R Time Series Object ts() Date of Minimum and Maximum

My favourite tool for time series is xts, and ts objects translate cleanly:

library(xts)
x = as.xts(data)

Outputs:

> min(index(x))
[1] "Jan 2012"
> max(index(x))
[1] "Dec 2016"

Here is how I deal with that but I'm not familiar with ts and I'm sure there is a better option.

To retrieve the date from the max/min position, you can index the object created by time on your ts. Eg: time(data)[which.max(data)] ; same for which.min.

Then to convert this into a proper year (easy) and month (tricky) index, I usually create this function:

numyear2monthyear <- function(x){   
   c(trunc(x),                   # entire part = year
     round((x-floor(x))*12 + 1)) # decimal part * 12 + 1 (Jan=0) = Month
}

Here is an example:

set.seed(123) # for the sake of reproducibility
data <- ts(round(rnorm(60), 2), frequency = 12, end = c(2016, 12))
data
       Jan   Feb   Mar   Apr   May   Jun   Jul   Aug
2012 -0.56 -0.23  1.56  0.07  0.13  1.72  0.46 -1.27
2013  0.40  0.11 -0.56  1.79  0.50 -1.97  0.70 -0.47
2014 -0.63 -1.69  0.84  0.15 -1.14  1.25  0.43 -0.30
2015  0.55 -0.06 -0.31 -0.38 -0.69 -0.21 -1.27  2.17
2016  0.78 -0.08  0.25 -0.03 -0.04  1.37 -0.23  1.52
Sep   Oct   Nov   Dec
2012 -0.69 -0.45  1.22  0.36
2013 -1.07 -0.22 -1.03 -0.73
2014  0.90  0.88  0.82  0.69
2015  1.21 -1.12 -0.40 -0.47
2016 -1.55  0.58  0.12  0.22

which.min(data)
[1] 18
which.max(data)
[1] 44

numyear2monthyear(time(data)[which.max(data)])
[1] 2015    8

numyear2monthyear(time(data)[which.min(data)])
[1] 2013    6

And usually I turn that into another handy function, like:

extrema_dates <- function(ts){
  ts_min_date <- numyear2monthyear(time(ts)[which.min(ts)])
  ts_max_date <- numyear2monthyear(time(ts)[which.max(ts)])
  list(min=min(ts),
       min_year=ts_min_date[1],
       min_month=ts_min_date[2],
       max=max(ts),
       max_year=ts_max_date[1],
       max_month=ts_max_date[2])
}

> extrema_dates(data)
$min
[1] -1.97

$min_year
[1] 2013

$min_month
[1] 6

$max
[1] 2.17

$max_year
[1] 2015

$max_month
[1] 8

I hope it solves your problem (and would be happy to see a better option to do it).

This is how you find the year and month of the min and max value in the data:

> data <- ts(round(rnorm(60), 2), frequency = 12, end = c(2016, 12))
> data
       Jan   Feb   Mar   Apr   May   Jun   Jul   Aug   Sep   Oct   Nov   Dec
2012  0.18 -0.07 -0.77  1.23 -0.97  1.20 -1.41  1.39 -0.72 -0.94  0.28  0.97
2013 -0.86 -0.57 -0.16 -1.24 -0.35 -0.06  0.78  1.32  1.80 -0.51 -1.91  1.14
2014 -0.51  1.21  0.14  0.30  1.18 -0.32 -0.92 -0.46 -0.97 -0.94 -1.56 -0.63
2015  0.13  0.93 -1.45  1.97  0.04  0.55  0.45  0.13  1.14  0.27  0.15 -1.39
2016  0.68  2.16 -1.56 -0.44  1.07  1.27  1.01 -2.93 -0.19 -0.70  1.44  0.09

The corresponding date of the minimum date is

> data_min_value <- data[which.min(data)]
> data_min_value
[1] -2.93
> data_min_value_time <- time(data)[which.min(data)]
> data_min_value_time
[1] 2016.583
> data_min_value_year <- floor(time(data)[which.min(data)])
> data_min_value_year
[1] 2016
> data_min_value_month <- (time(data)[which.min(data)] %% 1)*12
> data_min_value_month
[1] 7
> data_min_value_month_abb <- month.abb[(time(data)[which.min(data)] %% 1)*12+1]
> data_min_value_month_abb
[1] "Aug"

The date of the maximum value you get similarly

> data[which.max(data)]
[1] 2.16
> floor(time(data)[which.max(data)]) # Year
[1] 2016
> month.abb[(time(data)[which.max(data)] %% 1)*12+1] # Abbreviation of month
[1] "Feb"

Below is summary on the helpful functions which have been used in the above examples:

> floor(2016.563)  # find out the integer part on the number
[1] 2016
> 2016.563 %% 1  # find out the fractional part on the number
[1] 0.563
> month.abb[0.563*12+1]  # find out the abbreviation of the month name 
[1] "Jul"