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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 computationFri, 23 Dec 2011 09:09:56 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/23/t1324649425ou1fgkmpwid3e2s.htm/, Retrieved Mon, 29 Apr 2024 18:30:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160424, Retrieved Mon, 29 Apr 2024 18:30:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140

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   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
- RMP     [ARIMA Forecasting] [Unemployment] [2010-11-29 20:46:45] [b98453cac15ba1066b407e146608df68]
- R         [ARIMA Forecasting] [ws9] [2011-12-06 21:34:47] [8501ca4b76170905b8a207a77f626994]
-   P         [ARIMA Forecasting] [Paper deel 2 ARIM...] [2011-12-22 14:35:08] [8501ca4b76170905b8a207a77f626994]
-   PD            [ARIMA Forecasting] [Paper: ARIMA Fore...] [2011-12-23 14:09:56] [3e64eea457df40fcb7af8f28e1ee6256] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
24.90
25.06
25.10
24.92
25.46
25.89
25.39
25.38
25.25
24.88
25.00
25.00
24.07
23.60
23.18
23.25
23.04
22.77
22.25
22.41
22.50
22.91
22.88
21.69
21.19
21.56
22.00
22.13
22.27
22.30
21.94
22.40
22.77
22.90
23.03
23.05
22.41
22.26
21.90
22.01
22.62
22.76
23.40
23.63
24.05
23.82
23.71
23.95
23.61
23.98
23.56
23.99
24.33
24.48
24.31
24.38
24.63
25.54
25.75
25.73
25.85
25.78
25.86
26.86
27.36
27.38
26.58
27.65
27.73
27.18
27.32
27.30
26.90
26.70
26.75
26.41
26.29
27.51
27.91
27.70
27.28
28.25
27.62
27.30
25.94
24.99
25.50
24.42
26.58
25.84
26.76
26.74
26.68
25.55
26.40
25.19
23.94
24.20
24.20
23.07
24.07
25.02
24.65
24.68
24.63
24.49
25.05
24.31
23.90
23.68
24.50
25.22
25.48
26.00
26.07
26.06
26.22
26.70
27.20
26.77
26.11
25.43
24.99
25.51
24.00
23.86
22.96
23.41
23.17
24.12
23.87
24.27
24.40
24.16
25.15
25.09
24.60
24.33
24.14
24.36
25.40
26.15
26.77
26.94
26.33
26.24
26.23
25.88
27.00
26.91
27.15
27.78
28.73
28.83
28.68
27.56
27.15
27.41
27.47
28.76
28.47
27.94
27.23
27.01
26.15
26.11
27.20
27.36
27.33
27.43
28.92
29.45
29.01
29.25
29.14
29.64
30.40
30.62
31.25
31.75
31.30
30.70
31.03
31.46
31.28
31.03
30.95
31.17
31.29
31.91
32.10
31.71
31.90
32.02
32.65
33.77
33.51
34.26
34.21
34.13
34.73
34.73
34.57
34.80
33.98
34.40
34.21
34.61
35.25
35.23
35.00
34.52
33.82
34.35
34.81
34.96
36.69
36.42
36.44
37.41
36.40
36.15
35.78
36.95
36.14
36.36
37.31
37.58
38.00
37.23
37.00
37.87
37.70
36.17
36.56
37.70
38.77
39.02
39.88
39.56
38.52
37.20
38.58
39.41
39.08
38.81
38.73
38.70
39.23
39.82
39.97
40.37
39.54
39.21
39.07
39.78
39.40
38.92

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160424&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160424&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160424&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






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[246])
23436.17-------
23536.56-------
23637.7-------
23738.77-------
23839.02-------
23939.88-------
24039.56-------
24138.52-------
24237.2-------
24338.58-------
24439.41-------
24539.08-------
24638.81-------
24738.7338.854237.252240.52510.44210.52070.99640.5207
24838.738.995336.757441.36950.40370.58670.85750.5608
24939.2339.125736.380942.07760.47240.61130.59340.583
25039.8239.155735.994642.59450.35250.48310.53080.5781
25139.9739.257735.726743.13780.35950.38820.37660.5895
25240.3739.2235.369243.490.29880.36530.4380.5746
25339.5439.095534.963543.71570.42520.29440.59640.5482
25439.2138.933134.548743.87390.45630.40490.75410.5195
25539.0739.102734.446944.38780.49520.48410.57690.5432
25639.7839.202234.297144.80880.420.51840.4710.5545
25739.439.162934.038645.05850.46860.41870.5110.5467
25838.9239.130533.79845.30430.47340.46590.54050.5405

