# ::Free Statistics and Forecasting Software::

v1.2.1

### :: Smoothing Time Series Example - Free Statistics Software (Calculator) ::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This R module demonstrates with real data that gas consumption as usually measured by drivers is quite variable, and with no apparent trend, until a nonparametric smoother reveals a very distinct seasonal pattern. Ask students if they see anything in the data. The first graph you see is the raw data, and in the next graph the smoothed fit is displayed. The point of the demo is that nonparametric smoothing is easy to understand and useful, and should be taught in intro stats courses. The program can also be used to demonstrate the trial-and-error approach to choosing the degree of smoothing, by varying the parameter 'span'.

 Send output to: Browser Blue - Charts White Browser Black/White CSV Span Smooth? TRUEFALSE Chart options Width: Height:

 Source code of R module x <- c(1999.38 ,1999.39 ,1999.41 ,1999.42 ,1999.44 ,1999.45 ,1999.46 ,1999.47 ,1999.49 ,1999.5 ,1999.51 ,1999.52 ,1999.53 ,1999.54 ,1999.54 ,1999.58 ,1999.6 ,1999.64 ,1999.66 ,1999.59 ,1999.67 ,1999.68 ,1999.69 ,1999.71 ,1999.72 ,1999.73 ,1999.74 ,1999.76 ,1999.77 ,1999.78 ,1999.79 ,1999.81 ,1999.82 ,1999.84 ,1999.84 ,1999.86 ,1999.88 ,1999.89 ,1999.91 ,1999.92 ,1999.94 ,1999.95 ,1999.96 ,1999.98 ,2000 ,2000.02 ,2000.03 ,2000.04 ,2000.05 ,2000.16 ,2000.17 ,2000.19 ,2000.21 ,2000.21 ,2000.24 ,2000.25 ,2000.26 ,2000.27 ,2000.28 ,2000.29 ,2000.31 ,2000.34 ,2000.36 ,2000.36 ,2000.39 ,2000.4 ,2000.42 ,2000.43 ,2000.45 ,2000.46 ,2000.47 ,2000.51 ,2000.54 ,2000.56 ,2000.57 ,2000.59 ,2000.62 ,2000.63 ,2000.67 ,2000.67 ,2000.68 ,2000.7 ,2000.71 ,2000.73 ,2000.74 ,2000.76 ,2000.77 ,2000.78 ,2000.8 ,2000.81 ,2000.83 ,2000.84 ,2000.86 ,2000.87 ,2000.88 ,2000.88 ,2000.9 ,2000.91 ,2000.92 ,2000.93 ,2000.94 ,2000.96 ,2000.97 ,2000.98 ,2001.01 ,2001.03 ,2001.04 ,2001.06 ,2001.07 ,2001.08 ,2001.09 ,2001.12 ,2001.13 ,2001.16 ,2001.19 ,2001.2 ,2001.21 ,2001.23 ,2001.24 ,2001.26 ,2001.26 ,2001.27 ,2001.3 ,2001.31 ,2001.33 ,2001.34 ,2001.36 ,2001.36 ,2001.38 ,2001.4 ,2001.41 ,2001.43 ,2001.45 ,2001.46 ,2001.48 ,2001.5 ,2001.51 ,2001.53 ,2001.55 ,2001.57 ,2001.58 ,2001.59 ,2001.61 ,2001.62 ,2001.67 ,2001.69 ,2001.72 ,2001.73 ,2001.74 ,2001.76 ,2001.77 ,2001.78 ,2001.8 ,2001.81 ,2001.82 ,2001.84 ,2001.89 ,2001.9 ,2001.91 ,2001.92 ,2001.94 ,2001.96 ,2001.98 ,2002.01 ,2002.02 ,2002.04 ,2002.06 ,2002.07 ,2002.09 ,2002.1 ,2002.12 ,2002.14 ,2002.15 ,2002.16 ,2002.17 ,2002.19 ,2002.2 ,2002.21 ,2002.24 ,2002.24 ,2002.27 ,2002.28 ,2002.29 ,2002.31 ,2002.35 ,2002.37 ,2002.4 ,2002.34 ,2002.44 ,2002.5 ,2002.56 ,2002.6 ,2002.64 ,2002.65 ,2002.67 ,2002.69 ,2002.7 ,2002.72 ,2002.72 ,2002.74 ,2002.76 ,2002.77 ,2002.78 ,2002.8 ,2002.82 ,2002.84 ,2002.84 ,2002.87 ,2002.89 ,2002.9 ,2002.91 ,2002.92 ,2002.93 ,2002.99 ,2003.01 ,2003.04 ,2003.05 ,2003.07 ,2003.08 ,2003.1 ,2003.13 ,2003.15 ,2003.18 ,2003.19 ,2003.2 ,2003.22 ,2003.23 ,2003.24 ,2003.25 ,2003.26 ,2003.27 ,2003.29 ,2003.3 ,2003.32 ,2003.33 ,2003.34 ,2003.36 ,2003.36 ,2003.37 ,2003.39 ,2003.41 ,2003.42 ,2003.43 ,2003.46 ,2003.47 ,2003.48 ,2003.49 ,2003.51 ,2003.54 ,2003.55 ,2003.56 ,2003.58 ,2003.61 ,2003.66 ,2003.68 ,2003.68 ,2003.7 ,2003.72 ,2003.73 ,2003.74 ,2003.76 ,2003.81 ,2003.82 ,2003.84 ,2003.85 ,2003.86 ,2003.88 ,2003.88 ,2003.89 ,2003.91 ,2003.92 ,2003.94 ,2003.95 ,2003.96 ,2003.99 ,2004.02 ,2004.05 ,2004.03 ,2004.07 ,2004.08 ,2004.09 ,2004.11 ,2004.15 ,2004.17 ,2004.19 ,2004.21 ,2004.24 ,2004.26 ,2004.27 ,2004.28 ,2004.3 ,2004.31 ,2004.33 ,2004.34 ,2004.36 ,2004.38 ,2004.39 ,2004.41 ,2004.43 ,2004.44 ,2004.46 ,2004.48) y <- c(10.69 ,9.09 ,11.29 ,10.59 ,9.97 ,9.65 ,9.18 ,10.49 ,9.27 ,10.4 ,8.9 ,9.17 ,10.4 ,9.53 ,8.19 ,10.04 ,9.37 ,10.46 ,10.09 ,7.38 ,10.56 ,9.83 ,9.57 ,10.46 ,12.2 ,7.64 ,10.26 ,9.43 ,9.94 ,11.19 ,10.17 ,9.61 ,10.28 ,12.06 ,9.73 ,10.1 ,10.63 ,10.64 ,11.24 ,9.4 ,11.78 ,9.75 ,12.3 ,11.35 ,10.97 ,11.77 ,11.09 ,11.43 ,10.92 ,11.91 ,11.17 ,10.04 ,10.32 ,9.6 ,9.56 ,10.27 ,8.69 ,10.91 ,9.64 ,9.09 ,10.39 ,10.15 ,10.2 ,9.28 ,10.66 ,9.37 ,10.14 ,10.43 ,10.24 ,9.28 ,10.38 ,9.85 ,10.81 ,12.2 ,9.47 ,9.49 ,8.9 ,9.76 ,9.62 ,9.6 ,9.99 ,10.48 ,9.56 ,9.19 ,9.94 ,9.57 ,10.4 ,9.26 ,10.69 ,10.35 ,10 ,9.34 ,10.45 ,10.76 ,9.74 ,7.34 ,11.21 ,10.67 ,9.22 ,10.34 ,10.66 ,9.96 ,12.11 ,10.71 ,10.09 ,10.25 ,9.96 ,11.73 ,9.71 ,10.1 ,10.29 ,11.05 ,10.35 ,12 ,10.56 ,10.43 ,8.19 ,11.38 ,9.95 ,10.51 ,8.61 ,10.29 ,10.11 ,10.12 ,9.84 ,10.05 ,10.13 ,9.97 ,10.13 ,9.87 ,9.92 ,9.44 ,9.71 ,9.77 ,9.82 ,10.31 ,8.82 ,9.62 ,9.64 ,10.69 ,9.08 ,9.59 ,9.57 ,8.17 ,9.99 ,9.09 ,9.66 ,9.21 ,9.44 ,10.04 ,9.3 ,10.24 ,10.15 ,10.2 ,11.36 ,9.5 ,9.96 ,10.15 ,11.02 ,10.05 ,10.65 ,10.31 ,11.42 ,10.08 ,10.44 ,10.39 ,10.74 ,10.99 ,11.02 ,10.55 ,10.72 ,10.54 ,10.67 ,10.35 ,9.68 ,10.78 ,9.8 ,11.09 ,10.45 ,10.66 ,10.65 ,9.9 ,9.55 ,9.91 ,10.26 ,10.14 ,9.82 ,10.27 ,10.12 ,9.52 ,9.05 ,10.26 ,9.4 ,8.99 ,8.98 ,9.49 ,10.42 ,9.31 ,9.13 ,9.71 ,10.3 ,9.75 ,9.05 ,10.91 ,10.09 ,11.15 ,10.69 ,10.36 ,10.56 ,10.52 ,10.32 ,9.78 ,12.11 ,10.75 ,11.12 ,10.32 ,12.33 ,10.03 ,11.4 ,12.47 ,13.57 ,10.2 ,10.2 ,10.84 ,9.61 ,10.35 ,10 ,9.76 ,10.3 ,9.86 ,10.52 ,10.49 ,10.14 ,10.11 ,6.86 ,9.58 ,10.17 ,8.9 ,10.54 ,9.49 ,10.23 ,9.04 ,10.47 ,11.88 ,10.55 ,8.86 ,11.71 ,9.88 ,9.07 ,9.63 ,10.5 ,10.16 ,7.65 ,8.56 ,10.51 ,8.9 ,9.7 ,9.83 ,9.73 ,9.03 ,10.18 ,9.45 ,11.27 ,10.35 ,10.76 ,11.2 ,11.08 ,9.17 ,12.67 ,11.09 ,10.32 ,10.71 ,10.88 ,8.44 ,10.15 ,10.06 ,9.76 ,12.45 ,10.02 ,8.89 ,10.66 ,10.71 ,10.52 ,10.58 ,10.15 ,11.1 ,9.96 ,11.31 ,9.51 ,6.98 ,10.55 ,7.22 ,10.16 ,8.03 ,9.77 ,10.36 ,9.63 ,10.6 ,9.6 ,8.75 ,10.32 ,10.23) merc.df <- as.data.frame(cbind(x,y)) colnames(merc.df) <- c("date1","lp100km") span <- as.numeric(par1) if (par2 == "TRUE") smooth <- TRUE else smooth <- FALSE x=merc.df\$date1 y=merc.df\$lp100km yl=loess(y~x,span=span) bitmap(file="noloessplot.png") plot(yl,col="darkgreen",type="p",main="5 years gas consumption, 1999-2004 (raw data)",xlab="decimal date",ylab="litres per 100 km") dev.off() if (smooth==TRUE) { bitmap(file="loessplot.png") plot(yl,col="darkgreen",type="p",main="5 years gas consumption, 1999-2004 (incl. LOESS)",xlab="decimal date",ylab="litres per 100 km") mn=mean(yl\$y) lines(yl\$x,yl\$fitted,col="red",lwd=3) lines(yl\$x,mn*rep(1,length(yl\$x)),col="black",lwd=3) dev.off() bitmap(file="resplot.png") plot(yl\$x,yl\$residuals,col="darkgreen",ylab="residuals from smooth",xlab="decimal date",main="Residuals of (Data - Smooth)") lines(yl\$x,0*rep(1,length(yl\$x)),col="black",lwd=3) rl=loess(yl\$residuals~yl\$x,span=span) lines(rl\$x,rl\$fitted,col="red",lwd=3) dev.off() }
 Top | Output | Charts | References

