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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 computationSat, 12 Dec 2009 02:45:03 -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/12/t12606111437nflhs6bff082d6.htm/, Retrieved Mon, 29 Apr 2024 10:01:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=66855, Retrieved Mon, 29 Apr 2024 10:01:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact188

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] [4f297b039e1043ebee7ff7a83b1eaaaa] [Current]
-    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] [3425351e86519d261a643e224a0c8ee1]
-   PD              [ARIMA Forecasting] [ARIMA forecasting] [2009-12-21 15:59:35] [76ab39dc7a55316678260825bd5ad46c]
-   PD        [ARIMA Forecasting] [Forecasting] [2009-12-14 15:18:19] [24c4941ee50deadff4640c9c09cc70cb]
-   P         [ARIMA Forecasting] [Paper ARIMA F IGP] [2009-12-14 21:07:10] [134dc66689e3d457a82860db6471d419]
-   PD          [ARIMA Forecasting] [Paper ARIMA F ICP] [2009-12-15 20:21:11] [134dc66689e3d457a82860db6471d419]
-   P           [ARIMA Forecasting] [Paper ARIMA F IGP 12] [2009-12-15 20:24:19] [134dc66689e3d457a82860db6471d419]
- R PD            [ARIMA Forecasting] [Paper arima forec...] [2009-12-23 22:37:42] [62d3ced7fb1c10c35a82e9cb1d0d0e2b]
- R PD            [ARIMA Forecasting] [Paper arima forec...] [2009-12-23 23:25:41] [62d3ced7fb1c10c35a82e9cb1d0d0e2b]
-   P         [ARIMA Forecasting] [workshop 10] [2009-12-18 17:50:14] [28d531aeb5ea2ff1b676cbab66947a19]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100.01
103.84
104.48
95.43
104.80
108.64
105.65
108.42
115.35
113.64
115.24
100.33
101.29
104.48
99.26
100.11
103.52
101.18
96.39
97.56
96.39
85.10
79.77
79.13
80.84
82.75
92.55
96.60
96.92
95.32
98.52
100.22
104.91
103.10
97.13
103.42
111.72
118.11
111.62
100.22
102.03
105.76
107.68
110.77
105.44
112.26
114.07
117.90
124.72
126.42
134.73
135.79
143.36
140.37
144.74
151.98
150.92
163.38
154.43
146.66
157.95
162.10
180.42
179.57
171.58
185.43
190.64
203.00
202.36
193.41
186.17
192.24
209.60
206.41
209.82
230.37
235.80
232.07
244.64
242.19
217.48
209.39
211.73
221.00
203.11
214.71
224.19
238.04
238.36
246.24
259.87
249.97
266.48
282.98
306.31
301.73
314.62
332.62
355.51
370.32
408.13
433.58
440.51
386.29
342.84
254.97
203.42
170.09
174.03
167.85
177.01
188.19
211.20
240.91
230.26
251.25
241.66

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=66855&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=66855&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66855&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[105])
93266.48-------
94282.98-------
95306.31-------
96301.73-------
97314.62-------
98332.62-------
99355.51-------
100370.32-------
101408.13-------
102433.58-------
103440.51-------
104386.29-------
105342.84-------
106254.97299.39273.8088324.97123e-044e-040.89574e-04
107203.42255.94198.7386313.14140.0360.51330.04220.0015
108170.09212.49116.7738308.20620.19260.57370.03380.0038
109174.03169.0428.9258309.15420.47220.49410.02090.0075
110167.85125.59-64.1256315.30560.33120.30840.01620.0124
111177.0182.14-161.8895326.16950.2230.24560.01410.0181
112188.1938.69-263.9913341.37130.16650.18520.01590.0244
113211.2-4.76-370.1332360.61320.12330.15030.01340.0311
114240.91-48.21-480.0711383.65110.09470.11950.01440.038
115230.26-91.66-593.6002410.28020.10440.0970.01890.0449
116251.25-135.11-710.5458440.32580.09410.10670.03790.0518
117241.66-178.56-830.7562473.63620.10330.09820.05860.0586

