06[/C][C]109.2984[/C][C]107.7391[/C][C]110.8577[/C][C]0.0024[/C][C]0.5936[/C][C]1[/C][C]0.1086[/C][/ROW]
[ROW][C]100[/C][C]109.53[/C][C]111.6516[/C][C]109.9383[/C][C]113.3648[/C][C]0.0076[/C][C]1[/C][C]1[/C][C]0.9417[/C][/ROW]
[ROW][C]101[/C][C]108.92[/C][C]112.0281[/C][C]110.1737[/C][C]113.8826[/C][C]5e-04[/C][C]0.9959[/C][C]1[/C][C]0.9677[/C][/ROW]
[ROW][C]102[/C][C]109.24[/C][C]112.3774[/C][C]110.3918[/C][C]114.363[/C][C]0.001[/C][C]0.9997[/C][C]0.9999[/C][C]0.9808[/C][/ROW]
[ROW][C]103[/C][C]109.12[/C][C]112.8112[/C][C]110.7026[/C][C]114.9199[/C][C]3e-04[/C][C]0.9995[/C][C]0.9993[/C][C]0.9907[/C][/ROW]
[ROW][C]104[/C][C]109[/C][C]113.1834[/C][C]110.9586[/C][C]115.4083[/C][C]1e-04[/C][C]0.9998[/C][C]0.9962[/C][C]0.9947[/C][/ROW]
[ROW][C]105[/C][C]107.23[/C][C]112.1261[/C][C]109.7907[/C][C]114.4614[/C][C]0[/C][C]0.9957[/C][C]0.994[/C][C]0.9394[/C][/ROW]
[ROW][C]106[/C][C]109.49[/C][C]113.5746[/C][C]111.1338[/C][C]116.0153[/C][C]5e-04[/C][C]1[/C][C]0.9959[/C][C]0.9959[/C][/ROW]
[ROW][C]107[/C][C]109.04[/C][C]113.3657[/C][C]110.7393[/C][C]115.9922[/C][C]6e-04[/C][C]0.9981[/C][C]0.9915[/C][C]0.9894[/C][/ROW]
[ROW][C]108[/C][C]109.02[/C][C]113.4839[/C][C]110.6752[/C][C]116.2926[/C][C]9e-04[/C][C]0.999[/C][C]0.9926[/C][C]0.9873[/C][/ROW]
[ROW][C]109[/C][C]109.23[/C][C]113.876[/C][C]110.8961[/C][C]116.856[/C][C]0.0011[/C][C]0.9993[/C][C]0.9988[/C][C]0.991[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69818&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69818&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[94])
82104.66-------
83104.46-------
84104.95-------
85105.85-------
86106.23-------
87104.86-------
88107.44-------
89108.23-------
90108.45-------
91109.39-------
92110.15-------
93109.13-------
94110.28-------
95110.17110.0421109.3959110.68820.3490.235210.2352
96109.99110.1598109.2005111.11910.36430.491710.403
97109.26110.552109.3586111.74540.01690.82210.6725
98109.11110.7148109.3264112.10330.01170.9810.7303
99107.06109.2984107.7391110.85770.00240.593610.1086
100109.53111.6516109.9383113.36480.0076110.9417
101108.92112.0281110.1737113.88265e-040.995910.9677
102109.24112.3774110.3918114.3630.0010.99970.99990.9808
103109.12112.8112110.7026114.91993e-040.99950.99930.9907
104109113.1834110.9586115.40831e-040.99980.99620.9947
105107.23112.1261109.7907114.461400.99570.9940.9394
106109.49113.5746111.1338116.01535e-0410.99590.9959
107109.04113.3657110.7393115.99226e-040.99810.99150.9894
108109.02113.4839110.6752116.29269e-040.9990.99260.9873
109109.23113.876110.8961116.8560.00110.99930.99880.991






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
950.0030.00121e-040.01640.00110.033
960.0044-0.00151e-040.02880.00190.0439
970.0055-0.01178e-041.66930.11130.3336
980.0064-0.01450.0012.57550.17170.4144
990.0073-0.02050.00145.01040.3340.578
1000.0078-0.0190.00134.50110.30010.5478
1010.0084-0.02770.00189.66050.6440.8025
1020.009-0.02790.00199.84330.65620.8101
1030.0095-0.03270.002213.62530.90840.9531
1040.01-0.0370.002517.5011.16671.0802
1050.0106-0.04370.002923.97131.59811.2642
1060.011-0.0360.002416.68361.11221.0546
1070.0118-0.03820.002518.7121.24751.1169
1080.0126-0.03930.002619.92621.32841.1526
1090.0134-0.04080.002721.58571.4391.1996

