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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 computationThu, 21 Dec 2017 14:45:21 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/21/t1513863937jvizio5ghedpeu3.htm/, Retrieved Tue, 14 May 2024 15:27:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310639, Retrieved Tue, 14 May 2024 15:27:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact54

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [ARIMA Forecasting] [] [2017-12-21 13:45:21] [3e750cbf09f2d23face9e1dcccb73239] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
74,2
91,7
100,7
82,7
95,1
93,3
57,5
76,7
99,2
101,5
96,1
85,9
84,4
90,8
101,9
88,7
94
101,2
61,2
80,1
98,3
100,6
90,6
83,1
82,4
87,8
94,1
89,8
84,9
91,7
63,2
70,4
97
98,5
79,2
78,7
78,7
85,7
86,4
82,7
76,1
89,7
64,4
67,9
93,1
95,7
81,3
78,6
76,1
85,8
101,5
88,5
75,8
99,1
57,8
75,8
98,8
93
93,4
88,2
80,3
92,3
98,5
92,9
85,8
100,7
60,9
80,1
106,8
93,7
98,2
91,7
86,9
93,3
106,2
86,5
91,8
107,8
60,4
84
108,3
105,6
102
93,7
91,5
101,6
109,9
96,8
100,3
116,3
71,3
96,8
112,9
117,8
104,4
95,4
92,2
103,3
103,4
112
102,2
114,9
80,2
81,4
122,1
121,6
98,4
98,2
90,2
100,8
108,8
95,9
87,7
103,9
73,2
86,6
116,1
111,4
99,5
96,5
90,7
98,9
112
100,4
94,4
111,2
71
86,8
119,5
106,3
101,5
107,3
89,2
102,6
112,3
94,3
102,2
103,4
72,2
95,9
118,8
105,1
97,2
101,9
93,4
108,4
110,7
90,8
99,6
111,6
72,4
88,1
111,6
101,6
95,2
83,8
80,2
88,2
92,6
87,7
91,8
94,2
68,8
73,7
99,3
96,8
89,1
87,9
82,8
92,6
94,7
87,8
83,3
90,3
70,6
69,9
95,6
102,3
81,1
84,2
83,8
87,6
98,8
90
80,3
104
70,5
73,2
105,9
100,1
87,5
86
79
94,4
98,6
90,2
89,7
105,7
66,9
79,5
100,2
94,6
92,1
90,4
81
89,4
103,5
79,8
89
100
68
73,7

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time5 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310639&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]5 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=310639&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310639&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R ServerBig Analytics Cloud Computing Center






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[196])
18490-------
18580.3-------
186104-------
18770.5-------
18873.2-------
189105.9-------
190100.1-------
19187.5-------
19286-------
19379-------
19494.4-------
19598.6-------
19690.2000000000001-------
19789.787.242778.921496.63940.30410.26870.92620.2687
198105.7101.11391.149112.4130.21310.97610.30830.9708
19966.968.166461.764375.38150.365400.26310
20079.577.765169.494187.2460.35990.98770.82740.0051
201100.2105.395493.3715119.32590.23240.99990.47170.9837
20294.699.906588.3151113.37230.21990.4830.48880.9211
20392.190.310679.6421102.74080.38890.24940.67120.507
20490.487.7177.222699.95380.33340.24110.60790.3451
2058181.347971.534992.82150.47630.0610.65580.0652
20689.493.362281.538107.30470.28880.95890.4420.6717
207103.598.424685.6117113.60890.25620.8780.4910.8558
20879.889.147977.5302102.91850.09170.02050.44050.4405