\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[105]) \tabularnewline
93 & 266.48 & - & - & - & - & - & - & - \tabularnewline
94 & 282.98 & - & - & - & - & - & - & - \tabularnewline
95 & 306.31 & - & - & - & - & - & - & - \tabularnewline
96 & 301.73 & - & - & - & - & - & - & - \tabularnewline
97 & 314.62 & - & - & - & - & - & - & - \tabularnewline
98 & 332.62 & - & - & - & - & - & - & - \tabularnewline
99 & 355.51 & - & - & - & - & - & - & - \tabularnewline
100 & 370.32 & - & - & - & - & - & - & - \tabularnewline
101 & 408.13 & - & - & - & - & - & - & - \tabularnewline
102 & 433.58 & - & - & - & - & - & - & - \tabularnewline
103 & 440.51 & - & - & - & - & - & - & - \tabularnewline
104 & 386.29 & - & - & - & - & - & - & - \tabularnewline
105 & 342.84 & - & - & - & - & - & - & - \tabularnewline
106 & 254.97 & 299.39 & 273.8088 & 324.9712 & 3e-04 & 4e-04 & 0.8957 & 4e-04 \tabularnewline
107 & 203.42 & 255.94 & 198.7386 & 313.1414 & 0.036 & 0.5133 & 0.0422 & 0.0015 \tabularnewline
108 & 170.09 & 212.49 & 116.7738 & 308.2062 & 0.1926 & 0.5737 & 0.0338 & 0.0038 \tabularnewline
109 & 174.03 & 169.04 & 28.9258 & 309.1542 & 0.4722 & 0.4941 & 0.0209 & 0.0075 \tabularnewline
110 & 167.85 & 125.59 & -64.1256 & 315.3056 & 0.3312 & 0.3084 & 0.0162 & 0.0124 \tabularnewline
111 & 177.01 & 82.14 & -161.8895 & 326.1695 & 0.223 & 0.2456 & 0.0141 & 0.0181 \tabularnewline
112 & 188.19 & 38.69 & -263.9913 & 341.3713 & 0.1665 & 0.1852 & 0.0159 & 0.0244 \tabularnewline
113 & 211.2 & -4.76 & -370.1332 & 360.6132 & 0.1233 & 0.1503 & 0.0134 & 0.0311 \tabularnewline
114 & 240.91 & -48.21 & -480.0711 & 383.6511 & 0.0947 & 0.1195 & 0.0144 & 0.038 \tabularnewline
115 & 230.26 & -91.66 & -593.6002 & 410.2802 & 0.1044 & 0.097 & 0.0189 & 0.0449 \tabularnewline
116 & 251.25 & -135.11 & -710.5458 & 440.3258 & 0.0941 & 0.1067 & 0.0379 & 0.0518 \tabularnewline
117 & 241.66 & -178.56 & -830.7562 & 473.6362 & 0.1033 & 0.0982 & 0.0586 & 0.0586 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66855&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[105])[/C][/ROW]
[ROW][C]93[/C][C]266.48[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]94[/C][C]282.98[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]95[/C][C]306.31[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]96[/C][C]301.73[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]97[/C][C]314.62[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]98[/C][C]332.62[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]99[/C][C]355.51[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]100[/C][C]370.32[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]101[/C][C]408.13[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]102[/C][C]433.58[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]103[/C][C]440.51[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]104[/C][C]386.29[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]105[/C][C]342.84[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]106[/C][C]254.97[/C][C]299.39[/C][C]273.8088[/C][C]324.9712[/C][C]3e-04[/C][C]4e-04[/C][C]0.8957[/C][C]4e-04[/C][/ROW]
