## Thursday, March 5, 2015

### Is Time Series Clustering Meaningless? (lots of dplyr)

A kind reader directed me in a comment on Experiments in Time Series Clustering to this paper.

Clustering of Time Series Subsequences is Meaningless: Implications for Previous and Future Research

Eamonn Keogh  and Jessica Lin

Computer Science & Engineering Department University of California – Riverside

http://www.cs.ucr.edu/~eamonn/meaningless.pdf

As I said in my last post, I don’t know what I’m doing, so I have no basis for discussing or arguing time series clustering.  After reading the paper a couple of times, I think I understand their points, and I do not think what I am doing is “meaningless”.  In their financial time series examples, they use prices and speak of trying to find patterns.  I simply want to classify which years are most alike by various characteristics, such as autocorrelation of returns  not prices, distribution of returns, and all sorts of other classifiers.

More than anything this whole exercise gave me a good excuse to dig much, much deeper.  Iongtime readers might be wondering where are the interactive plots.  I wanted to share what I have done so far hoping that readers might elaborate, argue, or point me in good directions.

Regardless of your interest in time series clustering, you might enjoy the dplyr and piping that I used to generate the results.  Also, I have not seen dplyr `do` applied to autocorrelation `ACF`, so you might want to check that out in the last snippet of code.

All of the code for this post and last post is in this Github repo. ``library(TSclust)library(quantmod)library(dplyr)library(pipeR)library(tidyr)sp5 <- getSymbols("^GSPC",auto.assign=F,from="1900-01-01")[,4]sp5 %>>%  # dplyr doesn't like xts, so make a data.frame  (    data.frame(      date = index(.)      ,price = .[,1,drop=T]    )  ) %>>%  # add a column for Year  mutate( year = as.numeric(format(date,"%Y"))) %>>%  # group by our new Year column  group_by( year ) %>>%  # within each year, find what day in the year so we can join  mutate( pos = rank(date) ) %>>%  mutate( roc = price/lag(price,k=1) - 1 ) %>>%  # can remove date  select( -c(date,price) ) %>>%  as.data.frame %>>%  # years as columns as pos as row  spread( year, roc ) %>>%  # remove last year since assume not complete  ( .[,-ncol(.)] ) %>>%  # remove pos since index will be same  select( -pos ) %>>%  # fill nas with previous value  na.fill( 0 ) %>>%  t %>>%(~sp_wide) %>>%  # use TSclust diss; notes lots of METHOD options  diss( METHOD="ACF" ) %>>%  hclust %>>%(~hc) %>>%  ape::as.phylo() %>>%   treewidget #%>>%  #htmlwidgets::as.iframe(file="index.html",selfcontained=F,libdir = "./lib")library(lattice)library(ggplot2)# get wide to long the hard way#  could have easily changed to above pipe to save long#  as an intermediate step#  but this makes for a fun lapply#  and also we can add in our cluster heresp_wide %>>%  (    lapply(      rownames(.)      ,function(yr){        data.frame(          year = as.Date(paste0(yr,"-01-01"),"%Y-%m-%d")          ,cluster = cutree(hc,10)[yr]          ,pos = 1:length(.[yr,])          ,roc = .[yr,]        )      }    )  ) %>>%  (do.call(rbind,.)) %>>%(~sp_long)sp_long %>>%  ggplot( aes( x = roc, group = year, color = factor(cluster) ) ) %>>%  + geom_density() %>>%  + facet_wrap(  ~ cluster, ncol = 1 ) %>>%  + xlim(-0.05,0.05) %>>%  + labs(title='Density of S&P 500 Years Clustered by TSclust') %>>%  + theme_bw() %>>%  # thanks to my friend Zev Ross for his cheatsheet  + theme( plot.title = element_text(size=15, face="bold", hjust=0) ) %>>%  + theme( legend.position="none" )  %>>%  + scale_color_brewer( palette="Paired" )  `` ``# explore autocorrelationssp5 %>>%  # dplyr doesn't like xts, so make a data.frame  (    data.frame(      date = index(.)      ,price = .[,1,drop=T]    )  ) %>>%  # add a column for Year  mutate( year = as.numeric(format(date,"%Y"))) %>>%  # group by our new Year column  group_by( year ) %>>%  # within each year, find what day in the year so we can join  mutate( pos = rank(date) ) %>>%  mutate( roc = price/lag(price,k=1) - 1 ) %>>%  # can remove date  select( -c(date,price) ) %>>%  as.data.frame %>>%  # years as columns as pos as row  spread( year, roc ) %>>%  # remove last year since assume not complete  ( .[,-ncol(.)] ) %>>% t -> sPsp_long %>>%  group_by( cluster, year ) %>>%  do(    . %>>%    (      clustd ~       acf(clustd\$roc,plot=F) %>>%        (a ~          data.frame(            cluster = clustd[1,2]            ,year = clustd[1,1]            ,lag = a\$lag[-1]            ,acf = a\$acf[-1]          )        )    )  ) %>>%  as.data.frame %>>%  ggplot( aes( x = factor(cluster), y = acf, color = factor(cluster) ) ) %>>%    + geom_point() %>>%    + facet_wrap( ~lag, ncol = 4 ) %>>%    + labs(title='ACF of S&P 500 Years Clustered by TSclust') %>>%    + theme_bw() %>>%    # thanks to my friend Zev Ross for his cheatsheet    + theme(        plot.title = element_text(size=15, face="bold", hjust=0)        ,legend.title=element_blank()    ) %>>%    + theme(legend.position="none")  %>>%    + scale_color_brewer(palette="Paired")``

If you’ve made it this far, I would love to hear from you.

#### 1 comment:

1. Interesting thoughts here. The issue might be definitional. If you are clustering years as if they are independent of each other (maybe like wine vintages), then arguably it is not time series analysis to start with since you may not be concerned with the order of the years. If it is considered time series analysis, then maybe the paper's authors have a stricter definition.
Food for thought. Thanks for the thought-provoking post.