\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[246]) \tabularnewline
234 & 36.17 & - & - & - & - & - & - & - \tabularnewline
235 & 36.56 & - & - & - & - & - & - & - \tabularnewline
236 & 37.7 & - & - & - & - & - & - & - \tabularnewline
237 & 38.77 & - & - & - & - & - & - & - \tabularnewline
238 & 39.02 & - & - & - & - & - & - & - \tabularnewline
239 & 39.88 & - & - & - & - & - & - & - \tabularnewline
240 & 39.56 & - & - & - & - & - & - & - \tabularnewline
241 & 38.52 & - & - & - & - & - & - & - \tabularnewline
242 & 37.2 & - & - & - & - & - & - & - \tabularnewline
243 & 38.58 & - & - & - & - & - & - & - \tabularnewline
244 & 39.41 & - & - & - & - & - & - & - \tabularnewline
245 & 39.08 & - & - & - & - & - & - & - \tabularnewline
246 & 38.81 & - & - & - & - & - & - & - \tabularnewline
247 & 38.73 & 38.8542 & 37.2522 & 40.5251 & 0.4421 & 0.5207 & 0.9964 & 0.5207 \tabularnewline
248 & 38.7 & 38.9953 & 36.7574 & 41.3695 & 0.4037 & 0.5867 & 0.8575 & 0.5608 \tabularnewline
249 & 39.23 & 39.1257 & 36.3809 & 42.0776 & 0.4724 & 0.6113 & 0.5934 & 0.583 \tabularnewline
250 & 39.82 & 39.1557 & 35.9946 & 42.5945 & 0.3525 & 0.4831 & 0.5308 & 0.5781 \tabularnewline
251 & 39.97 & 39.2577 & 35.7267 & 43.1378 & 0.3595 & 0.3882 & 0.3766 & 0.5895 \tabularnewline
252 & 40.37 & 39.22 & 35.3692 & 43.49 & 0.2988 & 0.3653 & 0.438 & 0.5746 \tabularnewline
253 & 39.54 & 39.0955 & 34.9635 & 43.7157 & 0.4252 & 0.2944 & 0.5964 & 0.5482 \tabularnewline
254 & 39.21 & 38.9331 & 34.5487 & 43.8739 & 0.4563 & 0.4049 & 0.7541 & 0.5195 \tabularnewline
255 & 39.07 & 39.1027 & 34.4469 & 44.3878 & 0.4952 & 0.4841 & 0.5769 & 0.5432 \tabularnewline
256 & 39.78 & 39.2022 & 34.2971 & 44.8088 & 0.42 & 0.5184 & 0.471 & 0.5545 \tabularnewline
257 & 39.4 & 39.1629 & 34.0386 & 45.0585 & 0.4686 & 0.4187 & 0.511 & 0.5467 \tabularnewline
258 & 38.92 & 39.1305 & 33.798 & 45.3043 & 0.4734 & 0.4659 & 0.5405 & 0.5405 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160424&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[246])[/C][/ROW]
[ROW][C]234[/C][C]36.17[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]235[/C][C]36.56[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]236[/C][C]37.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]237[/C][C]38.77[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]238[/C][C]39.02[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]239[/C][C]39.88[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]240[/C][C]39.56[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]241[/C][C]38.52[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]242[/C][C]37.2[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]243[/C][C]38.58[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]244[/C][C]39.41[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]245[/C][C]39.08[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]246[/C][C]38.81[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]247[/C][C]38.73[/C][C]38.8542[/C][C]37.2522[/C][C]40.5251[/C][C]0.4421[/C][C]0.5207[/C][C]0.9964[/C][C]0.5207[/C][/ROW]