[ROW][C]107[/C][C]203.42[/C][C]255.94[/C][C]198.7386[/C][C]313.1414[/C][C]0.036[/C][C]0.5133[/C][C]0.0422[/C][C]0.0015[/C][/ROW]
[ROW][C]108[/C][C]170.09[/C][C]212.49[/C][C]116.7738[/C][C]308.2062[/C][C]0.1926[/C][C]0.5737[/C][C]0.0338[/C][C]0.0038[/C][/ROW]
[ROW][C]109[/C][C]174.03[/C][C]169.04[/C][C]28.9258[/C][C]309.1542[/C][C]0.4722[/C][C]0.4941[/C][C]0.0209[/C][C]0.0075[/C][/ROW]
[ROW][C]110[/C][C]167.85[/C][C]125.59[/C][C]-64.1256[/C][C]315.3056[/C][C]0.3312[/C][C]0.3084[/C][C]0.0162[/C][C]0.0124[/C][/ROW]
[ROW][C]111[/C][C]177.01[/C][C]82.14[/C][C]-161.8895[/C][C]326.1695[/C][C]0.223[/C][C]0.2456[/C][C]0.0141[/C][C]0.0181[/C][/ROW]
[ROW][C]112[/C][C]188.19[/C][C]38.69[/C][C]-263.9913[/C][C]341.3713[/C][C]0.1665[/C][C]0.1852[/C][C]0.0159[/C][C]0.0244[/C][/ROW]
[ROW][C]113[/C][C]211.2[/C][C]-4.76[/C][C]-370.1332[/C][C]360.6132[/C][C]0.1233[/C][C]0.1503[/C][C]0.0134[/C][C]0.0311[/C][/ROW]
[ROW][C]114[/C][C]240.91[/C][C]-48.21[/C][C]-480.0711[/C][C]383.6511[/C][C]0.0947[/C][C]0.1195[/C][C]0.0144[/C][C]0.038[/C][/ROW]
[ROW][C]115[/C][C]230.26[/C][C]-91.66[/C][C]-593.6002[/C][C]410.2802[/C][C]0.1044[/C][C]0.097[/C][C]0.0189[/C][C]0.0449[/C][/ROW]
[ROW][C]116[/C][C]251.25[/C][C]-135.11[/C][C]-710.5458[/C][C]440.3258[/C][C]0.0941[/C][C]0.1067[/C][C]0.0379[/C][C]0.0518[/C][/ROW]
[ROW][C]117[/C][C]241.66[/C][C]-178.56[/C][C]-830.7562[/C][C]473.6362[/C][C]0.1033[/C][C]0.0982[/C][C]0.0586[/C][C]0.0586[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66855&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66855&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[105])
93266.48-------
94282.98-------
95306.31-------
96301.73-------
97314.62-------
98332.62-------
99355.51-------
100370.32-------
101408.13-------
102433.58-------
103440.51-------
104386.29-------
105342.84-------
106254.97299.39273.8088324.97123e-044e-040.89574e-04
107203.42255.94198.7386313.14140.0360.51330.04220.0015
108170.09212.49116.7738308.20620.19260.57370.03380.0038
109174.03169.0428.9258309.15420.47220.49410.02090.0075
110167.85125.59-64.1256315.30560.33120.30840.01620.0124
111177.0182.14-161.8895326.16950.2230.24560.01410.0181
112188.1938.69-263.9913341.37130.16650.18520.01590.0244
113211.2-4.76-370.1332360.61320.12330.15030.01340.0311
114240.91-48.21-480.0711383.65110.09470.11950.01440.038
115230.26-91.66-593.6002410.28020.10440.0970.01890.0449
116251.25-135.11-710.5458440.32580.09410.10670.03790.0518
117241.66-178.56-830.7562473.63620.10330.09820.05860.0586






