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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 10:09:25 -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/t1229965823uuyctehkkxne64u.htm/, Retrieved Fri, 09 May 2025 16:23:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36150, Retrieved Fri, 09 May 2025 16:23:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact329

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
F    D  [Multiple Regression] [The Seatbelt Law ...] [2008-11-15 12:00:57] [93834488277b53a4510bfd06084ae13b]
-   PD    [Multiple Regression] [] [2008-11-15 18:50:27] [93834488277b53a4510bfd06084ae13b]
-    D      [Multiple Regression] [Paper - Multiple ...] [2008-12-21 14:45:31] [85841a4a203c2f9589565c024425a91b]
-   PD        [Multiple Regression] [Paper - Multiple ...] [2008-12-21 15:09:11] [85841a4a203c2f9589565c024425a91b]
- RMPD          [ARIMA Forecasting] [Paper - Arima for...] [2008-12-21 19:50:13] [85841a4a203c2f9589565c024425a91b]
-   PD              [ARIMA Forecasting] [arima forecast gas] [2008-12-22 17:09:25] [1aceffc2fa350402d9e8f8edd757a2e8] [Current]
Feedback Forum

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
127.96
127.47
126.47
125.75
125.42
125.14
125.15
125.51
125.63
126.22
126.88
127.96
128.74
129.6
131.2
132.72
134.67
135.94
136.39
136.74
137.2
137.36
138.63
141.07
143.32
147.91
152.56
151.61
156.56
157.45
158.13
159.18
159.47
159.79
161.65
162.77
163.48
166.16
163.86
162.12
149.08
145.32
141.21
134.68
133.65
139.17
138.61
144.96
157.99
167.18
174.48
182.77
190.00
189.70
188.90
198.28
201.18
204.14
221.02
221.12
220.68

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=36150&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=36150&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36150&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[49])
37163.48-------
38166.16-------
39163.86-------
40162.12-------
41149.08-------
42145.32-------
43141.21-------
44134.68-------
45133.65-------
46139.17-------
47138.61-------
48144.96-------
49157.99-------
50167.18163.7953158.0931169.49760.12230.9770.20820.977
51174.48170.572160.2991180.84490.22790.74120.89980.9918
52182.77177.5517162.8329192.27050.24360.65870.98010.9954
53190185.5764165.8787205.27420.32990.610.99990.997
54189.7190.7412166.1201215.36230.4670.52350.99990.9954
55188.9195.4575165.9617224.95330.33150.6490.99980.9936
56198.28200.1856165.8448234.52650.45670.74030.99990.992
57201.18202.9429163.8731242.01270.46480.59250.99970.9879
58204.14203.339159.6551247.02290.48570.53860.9980.9791
59221.02205.0467156.8705253.22290.25790.51470.99660.9722
60221.12204.4511151.9159256.98630.2670.26820.98680.9585
61220.68201.6585144.8952258.42180.25570.25080.93420.9342