[ROW][C]248[/C][C]38.7[/C][C]38.9953[/C][C]36.7574[/C][C]41.3695[/C][C]0.4037[/C][C]0.5867[/C][C]0.8575[/C][C]0.5608[/C][/ROW]
[ROW][C]249[/C][C]39.23[/C][C]39.1257[/C][C]36.3809[/C][C]42.0776[/C][C]0.4724[/C][C]0.6113[/C][C]0.5934[/C][C]0.583[/C][/ROW]
[ROW][C]250[/C][C]39.82[/C][C]39.1557[/C][C]35.9946[/C][C]42.5945[/C][C]0.3525[/C][C]0.4831[/C][C]0.5308[/C][C]0.5781[/C][/ROW]
[ROW][C]251[/C][C]39.97[/C][C]39.2577[/C][C]35.7267[/C][C]43.1378[/C][C]0.3595[/C][C]0.3882[/C][C]0.3766[/C][C]0.5895[/C][/ROW]
[ROW][C]252[/C][C]40.37[/C][C]39.22[/C][C]35.3692[/C][C]43.49[/C][C]0.2988[/C][C]0.3653[/C][C]0.438[/C][C]0.5746[/C][/ROW]
[ROW][C]253[/C][C]39.54[/C][C]39.0955[/C][C]34.9635[/C][C]43.7157[/C][C]0.4252[/C][C]0.2944[/C][C]0.5964[/C][C]0.5482[/C][/ROW]
[ROW][C]254[/C][C]39.21[/C][C]38.9331[/C][C]34.5487[/C][C]43.8739[/C][C]0.4563[/C][C]0.4049[/C][C]0.7541[/C][C]0.5195[/C][/ROW]
[ROW][C]255[/C][C]39.07[/C][C]39.1027[/C][C]34.4469[/C][C]44.3878[/C][C]0.4952[/C][C]0.4841[/C][C]0.5769[/C][C]0.5432[/C][/ROW]
[ROW][C]256[/C][C]39.78[/C][C]39.2022[/C][C]34.2971[/C][C]44.8088[/C][C]0.42[/C][C]0.5184[/C][C]0.471[/C][C]0.5545[/C][/ROW]
[ROW][C]257[/C][C]39.4[/C][C]39.1629[/C][C]34.0386[/C][C]45.0585[/C][C]0.4686[/C][C]0.4187[/C][C]0.511[/C][C]0.5467[/C][/ROW]
[ROW][C]258[/C][C]38.92[/C][C]39.1305[/C][C]33.798[/C][C]45.3043[/C][C]0.4734[/C][C]0.4659[/C][C]0.5405[/C][C]0.5405[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160424&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160424&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[246])
23436.17-------
23536.56-------
23637.7-------
23738.77-------
23839.02-------
23939.88-------
24039.56-------
24138.52-------
24237.2-------
24338.58-------
24439.41-------
24539.08-------
24638.81-------
24738.7338.854237.252240.52510.44210.52070.99640.5207
24838.738.995336.757441.36950.40370.58670.85750.5608
24939.2339.125736.380942.07760.47240.61130.59340.583
25039.8239.155735.994642.59450.35250.48310.53080.5781
25139.9739.257735.726743.13780.35950.38820.37660.5895
25240.3739.2235.369243.490.29880.36530.4380.5746
25339.5439.095534.963543.71570.42520.29440.59640.5482
25439.2138.933134.548743.87390.45630.40490.75410.5195
25539.0739.102734.446944.38780.49520.48410.57690.5432
25639.7839.202234.297144.80880.420.51840.4710.5545
25739.439.162934.038645.05850.46860.41870.5110.5467
25838.9239.130533.79845.30430.47340.46590.54050.5405