2098988.037675.4928103.1690.45040.8570.41480.3897
21010098.703284.0788116.48870.44320.85750.22030.8256
2116867.347857.808878.83930.455700.53040
21273.777.773266.04692.09010.28850.90950.40660.0444

\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[196]) \tabularnewline
184 & 90 & - & - & - & - & - & - & - \tabularnewline
185 & 80.3 & - & - & - & - & - & - & - \tabularnewline
186 & 104 & - & - & - & - & - & - & - \tabularnewline
187 & 70.5 & - & - & - & - & - & - & - \tabularnewline
188 & 73.2 & - & - & - & - & - & - & - \tabularnewline
189 & 105.9 & - & - & - & - & - & - & - \tabularnewline
190 & 100.1 & - & - & - & - & - & - & - \tabularnewline
191 & 87.5 & - & - & - & - & - & - & - \tabularnewline
192 & 86 & - & - & - & - & - & - & - \tabularnewline
193 & 79 & - & - & - & - & - & - & - \tabularnewline
194 & 94.4 & - & - & - & - & - & - & - \tabularnewline
195 & 98.6 & - & - & - & - & - & - & - \tabularnewline
196 & 90.2000000000001 & - & - & - & - & - & - & - \tabularnewline
197 & 89.7 & 87.2427 & 78.9214 & 96.6394 & 0.3041 & 0.2687 & 0.9262 & 0.2687 \tabularnewline
198 & 105.7 & 101.113 & 91.149 & 112.413 & 0.2131 & 0.9761 & 0.3083 & 0.9708 \tabularnewline
199 & 66.9 & 68.1664 & 61.7643 & 75.3815 & 0.3654 & 0 & 0.2631 & 0 \tabularnewline
200 & 79.5 & 77.7651 & 69.4941 & 87.246 & 0.3599 & 0.9877 & 0.8274 & 0.0051 \tabularnewline
201 & 100.2 & 105.3954 & 93.3715 & 119.3259 & 0.2324 & 0.9999 & 0.4717 & 0.9837 \tabularnewline
202 & 94.6 & 99.9065 & 88.3151 & 113.3723 & 0.2199 & 0.483 & 0.4888 & 0.9211 \tabularnewline
203 & 92.1 & 90.3106 & 79.6421 & 102.7408 & 0.3889 & 0.2494 & 0.6712 & 0.507 \tabularnewline
204 & 90.4 & 87.71 & 77.2226 & 99.9538 & 0.3334 & 0.2411 & 0.6079 & 0.3451 \tabularnewline
205 & 81 & 81.3479 & 71.5349 & 92.8215 & 0.4763 & 0.061 & 0.6558 & 0.0652 \tabularnewline
206 & 89.4 & 93.3622 & 81.538 & 107.3047 & 0.2888 & 0.9589 & 0.442 & 0.6717 \tabularnewline
207 & 103.5 & 98.4246 & 85.6117 & 113.6089 & 0.2562 & 0.878 & 0.491 & 0.8558 \tabularnewline
208 & 79.8 & 89.1479 & 77.5302 & 102.9185 & 0.0917 & 0.0205 & 0.4405 & 0.4405 \tabularnewline
209 & 89 & 88.0376 & 75.4928 & 103.169 & 0.4504 & 0.857 & 0.4148 & 0.3897 \tabularnewline
210 & 100 & 98.7032 & 84.0788 & 116.4887 & 0.4432 & 0.8575 & 0.2203 & 0.8256 \tabularnewline
211 & 68 & 67.3478 & 57.8088 & 78.8393 & 0.4557 & 0 & 0.5304 & 0 \tabularnewline
212 & 73.7 & 77.7732 & 66.046 & 92.0901 & 0.2885 & 0.9095 & 0.4066 & 0.0444 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310639&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[196])[/C][/ROW]