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
1060.0436-0.14840.01241973.1364164.42812.8229
1070.114-0.20520.01712758.3504229.862515.1612
1080.2298-0.19950.01661797.76149.813312.2398
1090.42290.02950.002524.90012.0751.4405
1100.77070.33650.0281785.9076148.825612.1994
1111.51581.1550.09629000.3169750.026427.3866
1123.99153.8640.32222350.251862.520843.1569
113-39.1628-45.36973.780846638.72163886.560162.3423
114-4.5704-5.99710.499883590.37446965.864583.4618
115-2.7939-3.51210.2927103632.48648636.040592.9303
116-2.173-2.85960.2383149274.049612439.5041111.5325
117-1.8635-2.35340.1961176584.848414715.404121.3071

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
106 & 0.0436 & -0.1484 & 0.0124 & 1973.1364 & 164.428 & 12.8229 \tabularnewline
107 & 0.114 & -0.2052 & 0.0171 & 2758.3504 & 229.8625 & 15.1612 \tabularnewline
108 & 0.2298 & -0.1995 & 0.0166 & 1797.76 & 149.8133 & 12.2398 \tabularnewline
109 & 0.4229 & 0.0295 & 0.0025 & 24.9001 & 2.075 & 1.4405 \tabularnewline
110 & 0.7707 & 0.3365 & 0.028 & 1785.9076 & 148.8256 & 12.1994 \tabularnewline
111 & 1.5158 & 1.155 & 0.0962 & 9000.3169 & 750.0264 & 27.3866 \tabularnewline
112 & 3.9915 & 3.864 & 0.322 & 22350.25 & 1862.5208 & 43.1569 \tabularnewline
113 & -39.1628 & -45.3697 & 3.7808 & 46638.7216 & 3886.5601 & 62.3423 \tabularnewline
114 & -4.5704 & -5.9971 & 0.4998 & 83590.3744 & 6965.8645 & 83.4618 \tabularnewline
115 & -2.7939 & -3.5121 & 0.2927 & 103632.4864 & 8636.0405 & 92.9303 \tabularnewline
116 & -2.173 & -2.8596 & 0.2383 & 149274.0496 & 12439.5041 & 111.5325 \tabularnewline
117 & -1.8635 & -2.3534 & 0.1961 & 176584.8484 & 14715.404 & 121.3071 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66855&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]106[/C][C]0.0436[/C][C]-0.1484[/C][C]0.0124[/C][C]1973.1364[/C][C]164.428[/C][C]12.8229[/C][/ROW]
[ROW][C]107[/C][C]0.114[/C][C]-0.2052[/C][C]0.0171[/C][C]2758.3504[/C][C]229.8625[/C][C]15.1612[/C][/ROW]
[ROW][C]108[/C][C]0.2298[/C][C]-0.1995[/C][C]0.0166[/C][C]1797.76[/C][C]149.8133[/C][C]12.2398[/C][/ROW]
[ROW][C]109[/C][C]0.4229[/C][C]0.0295[/C][C]0.0025[/C][C]24.9001[/C][C]2.075[/C][C]1.4405[/C][/ROW]
[ROW][C]110[/C][C]0.7707[/C][C]0.3365[/C][C]0.028[/C][C]1785.9076[/C][C]148.8256[/C][C]12.1994[/C][/ROW]
[ROW][C]111[/C][C]1.5158[/C][C]1.155[/C][C]0.0962[/C][C]9000.3169[/C][C]750.0264[/C][C]27.3866[/C][/ROW]
[ROW][C]112[/C][C]3.9915[/C][C]3.864[/C][C]0.322[/C][C]22350.25[/C][C]1862.5208[/C][C]43.1569[/C][/ROW]
[ROW][C]113[/C][C]-39.1628[/C][C]-45.3697[/C][C]3.7808[/C][C]46638.7216[/C][C]3886.5601[/C][C]62.3423[/C][/ROW]
[ROW][C]114[/C][C]-4.5704[/C][C]-5.9971[/C][C]0.4998[/C][C]83590.3744[/C][C]6965.8645[/C][C]83.4618[/C][/ROW]
[ROW][C]115[/C][C]-2.7939[/C][C]-3.5121[/C][C]0.2927[/C][C]103632.4864[/C][C]8636.0405[/C][C]92.9303[/C][/ROW]
[ROW][C]116[/C][C]-2.173[/C][C]-2.8596[/C][C]0.2383[/C][C]149274.0496[/C][C]12439.5041[/C][C]111.5325[/C][/ROW]
[ROW][C]117[/C][C]-1.8635[/C][C]-2.3534[/C][C]0.1961[/C][C]176584.8484[/C][C]14715.404[/C][C]121.3071[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66855&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66855&T=2

As an alternative you can also use a QR Code:  
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The GUIDs for individual cells are displayed in the table below:

Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
1060.0436-0.14840.01241973.1364164.42812.8229
1070.114-0.20520.01712758.3504229.862515.1612
1080.2298-0.19950.01661797.76149.813312.2398
1090.42290.02950.002524.90012.0751.4405
1100.77070.33650.0281785.9076148.825612.1994
1111.51581.1550.09629000.3169750.026427.3866
1123.99153.8640.32222350.251862.520843.1569
113-39.1628-45.36973.780846638.72163886.560162.3423
114-4.5704-5.99710.499883590.37446965.864583.4618
115-2.7939-3.51210.2927103632.48648636.040592.9303
116-2.173-2.85960.2383149274.049612439.5041111.5325
117-1.8635-2.35340.1961176584.848414715.404121.3071


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; 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')