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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_structuraltimeseries.wasp
Title produced by softwareStructural Time Series Models
Date of computationTue, 12 Nov 2013 08:57:00 -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/2013/Nov/12/t13842646490coftugmqdmnev5.htm/, Retrieved Fri, 03 May 2024 03:18:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=224394, Retrieved Fri, 03 May 2024 03:18:22 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [HPC Retail Sales] [2008-03-08 13:40:54] [1c0f2c85e8a48e42648374b3bcceca26]
- RMPD    [Structural Time Series Models] [ws8] [2013-11-12 13:57:00] [e931f330ae8eb739e69629b6955c783c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
38
40
39
48
54
55
56
63
52
59
57
62
50

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224394&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]5 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=224394&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224394&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 time5 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Structural Time Series Model
tObservedLevelSlopeSeasonalStand. Residuals
13838000
24038.33309011002980.4708512474729931.666909889970230.590230061685977
33939.63398522117960.942700257819702-0.6339852211795980.252662856587944
44844.71601743224472.93758796553033.283982567755341.25198469482982
55451.6427766392125.004151604683232.357223360788041.26767370788648
65556.44072193336024.89756864903266-1.44072193336018-0.0599616559974753
75658.2341749787353.33867445595584-2.23417497873498-0.875227000457784
86361.81528217901343.45981685480991.18471782098660.0689927948307368
95257.8217832413258-0.285186510137597-5.8217832413258-2.13376417073227
105957.0632951873811-0.5237287966560161.93670481261888-0.135547649903268
115756.6540083691436-0.4660253196817720.3459916308564350.0327736063066461
126259.39265707211261.149402122784572.607342927887410.91773987882119
135055.3267230895685-1.46047426184581-5.32672308956848-1.49136144431081

\begin{tabular}{lllllllll}
\hline
Structural Time Series Model \tabularnewline
t & Observed & Level & Slope & Seasonal & Stand. Residuals \tabularnewline
1 & 38 & 38 & 0 & 0 & 0 \tabularnewline
2 & 40 & 38.3330901100298 & 0.470851247472993 & 1.66690988997023 & 0.590230061685977 \tabularnewline
3 & 39 & 39.6339852211796 & 0.942700257819702 & -0.633985221179598 & 0.252662856587944 \tabularnewline
4 & 48 & 44.7160174322447 & 2.9375879655303 & 3.28398256775534 & 1.25198469482982 \tabularnewline
5 & 54 & 51.642776639212 & 5.00415160468323 & 2.35722336078804 & 1.26767370788648 \tabularnewline
6 & 55 & 56.4407219333602 & 4.89756864903266 & -1.44072193336018 & -0.0599616559974753 \tabularnewline
7 & 56 & 58.234174978735 & 3.33867445595584 & -2.23417497873498 & -0.875227000457784 \tabularnewline
8 & 63 & 61.8152821790134 & 3.4598168548099 & 1.1847178209866 & 0.0689927948307368 \tabularnewline
9 & 52 & 57.8217832413258 & -0.285186510137597 & -5.8217832413258 & -2.13376417073227 \tabularnewline
10 & 59 & 57.0632951873811 & -0.523728796656016 & 1.93670481261888 & -0.135547649903268 \tabularnewline
11 & 57 & 56.6540083691436 & -0.466025319681772 & 0.345991630856435 & 0.0327736063066461 \tabularnewline
12 & 62 & 59.3926570721126 & 1.14940212278457 & 2.60734292788741 & 0.91773987882119 \tabularnewline
13 & 50 & 55.3267230895685 & -1.46047426184581 & -5.32672308956848 & -1.49136144431081 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224394&T=1