 Cite this software as: Weldon Larry, (2017), Time Series Smoothing Example (v1.0.4) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL https://www.wessa.net/rwasp_gas.wasp/ The R code is based on : Weldon Larry, Stat Ed Programs for Demos in R, Simon Fraser University, URL http://www.stat.sfu.ca/~weldon/title.doc Weldon Larry, R Programs for Statistics Education, Simon Fraser University, URL http://www.stat.sfu.ca/~weldon/Programs Weldon Larry, Instructions for using R programs for Statistics Education, Simon Fraser University, URL http://www.stat.sfu.ca/~weldon/instructions.doc
 Top | Output | Charts | References
 To cite Wessa.net in publications use:Wessa, P. (2023), Free Statistics Software, Office for Research Development and Education, version 1.2.1, URL https://www.wessa.net/ © All rights reserved. Academic license for non-commercial use only. The free use of the scientific content, services, and applications in this website is granted for non commercial use only. In any case, the source (url) should always be clearly displayed. Under no circumstances are you allowed to reproduce, copy or redistribute the design, layout, or any content of this website (for commercial use) including any materials contained herein without the express written permission. Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. We make no warranties or representations as to the accuracy or completeness of such information (or software), and it assumes no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site. Software Version : 1.2.1Algorithms & Software : Patrick Wessa, PhDServer : www.wessa.net
 © Wessa.Net 2002-2023