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
2470.0219-0.003200.015400
2480.0311-0.00760.00540.08720.05130.2265
2490.03850.00270.00450.01090.03780.1945
2500.04480.0170.00760.44130.13870.3724
2510.05040.01810.00970.50730.21240.4609
2520.05550.02930.0131.32250.39740.6304
2530.06030.01140.01270.19760.36890.6074
2540.06470.00710.0120.07670.33240.5765
2550.069-8e-040.01080.00110.29560.5437
2560.0730.01470.01120.33380.29940.5472
2570.07680.00610.01070.05620.27730.5266
2580.0805-0.00540.01030.04430.25790.5078

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
247 & 0.0219 & -0.0032 & 0 & 0.0154 & 0 & 0 \tabularnewline
248 & 0.0311 & -0.0076 & 0.0054 & 0.0872 & 0.0513 & 0.2265 \tabularnewline
249 & 0.0385 & 0.0027 & 0.0045 & 0.0109 & 0.0378 & 0.1945 \tabularnewline
250 & 0.0448 & 0.017 & 0.0076 & 0.4413 & 0.1387 & 0.3724 \tabularnewline
251 & 0.0504 & 0.0181 & 0.0097 & 0.5073 & 0.2124 & 0.4609 \tabularnewline
252 & 0.0555 & 0.0293 & 0.013 & 1.3225 & 0.3974 & 0.6304 \tabularnewline
253 & 0.0603 & 0.0114 & 0.0127 & 0.1976 & 0.3689 & 0.6074 \tabularnewline
254 & 0.0647 & 0.0071 & 0.012 & 0.0767 & 0.3324 & 0.5765 \tabularnewline
255 & 0.069 & -8e-04 & 0.0108 & 0.0011 & 0.2956 & 0.5437 \tabularnewline
256 & 0.073 & 0.0147 & 0.0112 & 0.3338 & 0.2994 & 0.5472 \tabularnewline
257 & 0.0768 & 0.0061 & 0.0107 & 0.0562 & 0.2773 & 0.5266 \tabularnewline
258 & 0.0805 & -0.0054 & 0.0103 & 0.0443 & 0.2579 & 0.5078 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160424&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]247[/C][C]0.0219[/C][C]-0.0032[/C][C]0[/C][C]0.0154[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]248[/C][C]0.0311[/C][C]-0.0076[/C][C]0.0054[/C][C]0.0872[/C][C]0.0513[/C][C]0.2265[/C][/ROW]
[ROW][C]249[/C][C]0.0385[/C][C]0.0027[/C][C]0.0045[/C][C]0.0109[/C][C]0.0378[/C][C]0.1945[/C][/ROW]
[ROW][C]250[/C][C]0.0448[/C][C]0.017[/C][C]0.0076[/C][C]0.4413[/C][C]0.1387[/C][C]0.3724[/C][/ROW]
[ROW][C]251[/C][C]0.0504[/C][C]0.0181[/C][C]0.0097[/C][C]0.5073[/C][C]0.2124[/C][C]0.4609[/C][/ROW]
[ROW][C]252[/C][C]0.0555[/C][C]0.0293[/C][C]0.013[/C][C]1.3225[/C][C]0.3974[/C][C]0.6304[/C][/ROW]
[ROW][C]253[/C][C]0.0603[/C][C]0.0114[/C][C]0.0127[/C][C]0.1976[/C][C]0.3689[/C][C]0.6074[/C][/ROW]
[ROW][C]254[/C][C]0.0647[/C][C]0.0071[/C][C]0.012[/C][C]0.0767[/C][C]0.3324[/C][C]0.5765[/C][/ROW]
[ROW][C]255[/C][C]0.069[/C][C]-8e-04[/C][C]0.0108[/C][C]0.0011[/C][C]0.2956[/C][C]0.5437[/C][/ROW]
[ROW][C]256[/C][C]0.073[/C][C]0.0147[/C][C]0.0112[/C][C]0.3338[/C][C]0.2994[/C][C]0.5472[/C][/ROW]
[ROW][C]257[/C][C]0.0768[/C][C]0.0061[/C][C]0.0107[/C][C]0.0562[/C][C]0.2773[/C][C]0.5266[/C][/ROW]
[ROW][C]258[/C][C]0.0805[/C][C]-0.0054[/C][C]0.0103[/C][C]0.0443[/C][C]0.2579[/C][C]0.5078[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160424&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160424&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
2470.0219-0.003200.015400
2480.0311-0.00760.00540.08720.05130.2265
2490.03850.00270.00450.01090.03780.1945
2500.04480.0170.00760.44130.13870.3724
2510.05040.01810.00970.50730.21240.4609
2520.05550.02930.0131.32250.39740.6304
2530.06030.01140.01270.19760.36890.6074
2540.06470.00710.0120.07670.33240.5765
2550.069-8e-040.01080.00110.29560.5437
2560.0730.01470.01120.33380.29940.5472
2570.07680.00610.01070.05620.27730.5266
2580.0805-0.00540.01030.04430.25790.5078


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Valutakoersen Eur-Dollar ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 2 ; par7 = 0 ; par8 = 1 ; 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,par1))
(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.mape1 <- array(0, dim=fx)
perf.se <- array(0, dim=fx)
perf.mse <- array(0, dim=fx)
perf.mse1 <- 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$pred[i]
perf.se[i] = (x[nx+i] - forecast$pred[i])^2
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[1] = abs(perf.pe[1])
perf.mse[1] = abs(perf.se[1])
for (i in 2:fx) {
perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i])
perf.mape1[i] = perf.mape[i] / i
perf.mse[i] = perf.mse[i-1] + perf.se[i]
perf.mse1[i] = perf.mse[i] / i
}
perf.rmse = sqrt(perf.mse1)
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:par1] <- 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.mape1[i],4))
a<-table.element(a,round(perf.se[i],4))
a<-table.element(a,round(perf.mse1[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')