[TABLE]
[ROW][C]Structural Time Series Model[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Level[/C][C]Slope[/C][C]Seasonal[/C][C]Stand. Residuals[/C][/ROW]
[ROW][C]1[/C][C]38[/C][C]38[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]40[/C][C]38.3330901100298[/C][C]0.470851247472993[/C][C]1.66690988997023[/C][C]0.590230061685977[/C][/ROW]
[ROW][C]3[/C][C]39[/C][C]39.6339852211796[/C][C]0.942700257819702[/C][C]-0.633985221179598[/C][C]0.252662856587944[/C][/ROW]
[ROW][C]4[/C][C]48[/C][C]44.7160174322447[/C][C]2.9375879655303[/C][C]3.28398256775534[/C][C]1.25198469482982[/C][/ROW]
[ROW][C]5[/C][C]54[/C][C]51.642776639212[/C][C]5.00415160468323[/C][C]2.35722336078804[/C][C]1.26767370788648[/C][/ROW]
[ROW][C]6[/C][C]55[/C][C]56.4407219333602[/C][C]4.89756864903266[/C][C]-1.44072193336018[/C][C]-0.0599616559974753[/C][/ROW]
[ROW][C]7[/C][C]56[/C][C]58.234174978735[/C][C]3.33867445595584[/C][C]-2.23417497873498[/C][C]-0.875227000457784[/C][/ROW]
[ROW][C]8[/C][C]63[/C][C]61.8152821790134[/C][C]3.4598168548099[/C][C]1.1847178209866[/C][C]0.0689927948307368[/C][/ROW]
[ROW][C]9[/C][C]52[/C][C]57.8217832413258[/C][C]-0.285186510137597[/C][C]-5.8217832413258[/C][C]-2.13376417073227[/C][/ROW]
[ROW][C]10[/C][C]59[/C][C]57.0632951873811[/C][C]-0.523728796656016[/C][C]1.93670481261888[/C][C]-0.135547649903268[/C][/ROW]
[ROW][C]11[/C][C]57[/C][C]56.6540083691436[/C][C]-0.466025319681772[/C][C]0.345991630856435[/C][C]0.0327736063066461[/C][/ROW]
[ROW][C]12[/C][C]62[/C][C]59.3926570721126[/C][C]1.14940212278457[/C][C]2.60734292788741[/C][C]0.91773987882119[/C][/ROW]
[ROW][C]13[/C][C]50[/C][C]55.3267230895685[/C][C]-1.46047426184581[/C][C]-5.32672308956848[/C][C]-1.49136144431081[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224394&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224394&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:

Structural Time Series Model
tObservedLevelSlopeSeasonalStand. Residuals
13838000
24038.33309011002980.4708512474729931.666909889970230.590230061685977
33939.63398522117960.942700257819702-0.6339852211795980.252662856587944
44844.71601743224472.93758796553033.283982567755341.25198469482982
55451.6427766392125.004151604683232.357223360788041.26767370788648
65556.44072193336024.89756864903266-1.44072193336018-0.0599616559974753
75658.2341749787353.33867445595584-2.23417497873498-0.875227000457784
86361.81528217901343.45981685480991.18471782098660.0689927948307368
95257.8217832413258-0.285186510137597-5.8217832413258-2.13376417073227
105957.0632951873811-0.5237287966560161.93670481261888-0.135547649903268
115756.6540083691436-0.4660253196817720.3459916308564350.0327736063066461
126259.39265707211261.149402122784572.607342927887410.91773987882119
135055.3267230895685-1.46047426184581-5.32672308956848-1.49136144431081


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
nx <- length(x)
x <- ts(x,frequency=par1)
m <- StructTS(x,type='BSM')
m$coef
m$fitted
m$resid
mylevel <- as.numeric(m$fitted[,'level'])
myslope <- as.numeric(m$fitted[,'slope'])
myseas <- as.numeric(m$fitted[,'sea'])
myresid <- as.numeric(m$resid)
myfit <- mylevel+myseas
mylagmax <- nx/2
bitmap(file='test2.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(x),lag.max = mylagmax,main='Observed')
acf(mylevel,na.action=na.pass,lag.max = mylagmax,main='Level')
acf(myseas,na.action=na.pass,lag.max = mylagmax,main='Seasonal')
acf(myresid,na.action=na.pass,lag.max = mylagmax,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
spectrum(as.numeric(x),main='Observed')
spectrum(mylevel,main='Level')
spectrum(myseas,main='Seasonal')
spectrum(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test4.png')
op <- par(mfrow = c(2,2))
cpgram(as.numeric(x),main='Observed')
cpgram(mylevel,main='Level')
cpgram(myseas,main='Seasonal')
cpgram(myresid,main='Standardized Residals')
par(op)
dev.off()
bitmap(file='test1.png')
plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time',type='b')
grid()
dev.off()
bitmap(file='test5.png')
op <- par(mfrow = c(2,2))
hist(m$resid,main='Residual Histogram')
plot(density(m$resid),main='Residual Kernel Density')
qqnorm(m$resid,main='Residual Normal QQ Plot')
qqline(m$resid)
plot(m$resid^2, myfit^2,main='Sq.Resid vs. Sq.Fit',xlab='Squared residuals',ylab='Squared Fit')
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Structural Time Series Model',6,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Level',header=TRUE)
a<-table.element(a,'Slope',header=TRUE)
a<-table.element(a,'Seasonal',header=TRUE)
a<-table.element(a,'Stand. Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nx) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.element(a,mylevel[i])
a<-table.element(a,myslope[i])
a<-table.element(a,myseas[i])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')