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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 computationWed, 30 Dec 2009 16:46:48 -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/31/t1262216907ttje6cbawp4w0h0.htm/, Retrieved Thu, 02 May 2024 12:59:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71402, Retrieved Thu, 02 May 2024 12:59:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [ARIMA Backward Selection] [] [2009-11-27 14:53:14] [b98453cac15ba1066b407e146608df68]
-   PD    [ARIMA Backward Selection] [WS09 - Problem if...] [2009-12-02 16:23:55] [df6326eec97a6ca984a853b142930499]
-           [ARIMA Backward Selection] [WS09 - Backward A...] [2009-12-02 20:17:40] [df6326eec97a6ca984a853b142930499]
- RM          [ARIMA Forecasting] [WS10 - Voorspelling] [2009-12-02 21:21:36] [df6326eec97a6ca984a853b142930499]
-    D            [ARIMA Forecasting] [CaseStatistiek - ...] [2009-12-30 23:46:48] [0cc924834281808eda7297686c82928f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15
14.4
13.5
12.8
12.3
12.2
14.5
17.2
18
18.1
18
18.3
18.7
18.6
18.3
17.9
17.4
17.4
20.1
23.2
24.2
24.2
23.9
23.8
23.8
23.3
22.4
21.5
20.5
19.9
22
24.9
25.7
25.3
24.4
23.8
23.5
23
22.2
21.4
20.3
19.5
21.7
24.7
25.3
24.9
24.1
23.4
23.1
22.4
21.3
20.3
19.3
18.7
21
24
24.8
24.2
23.3
22.7
22.3
21.8
21.2
20.5
19.7
19.2
21.2
23.9
24.8
24.2
23
22.2
21.8
21.2
20.5
19.7
19
18.4
20.7
24.5
26
25.2
24.1
23.7
23.5
23.1
22.7
22.5
21.7
20.5
21.9
22.9
21.5
19
17
16.1
15.9
15.7
15.1
14.8
14.3
14.5
18.9
21.6
20.4
17.9
15.7
14.5
14
13.9
14.4
15.8
15.6
14.7
16.7
17.9
18.7
20.1
19.5
19.4
18.6
17.8
17.1
16.5
15.5
14.9
18.6
19.1
18.8
18.2
18
19
20.7
21.2
20.7
19.6
18.6
18.7
23.8
24.9
24.8
23.8
22.3
21.7
20.7
19.7
18.4
17.4
17
18
23.8
25.5
25.6
23.7
22
21.3
20.7
20.4
20.3
20.4
19.8
19.5
23.1
23.5
23.5
22.9
21.9
21.5
20.5
20.2
19.4
19.2
18.8
18.8
22.6
23.3
23
21.4
19.9
18.8
18.6
18.4
18.6
19.9
19.2
18.4
21.1
20.5
19.1
18.1
17
17.1
17.4
16.8
15.3
14.3
13.4
15.3
22.1
23.7
22.2
19.5
16.6
17.3
19.8
21.2
21.5
20.6
19.1
19.6
23.5
24
23.2
21.2

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=71402&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=71402&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71402&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[202])
19018.1-------
19117-------
19217.1-------
19317.4-------
19416.8-------
19515.3-------
19614.3-------
19713.4-------
19815.3-------
19922.1-------
20023.7-------
20122.2-------
20219.5-------
20316.616.815315.657217.97330.357800.37730
20417.315.901513.488918.31410.1280.28520.16510.0017
20519.816.135912.609319.66260.02090.25880.24120.0308
20621.216.350112.067820.63250.01320.05720.41840.0747
20721.516.016311.298820.73380.01140.01560.6170.0739
20820.615.96110.994520.92750.03360.01440.74390.0813
20919.115.07879.92920.22850.06290.01780.73860.0462
21019.615.752510.410321.09470.0790.10970.56590.0846
21123.520.867815.287126.44860.17760.67190.33260.6845
2122421.691315.828427.55430.22010.27270.25090.7681