\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[49]) \tabularnewline
37 & 163.48 & - & - & - & - & - & - & - \tabularnewline
38 & 166.16 & - & - & - & - & - & - & - \tabularnewline
39 & 163.86 & - & - & - & - & - & - & - \tabularnewline
40 & 162.12 & - & - & - & - & - & - & - \tabularnewline
41 & 149.08 & - & - & - & - & - & - & - \tabularnewline
42 & 145.32 & - & - & - & - & - & - & - \tabularnewline
43 & 141.21 & - & - & - & - & - & - & - \tabularnewline
44 & 134.68 & - & - & - & - & - & - & - \tabularnewline
45 & 133.65 & - & - & - & - & - & - & - \tabularnewline
46 & 139.17 & - & - & - & - & - & - & - \tabularnewline
47 & 138.61 & - & - & - & - & - & - & - \tabularnewline
48 & 144.96 & - & - & - & - & - & - & - \tabularnewline
49 & 157.99 & - & - & - & - & - & - & - \tabularnewline
50 & 167.18 & 163.7953 & 158.0931 & 169.4976 & 0.1223 & 0.977 & 0.2082 & 0.977 \tabularnewline
51 & 174.48 & 170.572 & 160.2991 & 180.8449 & 0.2279 & 0.7412 & 0.8998 & 0.9918 \tabularnewline
52 & 182.77 & 177.5517 & 162.8329 & 192.2705 & 0.2436 & 0.6587 & 0.9801 & 0.9954 \tabularnewline
53 & 190 & 185.5764 & 165.8787 & 205.2742 & 0.3299 & 0.61 & 0.9999 & 0.997 \tabularnewline
54 & 189.7 & 190.7412 & 166.1201 & 215.3623 & 0.467 & 0.5235 & 0.9999 & 0.9954 \tabularnewline
55 & 188.9 & 195.4575 & 165.9617 & 224.9533 & 0.3315 & 0.649 & 0.9998 & 0.9936 \tabularnewline
56 & 198.28 & 200.1856 & 165.8448 & 234.5265 & 0.4567 & 0.7403 & 0.9999 & 0.992 \tabularnewline
57 & 201.18 & 202.9429 & 163.8731 & 242.0127 & 0.4648 & 0.5925 & 0.9997 & 0.9879 \tabularnewline
58 & 204.14 & 203.339 & 159.6551 & 247.0229 & 0.4857 & 0.5386 & 0.998 & 0.9791 \tabularnewline
59 & 221.02 & 205.0467 & 156.8705 & 253.2229 & 0.2579 & 0.5147 & 0.9966 & 0.9722 \tabularnewline
60 & 221.12 & 204.4511 & 151.9159 & 256.9863 & 0.267 & 0.2682 & 0.9868 & 0.9585 \tabularnewline
61 & 220.68 & 201.6585 & 144.8952 & 258.4218 & 0.2557 & 0.2508 & 0.9342 & 0.9342 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36150&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[49])[/C][/ROW]
[ROW][C]37[/C][C]163.48[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]166.16[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]163.86[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]162.12[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]149.08[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]145.32[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]141.21[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]134.68[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]133.65[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]139.17[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]138.61[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]144.96[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]157.99[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]50[/C][C]167.18[/C][C]163.7953[/C][C]158.0931[/C][C]169.4976[/C][C]0.1223[/C][C]0.977[/C][C]0.2082[/C][C]0.977[/C][/ROW]
[ROW][C]51[/C][C]174.48[/C][C]170.572[/C][C]160.2991[/C][C]180.8449[/C][C]0.2279[/C][C]0.7412[/C][C]0.8998[/C][C]0.9918[/C][/ROW]
[ROW][C]52[/C][C]182.77[/C][C]177.5517[/C][C]162.8329[/C][C]192.2705[/C][C]0.2436[/C][C]0.6587[/C][C]0.9801[/C][C]0.9954[/C][/ROW]
[ROW][C]53[/C][C]190[/C][C]185.5764[/C][C]165.8787[/C][C]205.2742[/C][C]0.3299[/C][C]0.61[/C][C]0.9999[/C][C]0.997[/C][/ROW]
[ROW][C]54[/C][C]189.7[/C][C]190.7412[/C][C]166.1201[/C][C]215.3623[/C][C]0.467[/C][C]0.5235[/C][C]0.9999[/C][C]0.9954[/C][/ROW]
[ROW][C]55[/C][C]188.9[/C][C]195.4575[/C][C]165.9617[/C][C]224.9533[/C][C]0.3315[/C][C]0.649[/C][C]0.9998[/C][C]0.9936[/C][/ROW]
[ROW][C]56[/C][C]198.28[/C][C]200.1856[/C][C]165.8448[/C][C]234.5265[/C][C]0.4567[/C][C]0.7403[/C][C]0.9999[/C][C]0.992[/C][/ROW]
[ROW][C]57[/C][C]201.18[/C][C]202.9429[/C][C]163.8731[/C][C]242.0127[/C][C]0.4648[/C][C]0.5925[/C][C]0.9997[/C][C]0.9879[/C][/ROW]
[ROW][C]58[/C][C]204.14[/C][C]203.339[/C][C]159.6551[/C][C]247.0229[/C][C]0.4857[/C][C]0.5386[/C][C]0.998[/C][C]0.9791[/C][/ROW]
[ROW][C]59[/C][C]221.02[/C][C]205.0467[/C][C]156.8705[/C][C]253.2229[/C][C]0.2579[/C][C]0.5147[/C][C]0.9966[/C][C]0.9722[/C][/ROW]
[ROW][C]60[/C][C]221.12[/C][C]204.4511[/C][C]151.9159[/C][C]256.9863[/C][C]0.267[/C][C]0.2682[/C][C]0.9868[/C][C]0.9585[/C][/ROW]
[ROW][C]61[/C][C]220.68[/C][C]201.6585[/C][C]144.8952[/C][C]258.4218[/C][C]0.2557[/C][C]0.2508[/C][C]0.9342[/C][C]0.9342[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36150&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36150&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[49])
37163.48-------
38166.16-------
39163.86-------
40162.12-------
41149.08-------
42145.32-------
43141.21-------
44134.68-------
45133.65-------
46139.17-------
47138.61-------
48144.96-------
49157.99-------
50167.18163.7953158.0931169.49760.12230.9770.20820.977
51174.48170.572160.2991180.84490.22790.74120.89980.9918
52182.77177.5517162.8329192.27050.24360.65870.98010.9954
53190185.5764165.8787205.27420.32990.610.99990.997
54189.7190.7412166.1201215.36230.4670.52350.99990.9954
55188.9195.4575165.9617224.95330.33150.6490.99980.9936
56198.28200.1856165.8448234.52650.45670.74030.99990.992
57201.18202.9429163.8731242.01270.46480.59250.99970.9879
58204.14203.339159.6551247.02290.48570.53860.9980.9791
59221.02205.0467156.8705253.22290.25790.51470.99660.9722
60221.12204.4511151.9159256.98630.2670.26820.98680.9585
61220.68201.6585144.8952258.42180.25570.25080.93420.9342