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
95 & 0.003 & 0.0012 & 1e-04 & 0.0164 & 0.0011 & 0.033 \tabularnewline
96 & 0.0044 & -0.0015 & 1e-04 & 0.0288 & 0.0019 & 0.0439 \tabularnewline
97 & 0.0055 & -0.0117 & 8e-04 & 1.6693 & 0.1113 & 0.3336 \tabularnewline
98 & 0.0064 & -0.0145 & 0.001 & 2.5755 & 0.1717 & 0.4144 \tabularnewline
99 & 0.0073 & -0.0205 & 0.0014 & 5.0104 & 0.334 & 0.578 \tabularnewline
100 & 0.0078 & -0.019 & 0.0013 & 4.5011 & 0.3001 & 0.5478 \tabularnewline
101 & 0.0084 & -0.0277 & 0.0018 & 9.6605 & 0.644 & 0.8025 \tabularnewline
102 & 0.009 & -0.0279 & 0.0019 & 9.8433 & 0.6562 & 0.8101 \tabularnewline
103 & 0.0095 & -0.0327 & 0.0022 & 13.6253 & 0.9084 & 0.9531 \tabularnewline
104 & 0.01 & -0.037 & 0.0025 & 17.501 & 1.1667 & 1.0802 \tabularnewline
105 & 0.0106 & -0.0437 & 0.0029 & 23.9713 & 1.5981 & 1.2642 \tabularnewline
106 & 0.011 & -0.036 & 0.0024 & 16.6836 & 1.1122 & 1.0546 \tabularnewline
107 & 0.0118 & -0.0382 & 0.0025 & 18.712 & 1.2475 & 1.1169 \tabularnewline
108 & 0.0126 & -0.0393 & 0.0026 & 19.9262 & 1.3284 & 1.1526 \tabularnewline
109 & 0.0134 & -0.0408 & 0.0027 & 21.5857 & 1.439 & 1.1996 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69818&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]95[/C][C]0.003[/C][C]0.0012[/C][C]1e-04[/C][C]0.0164[/C][C]0.0011[/C][C]0.033[/C][/ROW]
[ROW][C]96[/C][C]0.0044[/C][C]-0.0015[/C][C]1e-04[/C][C]0.0288[/C][C]0.0019[/C][C]0.0439[/C][/ROW]
[ROW][C]97[/C][C]0.0055[/C][C]-0.0117[/C][C]8e-04[/C][C]1.6693[/C][C]0.1113[/C][C]0.3336[/C][/ROW]
[ROW][C]98[/C][C]0.0064[/C][C]-0.0145[/C][C]0.001[/C][C]2.5755[/C][C]0.1717[/C][C]0.4144[/C][/ROW]
[ROW][C]99[/C][C]0.0073[/C][C]-0.0205[/C][C]0.0014[/C][C]5.0104[/C][C]0.334[/C][C]0.578[/C][/ROW]
[ROW][C]100[/C][C]0.0078[/C][C]-0.019[/C][C]0.0013[/C][C]4.5011[/C][C]0.3001[/C][C]0.5478[/C][/ROW]
[ROW][C]101[/C][C]0.0084[/C][C]-0.0277[/C][C]0.0018[/C][C]9.6605[/C][C]0.644[/C][C]0.8025[/C][/ROW]
[ROW][C]102[/C][C]0.009[/C][C]-0.0279[/C][C]0.0019[/C][C]9.8433[/C][C]0.6562[/C][C]0.8101[/C][/ROW]
[ROW][C]103[/C][C]0.0095[/C][C]-0.0327[/C][C]0.0022[/C][C]13.6253[/C][C]0.9084[/C][C]0.9531[/C][/ROW]
[ROW][C]104[/C][C]0.01[/C][C]-0.037[/C][C]0.0025[/C][C]17.501[/C][C]1.1667[/C][C]1.0802[/C][/ROW]
[ROW][C]105[/C][C]0.0106[/C][C]-0.0437[/C][C]0.0029[/C][C]23.9713[/C][C]1.5981[/C][C]1.2642[/C][/ROW]
[ROW][C]106[/C][C]0.011[/C][C]-0.036[/C][C]0.0024[/C][C]16.6836[/C][C]1.1122[/C][C]1.0546[/C][/ROW]
[ROW][C]107[/C][C]0.0118[/C][C]-0.0382[/C][C]0.0025[/C][C]18.712[/C][C]1.2475[/C][C]1.1169[/C][/ROW]
[ROW][C]108[/C][C]0.0126[/C][C]-0.0393[/C][C]0.0026[/C][C]19.9262[/C][C]1.3284[/C][C]1.1526[/C][/ROW]
[ROW][C]109[/C][C]0.0134[/C][C]-0.0408[/C][C]0.0027[/C][C]21.5857[/C][C]1.439[/C][C]1.1996[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69818&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69818&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
950.0030.00121e-040.01640.00110.033
960.0044-0.00151e-040.02880.00190.0439
970.0055-0.01178e-041.66930.11130.3336
980.0064-0.01450.0012.57550.17170.4144
990.0073-0.02050.00145.01040.3340.578
1000.0078-0.0190.00134.50110.30010.5478
1010.0084-0.02770.00189.66050.6440.8025
1020.009-0.02790.00199.84330.65620.8101
1030.0095-0.03270.002213.62530.90840.9531
1040.01-0.0370.002517.5011.16671.0802
1050.0106-0.04370.002923.97131.59811.2642
1060.011-0.0360.002416.68361.11221.0546
1070.0118-0.03820.002518.7121.24751.1169
1080.0126-0.03930.002619.92621.32841.1526
1090.0134-0.04080.002721.58571.4391.1996


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 15 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;
Parameters (R input):
par1 = 15 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 0 ; par9 = 1 ; 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')