21323.220.459414.302626.61610.19150.12980.28970.62
21421.218.499512.069624.92940.20520.0760.38020.3802

\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[202]) \tabularnewline
190 & 18.1 & - & - & - & - & - & - & - \tabularnewline
191 & 17 & - & - & - & - & - & - & - \tabularnewline
192 & 17.1 & - & - & - & - & - & - & - \tabularnewline
193 & 17.4 & - & - & - & - & - & - & - \tabularnewline
194 & 16.8 & - & - & - & - & - & - & - \tabularnewline
195 & 15.3 & - & - & - & - & - & - & - \tabularnewline
196 & 14.3 & - & - & - & - & - & - & - \tabularnewline
197 & 13.4 & - & - & - & - & - & - & - \tabularnewline
198 & 15.3 & - & - & - & - & - & - & - \tabularnewline
199 & 22.1 & - & - & - & - & - & - & - \tabularnewline
200 & 23.7 & - & - & - & - & - & - & - \tabularnewline
201 & 22.2 & - & - & - & - & - & - & - \tabularnewline
202 & 19.5 & - & - & - & - & - & - & - \tabularnewline
203 & 16.6 & 16.8153 & 15.6572 & 17.9733 & 0.3578 & 0 & 0.3773 & 0 \tabularnewline
204 & 17.3 & 15.9015 & 13.4889 & 18.3141 & 0.128 & 0.2852 & 0.1651 & 0.0017 \tabularnewline
205 & 19.8 & 16.1359 & 12.6093 & 19.6626 & 0.0209 & 0.2588 & 0.2412 & 0.0308 \tabularnewline
206 & 21.2 & 16.3501 & 12.0678 & 20.6325 & 0.0132 & 0.0572 & 0.4184 & 0.0747 \tabularnewline
207 & 21.5 & 16.0163 & 11.2988 & 20.7338 & 0.0114 & 0.0156 & 0.617 & 0.0739 \tabularnewline
208 & 20.6 & 15.961 & 10.9945 & 20.9275 & 0.0336 & 0.0144 & 0.7439 & 0.0813 \tabularnewline
209 & 19.1 & 15.0787 & 9.929 & 20.2285 & 0.0629 & 0.0178 & 0.7386 & 0.0462 \tabularnewline
210 & 19.6 & 15.7525 & 10.4103 & 21.0947 & 0.079 & 0.1097 & 0.5659 & 0.0846 \tabularnewline
211 & 23.5 & 20.8678 & 15.2871 & 26.4486 & 0.1776 & 0.6719 & 0.3326 & 0.6845 \tabularnewline
212 & 24 & 21.6913 & 15.8284 & 27.5543 & 0.2201 & 0.2727 & 0.2509 & 0.7681 \tabularnewline
213 & 23.2 & 20.4594 & 14.3026 & 26.6161 & 0.1915 & 0.1298 & 0.2897 & 0.62 \tabularnewline
214 & 21.2 & 18.4995 & 12.0696 & 24.9294 & 0.2052 & 0.076 & 0.3802 & 0.3802 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71402&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[202])[/C][/ROW]
[ROW][C]190[/C][C]18.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]191[/C][C]17[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]192[/C][C]17.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]193[/C][C]17.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]194[/C][C]16.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]195[/C][C]15.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]196[/C][C]14.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]197[/C][C]13.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]198[/C][C]15.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]199[/C][C]22.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]200[/C][C]23.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]201[/C][C]22.2[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]202[/C][C]19.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]203[/C][C]16.6[/C][C]16.8153[/C][C]15.6572[/C][C]17.9733[/C][C]0.3578[/C][C]0[/C][C]0.3773[/C][C]0[/C][/ROW]