[ROW][C]184[/C][C]90[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]185[/C][C]80.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]186[/C][C]104[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]187[/C][C]70.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]188[/C][C]73.2[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]189[/C][C]105.9[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]190[/C][C]100.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]191[/C][C]87.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]192[/C][C]86[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]193[/C][C]79[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]194[/C][C]94.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]195[/C][C]98.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]196[/C][C]90.2000000000001[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]197[/C][C]89.7[/C][C]87.2427[/C][C]78.9214[/C][C]96.6394[/C][C]0.3041[/C][C]0.2687[/C][C]0.9262[/C][C]0.2687[/C][/ROW]
[ROW][C]198[/C][C]105.7[/C][C]101.113[/C][C]91.149[/C][C]112.413[/C][C]0.2131[/C][C]0.9761[/C][C]0.3083[/C][C]0.9708[/C][/ROW]
[ROW][C]199[/C][C]66.9[/C][C]68.1664[/C][C]61.7643[/C][C]75.3815[/C][C]0.3654[/C][C]0[/C][C]0.2631[/C][C]0[/C][/ROW]
[ROW][C]200[/C][C]79.5[/C][C]77.7651[/C][C]69.4941[/C][C]87.246[/C][C]0.3599[/C][C]0.9877[/C][C]0.8274[/C][C]0.0051[/C][/ROW]
[ROW][C]201[/C][C]100.2[/C][C]105.3954[/C][C]93.3715[/C][C]119.3259[/C][C]0.2324[/C][C]0.9999[/C][C]0.4717[/C][C]0.9837[/C][/ROW]
[ROW][C]202[/C][C]94.6[/C][C]99.9065[/C][C]88.3151[/C][C]113.3723[/C][C]0.2199[/C][C]0.483[/C][C]0.4888[/C][C]0.9211[/C][/ROW]
[ROW][C]203[/C][C]92.1[/C][C]90.3106[/C][C]79.6421[/C][C]102.7408[/C][C]0.3889[/C][C]0.2494[/C][C]0.6712[/C][C]0.507[/C][/ROW]
[ROW][C]204[/C][C]90.4[/C][C]87.71[/C][C]77.2226[/C][C]99.9538[/C][C]0.3334[/C][C]0.2411[/C][C]0.6079[/C][C]0.3451[/C][/ROW]
[ROW][C]205[/C][C]81[/C][C]81.3479[/C][C]71.5349[/C][C]92.8215[/C][C]0.4763[/C][C]0.061[/C][C]0.6558[/C][C]0.0652[/C][/ROW]
[ROW][C]206[/C][C]89.4[/C][C]93.3622[/C][C]81.538[/C][C]107.3047[/C][C]0.2888[/C][C]0.9589[/C][C]0.442[/C][C]0.6717[/C][/ROW]
[ROW][C]207[/C][C]103.5[/C][C]98.4246[/C][C]85.6117[/C][C]113.6089[/C][C]0.2562[/C][C]0.878[/C][C]0.491[/C][C]0.8558[/C][/ROW]
[ROW][C]208[/C][C]79.8[/C][C]89.1479[/C][C]77.5302[/C][C]102.9185[/C][C]0.0917[/C][C]0.0205[/C][C]0.4405[/C][C]0.4405[/C][/ROW]
[ROW][C]209[/C][C]89[/C][C]88.0376[/C][C]75.4928[/C][C]103.169[/C][C]0.4504[/C][C]0.857[/C][C]0.4148[/C][C]0.3897[/C][/ROW]
[ROW][C]210[/C][C]100[/C][C]98.7032[/C][C]84.0788[/C][C]116.4887[/C][C]0.4432[/C][C]0.8575[/C][C]0.2203[/C][C]0.8256[/C][/ROW]
[ROW][C]211[/C][C]68[/C][C]67.3478[/C][C]57.8088[/C][C]78.8393[/C][C]0.4557[/C][C]0[/C][C]0.5304[/C][C]0[/C][/ROW]
[ROW][C]212[/C][C]73.7[/C][C]77.7732[/C][C]66.046[/C][C]92.0901[/C][C]0.2885[/C][C]0.9095[/C][C]0.4066[/C][C]0.0444[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310639&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310639&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[196])
18490-------
18580.3-------
186104-------
18770.5-------
18873.2-------
189105.9-------
190100.1-------
19187.5-------
19286-------
19379-------
19494.4-------
19598.6-------
19690.2000000000001-------
19789.787.242778.921496.63940.30410.26870.92620.2687
198105.7101.11391.149112.4130.21310.97610.30830.9708
19966.968.166461.764375.38150.365400.26310
