# How to find which time series is trending more?

Let us say I have two sets of time varying series as shown below:

a <- c(895,0,0,0,0,832,0,3084,0,434,0,0,0,0,853,0,3727,0,513,0,0,0,0,1248,0,3704,0,646,0,0,0,0,2066,0,5500,0,424,0,0,0,0,1069,0)
b <- c(234,0,0,0,0,521,0,1683,0,152,0,0,0,0,740,0,3242,0,355,0,0,0,0,1117,0,3047,0,443,0,0,0,0,832,0,3213,0,326,0,0,0,0,1235,0)

Here, each value represents the number of times a person has listened to a song. Also, the data is daily which means if the first value (a[1] = 895) is for 10th Feb then the last value will be for 25th Mar.

I want to find out whether a or b is trending more and by what margin, so if I have let say another series c then I can arrange them in the trending order for example c > a > b . Is there a statistical approach to do this.

You need to use decompose function. I assumed frequency =7.

> a <- c(895,0,0,0,0,832,0,3084,0,434,0,0,0,0,853,0,3727,0,513,0,0,0,0,1248,0,3704,0,646,0,0,0,0,2066,0,5500,0,424,0,0,0,0,1069,0)
> b <- c(234,0,0,0,0,521,0,1683,0,152,0,0,0,0,740,0,3242,0,355,0,0,0,0,1117,0,3047,0,443,0,0,0,0,832,0,3213,0,326,0,0,0,0,1235,0)
> n=length(a)
> a.ts=ts(a,frequency =7)
> a.component=decompose(a.ts)
>
> b.ts=ts(b,frequency =7)
> b.component=decompose(b.ts)

Looking at decomposition for a

> plot(a.component)

Looking at decomposition for b

> plot(b.component)

Comparing the trends:

> plot(1:n,a.component$trend,type="l",ylim=c(100,1150),ylab="Trend",xlab="Time") > points(1:n,b.component$trend,type="l",col="blue",lwd=2)
> legend("topleft",lty=rep(1,2),lwd=c(1,2),col=c("black","blue"),legend=c("Trend for a", "Trend for b"))

• That is good, as I can see which one is trending but how do I a parameter whose value determine which is trending more as I have something around 1M time series sequences – Ankit Apr 8 '14 at 6:32
• Will fitting a Linear Regression model help here? or are there any other options as well ? – Ankit Apr 8 '14 at 6:33
• You have too many zeros in your time series data. Basically you have count time series with excess zeros. So maybe Package 'ZIM' in R can help. I don't think linear regression helps in this case. – Stat Apr 8 '14 at 16:14