[ROW][C]204[/C][C]17.3[/C][C]15.9015[/C][C]13.4889[/C][C]18.3141[/C][C]0.128[/C][C]0.2852[/C][C]0.1651[/C][C]0.0017[/C][/ROW]
[ROW][C]205[/C][C]19.8[/C][C]16.1359[/C][C]12.6093[/C][C]19.6626[/C][C]0.0209[/C][C]0.2588[/C][C]0.2412[/C][C]0.0308[/C][/ROW]
[ROW][C]206[/C][C]21.2[/C][C]16.3501[/C][C]12.0678[/C][C]20.6325[/C][C]0.0132[/C][C]0.0572[/C][C]0.4184[/C][C]0.0747[/C][/ROW]
[ROW][C]207[/C][C]21.5[/C][C]16.0163[/C][C]11.2988[/C][C]20.7338[/C][C]0.0114[/C][C]0.0156[/C][C]0.617[/C][C]0.0739[/C][/ROW]
[ROW][C]208[/C][C]20.6[/C][C]15.961[/C][C]10.9945[/C][C]20.9275[/C][C]0.0336[/C][C]0.0144[/C][C]0.7439[/C][C]0.0813[/C][/ROW]
[ROW][C]209[/C][C]19.1[/C][C]15.0787[/C][C]9.929[/C][C]20.2285[/C][C]0.0629[/C][C]0.0178[/C][C]0.7386[/C][C]0.0462[/C][/ROW]
[ROW][C]210[/C][C]19.6[/C][C]15.7525[/C][C]10.4103[/C][C]21.0947[/C][C]0.079[/C][C]0.1097[/C][C]0.5659[/C][C]0.0846[/C][/ROW]
[ROW][C]211[/C][C]23.5[/C][C]20.8678[/C][C]15.2871[/C][C]26.4486[/C][C]0.1776[/C][C]0.6719[/C][C]0.3326[/C][C]0.6845[/C][/ROW]
[ROW][C]212[/C][C]24[/C][C]21.6913[/C][C]15.8284[/C][C]27.5543[/C][C]0.2201[/C][C]0.2727[/C][C]0.2509[/C][C]0.7681[/C][/ROW]
[ROW][C]213[/C][C]23.2[/C][C]20.4594[/C][C]14.3026[/C][C]26.6161[/C][C]0.1915[/C][C]0.1298[/C][C]0.2897[/C][C]0.62[/C][/ROW]
[ROW][C]214[/C][C]21.2[/C][C]18.4995[/C][C]12.0696[/C][C]24.9294[/C][C]0.2052[/C][C]0.076[/C][C]0.3802[/C][C]0.3802[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71402&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71402&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[202])
19018.1-------
19117-------
19217.1-------
19317.4-------
19416.8-------
19515.3-------
19614.3-------
19713.4-------
19815.3-------
19922.1-------
20023.7-------
20122.2-------
20219.5-------
20316.616.815315.657217.97330.357800.37730
20417.315.901513.488918.31410.1280.28520.16510.0017
20519.816.135912.609319.66260.02090.25880.24120.0308
20621.216.350112.067820.63250.01320.05720.41840.0747
20721.516.016311.298820.73380.01140.01560.6170.0739
20820.615.96110.994520.92750.03360.01440.74390.0813
20919.115.07879.92920.22850.06290.01780.73860.0462
21019.615.752510.410321.09470.0790.10970.56590.0846
21123.520.867815.287126.44860.17760.67190.33260.6845
2122421.691315.828427.55430.22010.27270.25090.7681
21323.220.459414.302626.61610.19150.12980.28970.62
21421.218.499512.069624.92940.20520.0760.38020.3802






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
2030.0351-0.01280.00110.04630.00390.0621
2040.07740.08790.00731.95580.1630.4037
2050.11150.22710.018913.42541.11881.0577
2060.13360.29660.024723.5211.96011.4
2070.15030.34240.028530.07092.50591.583
2080.15880.29060.024221.52011.79331.3392
2090.17420.26670.022216.17051.34751.1608
2100.1730.24420.020414.80341.23361.1107
2110.13640.12610.01056.92830.57740.7598
2120.13790.10640.00895.32990.44420.6665
2130.15350.1340.01127.51110.62590.7912
2140.17730.1460.01227.29250.60770.7796

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