20079.577.765169.494187.2460.35990.98770.82740.0051
201100.2105.395493.3715119.32590.23240.99990.47170.9837
20294.699.906588.3151113.37230.21990.4830.48880.9211
20392.190.310679.6421102.74080.38890.24940.67120.507
20490.487.7177.222699.95380.33340.24110.60790.3451
2058181.347971.534992.82150.47630.0610.65580.0652
20689.493.362281.538107.30470.28880.95890.4420.6717
207103.598.424685.6117113.60890.25620.8780.4910.8558
20879.889.147977.5302102.91850.09170.02050.44050.4405
2098988.037675.4928103.1690.45040.8570.41480.3897
21010098.703284.0788116.48870.44320.85750.22030.8256
2116867.347857.808878.83930.455700.53040
21273.777.773266.04692.09010.28850.90950.40660.0444






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPEsMAPESq.EMSERMSEScaledEMASE
1970.0550.02740.02740.02786.0381000.17440.1744
1980.0570.04340.03540.036121.040513.53933.67960.32550.2499
1990.054-0.01890.02990.03031.60379.56083.0921-0.08990.1966
2000.06220.02180.02790.02823.00977.9232.81480.12310.1782
2010.0674-0.05190.03270.032726.99211.73683.4259-0.36860.2163
2020.0688-0.05610.03660.036328.158814.47383.8044-0.37650.243
2030.07020.01940.03410.0343.20212.86363.58660.1270.2264
2040.07120.02980.03360.03357.23612.16013.48710.19090.222
2050.072-0.00430.03030.03020.12110.82243.2897-0.02470.2001
2060.0762-0.04430.03170.031615.698711.31013.363-0.28110.2082
2070.07870.0490.03330.033325.759812.62373.5530.36010.222
2080.0788-0.11710.04030.039787.383118.85364.3421-0.66330.2588
2090.08770.01080.0380.03750.926217.47464.18030.06830.2441
2100.09190.0130.03620.03571.681716.34654.04310.0920.2332
2110.08710.00960.03450.0340.425415.28513.90960.04630.2208
2120.0939-0.05530.03580.035216.591115.36673.92-0.2890.225

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & sMAPE & Sq.E & MSE & RMSE & ScaledE & MASE \tabularnewline
197 & 0.055 & 0.0274 & 0.0274 & 0.0278 & 6.0381 & 0 & 0 & 0.1744 & 0.1744 \tabularnewline
198 & 0.057 & 0.0434 & 0.0354 & 0.0361 & 21.0405 & 13.5393 & 3.6796 & 0.3255 & 0.2499 \tabularnewline
199 & 0.054 & -0.0189 & 0.0299 & 0.0303 & 1.6037 & 9.5608 & 3.0921 & -0.0899 & 0.1966 \tabularnewline
200 & 0.0622 & 0.0218 & 0.0279 & 0.0282 & 3.0097 & 7.923 & 2.8148 & 0.1231 & 0.1782 \tabularnewline
201 & 0.0674 & -0.0519 & 0.0327 & 0.0327 & 26.992 & 11.7368 & 3.4259 & -0.3686 & 0.2163 \tabularnewline
202 & 0.0688 & -0.0561 & 0.0366 & 0.0363 & 28.1588 & 14.4738 & 3.8044 & -0.3765 & 0.243 \tabularnewline
203 & 0.0702 & 0.0194 & 0.0341 & 0.034 & 3.202 & 12.8636 & 3.5866 & 0.127 & 0.2264 \tabularnewline
204 & 0.0712 & 0.0298 & 0.0336 & 0.0335 & 7.236 & 12.1601 & 3.4871 & 0.1909 & 0.222 \tabularnewline
205 & 0.072 & -0.0043 & 0.0303 & 0.0302 & 0.121 & 10.8224 & 3.2897 & -0.0247 & 0.2001 \tabularnewline
206 & 0.0762 & -0.0443 & 0.0317 & 0.0316 & 15.6987 & 11.3101 & 3.363 & -0.2811 & 0.2082 \tabularnewline
207 & 0.0787 & 0.049 & 0.0333 & 0.0333 & 25.7598 & 12.6237 & 3.553 & 0.3601 & 0.222 \tabularnewline
208 & 0.0788 & -0.1171 & 0.0403 & 0.0397 & 87.3831 & 18.8536 & 4.3421 & -0.6633 & 0.2588 \tabularnewline