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
500.01780.02070.001711.45610.95470.9771
510.03070.02290.001915.27251.27271.1281
520.04230.02940.002427.23072.26921.5064
530.05420.02380.00219.56781.63071.277
540.0659-0.00555e-041.08410.09030.3006
550.077-0.03350.002843.00073.58341.893
560.0875-0.00958e-043.63140.30260.5501
570.0982-0.00877e-043.10780.2590.5089
580.10960.00393e-040.64160.05350.2312
590.11990.07790.0065255.146121.26224.6111
600.13110.08150.0068277.852723.15444.8119
610.14360.09430.0079361.816830.15145.491

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
50 & 0.0178 & 0.0207 & 0.0017 & 11.4561 & 0.9547 & 0.9771 \tabularnewline
51 & 0.0307 & 0.0229 & 0.0019 & 15.2725 & 1.2727 & 1.1281 \tabularnewline
52 & 0.0423 & 0.0294 & 0.0024 & 27.2307 & 2.2692 & 1.5064 \tabularnewline
53 & 0.0542 & 0.0238 & 0.002 & 19.5678 & 1.6307 & 1.277 \tabularnewline
54 & 0.0659 & -0.0055 & 5e-04 & 1.0841 & 0.0903 & 0.3006 \tabularnewline
55 & 0.077 & -0.0335 & 0.0028 & 43.0007 & 3.5834 & 1.893 \tabularnewline
56 & 0.0875 & -0.0095 & 8e-04 & 3.6314 & 0.3026 & 0.5501 \tabularnewline
57 & 0.0982 & -0.0087 & 7e-04 & 3.1078 & 0.259 & 0.5089 \tabularnewline
58 & 0.1096 & 0.0039 & 3e-04 & 0.6416 & 0.0535 & 0.2312 \tabularnewline
59 & 0.1199 & 0.0779 & 0.0065 & 255.1461 & 21.2622 & 4.6111 \tabularnewline
60 & 0.1311 & 0.0815 & 0.0068 & 277.8527 & 23.1544 & 4.8119 \tabularnewline
61 & 0.1436 & 0.0943 & 0.0079 & 361.8168 & 30.1514 & 5.491 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36150&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]50[/C][C]0.0178[/C][C]0.0207[/C][C]0.0017[/C][C]11.4561[/C][C]0.9547[/C][C]0.9771[/C][/ROW]
[ROW][C]51[/C][C]0.0307[/C][C]0.0229[/C][C]0.0019[/C][C]15.2725[/C][C]1.2727[/C][C]1.1281[/C][/ROW]
[ROW][C]52[/C][C]0.0423[/C][C]0.0294[/C][C]0.0024[/C][C]27.2307[/C][C]2.2692[/C][C]1.5064[/C][/ROW]
[ROW][C]53[/C][C]0.0542[/C][C]0.0238[/C][C]0.002[/C][C]19.5678[/C][C]1.6307[/C][C]1.277[/C][/ROW]
[ROW][C]54[/C][C]0.0659[/C][C]-0.0055[/C][C]5e-04[/C][C]1.0841[/C][C]0.0903[/C][C]0.3006[/C][/ROW]
[ROW][C]55[/C][C]0.077[/C][C]-0.0335[/C][C]0.0028[/C][C]43.0007[/C][C]3.5834[/C][C]1.893[/C][/ROW]
[ROW][C]56[/C][C]0.0875[/C][C]-0.0095[/C][C]8e-04[/C][C]3.6314[/C][C]0.3026[/C][C]0.5501[/C][/ROW]
[ROW][C]57[/C][C]0.0982[/C][C]-0.0087[/C][C]7e-04[/C][C]3.1078[/C][C]0.259[/C][C]0.5089[/C][/ROW]
[ROW][C]58[/C][C]0.1096[/C][C]0.0039[/C][C]3e-04[/C][C]0.6416[/C][C]0.0535[/C][C]0.2312[/C][/ROW]
[ROW][C]59[/C][C]0.1199[/C][C]0.0779[/C][C]0.0065[/C][C]255.1461[/C][C]21.2622[/C][C]4.6111[/C][/ROW]
[ROW][C]60[/C][C]0.1311[/C][C]0.0815[/C][C]0.0068[/C][C]277.8527[/C][C]23.1544[/C][C]4.8119[/C][/ROW]
[ROW][C]61[/C][C]0.1436[/C][C]0.0943[/C][C]0.0079[/C][C]361.8168[/C][C]30.1514[/C][C]5.491[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36150&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36150&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
500.01780.02070.001711.45610.95470.9771
510.03070.02290.001915.27251.27271.1281
520.04230.02940.002427.23072.26921.5064
530.05420.02380.00219.56781.63071.277
540.0659-0.00555e-041.08410.09030.3006
550.077-0.03350.002843.00073.58341.893
560.0875-0.00958e-043.63140.30260.5501
570.0982-0.00877e-043.10780.2590.5089
580.10960.00393e-040.64160.05350.2312
590.11990.07790.0065255.146121.26224.6111
600.13110.08150.0068277.852723.15444.8119
610.14360.09430.0079361.816830.15145.491


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; 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')