203 & 0.0351 & -0.0128 & 0.0011 & 0.0463 & 0.0039 & 0.0621 \tabularnewline
204 & 0.0774 & 0.0879 & 0.0073 & 1.9558 & 0.163 & 0.4037 \tabularnewline
205 & 0.1115 & 0.2271 & 0.0189 & 13.4254 & 1.1188 & 1.0577 \tabularnewline
206 & 0.1336 & 0.2966 & 0.0247 & 23.521 & 1.9601 & 1.4 \tabularnewline
207 & 0.1503 & 0.3424 & 0.0285 & 30.0709 & 2.5059 & 1.583 \tabularnewline
208 & 0.1588 & 0.2906 & 0.0242 & 21.5201 & 1.7933 & 1.3392 \tabularnewline
209 & 0.1742 & 0.2667 & 0.0222 & 16.1705 & 1.3475 & 1.1608 \tabularnewline
210 & 0.173 & 0.2442 & 0.0204 & 14.8034 & 1.2336 & 1.1107 \tabularnewline
211 & 0.1364 & 0.1261 & 0.0105 & 6.9283 & 0.5774 & 0.7598 \tabularnewline
212 & 0.1379 & 0.1064 & 0.0089 & 5.3299 & 0.4442 & 0.6665 \tabularnewline
213 & 0.1535 & 0.134 & 0.0112 & 7.5111 & 0.6259 & 0.7912 \tabularnewline
214 & 0.1773 & 0.146 & 0.0122 & 7.2925 & 0.6077 & 0.7796 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71402&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]203[/C][C]0.0351[/C][C]-0.0128[/C][C]0.0011[/C][C]0.0463[/C][C]0.0039[/C][C]0.0621[/C][/ROW]
[ROW][C]204[/C][C]0.0774[/C][C]0.0879[/C][C]0.0073[/C][C]1.9558[/C][C]0.163[/C][C]0.4037[/C][/ROW]
[ROW][C]205[/C][C]0.1115[/C][C]0.2271[/C][C]0.0189[/C][C]13.4254[/C][C]1.1188[/C][C]1.0577[/C][/ROW]
[ROW][C]206[/C][C]0.1336[/C][C]0.2966[/C][C]0.0247[/C][C]23.521[/C][C]1.9601[/C][C]1.4[/C][/ROW]
[ROW][C]207[/C][C]0.1503[/C][C]0.3424[/C][C]0.0285[/C][C]30.0709[/C][C]2.5059[/C][C]1.583[/C][/ROW]
[ROW][C]208[/C][C]0.1588[/C][C]0.2906[/C][C]0.0242[/C][C]21.5201[/C][C]1.7933[/C][C]1.3392[/C][/ROW]
[ROW][C]209[/C][C]0.1742[/C][C]0.2667[/C][C]0.0222[/C][C]16.1705[/C][C]1.3475[/C][C]1.1608[/C][/ROW]
[ROW][C]210[/C][C]0.173[/C][C]0.2442[/C][C]0.0204[/C][C]14.8034[/C][C]1.2336[/C][C]1.1107[/C][/ROW]
[ROW][C]211[/C][C]0.1364[/C][C]0.1261[/C][C]0.0105[/C][C]6.9283[/C][C]0.5774[/C][C]0.7598[/C][/ROW]
[ROW][C]212[/C][C]0.1379[/C][C]0.1064[/C][C]0.0089[/C][C]5.3299[/C][C]0.4442[/C][C]0.6665[/C][/ROW]
[ROW][C]213[/C][C]0.1535[/C][C]0.134[/C][C]0.0112[/C][C]7.5111[/C][C]0.6259[/C][C]0.7912[/C][/ROW]
[ROW][C]214[/C][C]0.1773[/C][C]0.146[/C][C]0.0122[/C][C]7.2925[/C][C]0.6077[/C][C]0.7796[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71402&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71402&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
2030.0351-0.01280.00110.04630.00390.0621
2040.07740.08790.00731.95580.1630.4037
2050.11150.22710.018913.42541.11881.0577
2060.13360.29660.024723.5211.96011.4
2070.15030.34240.028530.07092.50591.583
2080.15880.29060.024221.52011.79331.3392
2090.17420.26670.022216.17051.34751.1608
2100.1730.24420.020414.80341.23361.1107
2110.13640.12610.01056.92830.57740.7598
2120.13790.10640.00895.32990.44420.6665
2130.15350.1340.01127.51110.62590.7912
2140.17730.1460.01227.29250.60770.7796


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
Parameters (R input):
par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; 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')