209 & 0.0877 & 0.0108 & 0.038 & 0.0375 & 0.9262 & 17.4746 & 4.1803 & 0.0683 & 0.2441 \tabularnewline
210 & 0.0919 & 0.013 & 0.0362 & 0.0357 & 1.6817 & 16.3465 & 4.0431 & 0.092 & 0.2332 \tabularnewline
211 & 0.0871 & 0.0096 & 0.0345 & 0.034 & 0.4254 & 15.2851 & 3.9096 & 0.0463 & 0.2208 \tabularnewline
212 & 0.0939 & -0.0553 & 0.0358 & 0.0352 & 16.5911 & 15.3667 & 3.92 & -0.289 & 0.225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310639&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]sMAPE[/C][C]Sq.E[/C][C]MSE[/C][C]RMSE[/C][C]ScaledE[/C][C]MASE[/C][/ROW]
[ROW][C]197[/C][C]0.055[/C][C]0.0274[/C][C]0.0274[/C][C]0.0278[/C][C]6.0381[/C][C]0[/C][C]0[/C][C]0.1744[/C][C]0.1744[/C][/ROW]
[ROW][C]198[/C][C]0.057[/C][C]0.0434[/C][C]0.0354[/C][C]0.0361[/C][C]21.0405[/C][C]13.5393[/C][C]3.6796[/C][C]0.3255[/C][C]0.2499[/C][/ROW]
[ROW][C]199[/C][C]0.054[/C][C]-0.0189[/C][C]0.0299[/C][C]0.0303[/C][C]1.6037[/C][C]9.5608[/C][C]3.0921[/C][C]-0.0899[/C][C]0.1966[/C][/ROW]
[ROW][C]200[/C][C]0.0622[/C][C]0.0218[/C][C]0.0279[/C][C]0.0282[/C][C]3.0097[/C][C]7.923[/C][C]2.8148[/C][C]0.1231[/C][C]0.1782[/C][/ROW]
[ROW][C]201[/C][C]0.0674[/C][C]-0.0519[/C][C]0.0327[/C][C]0.0327[/C][C]26.992[/C][C]11.7368[/C][C]3.4259[/C][C]-0.3686[/C][C]0.2163[/C][/ROW]
[ROW][C]202[/C][C]0.0688[/C][C]-0.0561[/C][C]0.0366[/C][C]0.0363[/C][C]28.1588[/C][C]14.4738[/C][C]3.8044[/C][C]-0.3765[/C][C]0.243[/C][/ROW]
[ROW][C]203[/C][C]0.0702[/C][C]0.0194[/C][C]0.0341[/C][C]0.034[/C][C]3.202[/C][C]12.8636[/C][C]3.5866[/C][C]0.127[/C][C]0.2264[/C][/ROW]
[ROW][C]204[/C][C]0.0712[/C][C]0.0298[/C][C]0.0336[/C][C]0.0335[/C][C]7.236[/C][C]12.1601[/C][C]3.4871[/C][C]0.1909[/C][C]0.222[/C][/ROW]
[ROW][C]205[/C][C]0.072[/C][C]-0.0043[/C][C]0.0303[/C][C]0.0302[/C][C]0.121[/C][C]10.8224[/C][C]3.2897[/C][C]-0.0247[/C][C]0.2001[/C][/ROW]
[ROW][C]206[/C][C]0.0762[/C][C]-0.0443[/C][C]0.0317[/C][C]0.0316[/C][C]15.6987[/C][C]11.3101[/C][C]3.363[/C][C]-0.2811[/C][C]0.2082[/C][/ROW]
[ROW][C]207[/C][C]0.0787[/C][C]0.049[/C][C]0.0333[/C][C]0.0333[/C][C]25.7598[/C][C]12.6237[/C][C]3.553[/C][C]0.3601[/C][C]0.222[/C][/ROW]
[ROW][C]208[/C][C]0.0788[/C][C]-0.1171[/C][C]0.0403[/C][C]0.0397[/C][C]87.3831[/C][C]18.8536[/C][C]4.3421[/C][C]-0.6633[/C][C]0.2588[/C][/ROW]
[ROW][C]209[/C][C]0.0877[/C][C]0.0108[/C][C]0.038[/C][C]0.0375[/C][C]0.9262[/C][C]17.4746[/C][C]4.1803[/C][C]0.0683[/C][C]0.2441[/C][/ROW]
[ROW][C]210[/C][C]0.0919[/C][C]0.013[/C][C]0.0362[/C][C]0.0357[/C][C]1.6817[/C][C]16.3465[/C][C]4.0431[/C][C]0.092[/C][C]0.2332[/C][/ROW]
[ROW][C]211[/C][C]0.0871[/C][C]0.0096[/C][C]0.0345[/C][C]0.034[/C][C]0.4254[/C][C]15.2851[/C][C]3.9096[/C][C]0.0463[/C][C]0.2208[/C][/ROW]
[ROW][C]212[/C][C]0.0939[/C][C]-0.0553[/C][C]0.0358[/C][C]0.0352[/C][C]16.5911[/C][C]15.3667[/C][C]3.92[/C][C]-0.289[/C][C]0.225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310639&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310639&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.PEMAPEsMAPESq.EMSERMSEScaledEMASE
1970.0550.02740.02740.02786.0381000.17440.1744
1980.0570.04340.03540.036121.040513.53933.67960.32550.2499
1990.054-0.01890.02990.03031.60379.56083.0921-0.08990.1966
2000.06220.02180.02790.02823.00977.9232.81480.12310.1782
2010.0674-0.05190.03270.032726.99211.73683.4259-0.36860.2163
2020.0688-0.05610.03660.036328.158814.47383.8044-0.37650.243
2030.07020.01940.03410.0343.20212.86363.58660.1270.2264
2040.07120.02980.03360.03357.23612.16013.48710.19090.222
2050.072-0.00430.03030.03020.12110.82243.2897-0.02470.2001
2060.0762-0.04430.03170.031615.698711.31013.363-0.28110.2082
2070.07870.0490.03330.033325.759812.62373.5530.36010.222
2080.0788-0.11710.04030.039787.383118.85364.3421-0.66330.2588
2090.08770.01080.0380.03750.926217.47464.18030.06830.2441
2100.09190.0130.03620.03571.681716.34654.04310.0920.2332
2110.08710.00960.03450.0340.425415.28513.90960.04630.2208
2120.0939-0.05530.03580.035216.591115.36673.92-0.2890.225


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 16 ; par2 = -0.2 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ; par10 = FALSE ;
Parameters (R input):
par1 = 16 ; par2 = -0.2 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; 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*2
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.spe <- array(0, dim=fx)
perf.scalederr <- array(0, dim=fx)
perf.mase <- array(0, dim=fx)
perf.mase1 <- array(0, dim=fx)
perf.mape <- array(0, dim=fx)
perf.smape <- array(0, dim=fx)
perf.mape1 <- array(0, dim=fx)
perf.smape1 <- 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)
perf.scaleddenom <- 0
for (i in 2:fx) {
perf.scaleddenom = perf.scaleddenom + abs(x[nx+i] - x[nx+i-1])
}
perf.scaleddenom = perf.scaleddenom / (fx-1)
for (i in 1:fx) {
locSD <- (ub[i] - forecast$pred[i]) / 1.96
perf.scalederr[i] = (x[nx+i] - forecast$pred[i]) / perf.scaleddenom
perf.pe[i] = (x[nx+i] - forecast$pred[i]) / x[nx+i]
perf.spe[i] = 2*(x[nx+i] - forecast$pred[i]) / (x[nx+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.smape[1] = abs(perf.spe[1])
perf.mape1[1] = perf.mape[1]
perf.smape1[1] = perf.smape[1]
perf.mse[1] = perf.se[1]
perf.mase[1] = abs(perf.scalederr[1])
perf.mase1[1] = perf.mase[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.smape[i] = perf.smape[i-1] + abs(perf.spe[i])
perf.smape1[i] = perf.smape[i] / i
perf.mse[i] = perf.mse[i-1] + perf.se[i]
perf.mse1[i] = perf.mse[i] / i
perf.mase[i] = perf.mase[i-1] + abs(perf.scalederr[i])
perf.mase1[i] = perf.mase[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',10,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,'sMAPE',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.element(a,'ScaledE',1,header=TRUE)
a<-table.element(a,'MASE',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.smape1[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.element(a,round(perf.scalederr[i],4))
a<-table.element(a,round(perf.mase1[i],4))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')