Trends and seasonality in Multiple Time Series (in R)

Question

In the past last days I have been struggling a lot trying to handle my data. The question is that all the information I find online and in books dont suit my data.

My original data is +100 columns of time series (independent from each others), each with 48 months, starting in 08/2017 and finishing in 07/2021.

The objective is to obtain a value/metric representing the trend/seasonality, for each time series, so I can then make comparisons between them.

Below a data sample and two approaches that I tried to follow but failed.

Data sample (with only 6 columns of data, named orderly from 287 to 293):

                 287        288       289       290        292        293
2017-08-01 0.1613709 0.09907194 0.2542814 0.2179386 0.08020622 0.07926023
2017-09-01 0.1774719 0.10227714 0.2211257 0.1979846 0.09384094 0.10182659
2017-10-01 0.1738235 0.11191972 0.2099357 0.1930938 0.08038543 0.09304474
2017-11-01 0.1999949 0.14005038 0.2282944 0.2140095 0.08814765 0.10820706
2017-12-01 0.2203560 0.16408010 0.1864422 0.1890152 0.08735655 0.11958204
2018-01-01 0.2728642 0.22230381 0.1906515 0.1954573 0.10269819 0.13728082
2018-02-01 0.2771547 0.24142554 0.2287340 0.2431592 0.12353792 0.15428189
2018-03-01 0.2610135 0.24747148 0.2631311 0.2862447 0.18993516 0.17344621
2018-04-01 0.3502901 0.32087711 0.3012136 0.3339466 0.18706540 0.20857209
2018-05-01 0.3669179 0.36063092 0.3789247 0.3781572 0.18566273 0.20633488
2018-06-01 0.2643827 0.27359616 0.3415491 0.3172041 0.19025036 0.18735599
2018-07-01 0.2335092 0.29352583 0.3298348 0.2986179 0.17155325 0.15914827
2018-08-01 0.1994154 0.24043388 0.2868625 0.2659566 0.16226752 0.14772256
2018-09-01 0.1709875 0.20753322 0.2648888 0.2465150 0.15494714 0.14099699
2018-10-01 0.1843677 0.20504727 0.2600666 0.2480716 0.14583226 0.13660546
2018-11-01 0.2662550 0.23209503 0.1921081 0.2067601 0.14891306 0.14775722
2018-12-01 0.3455008 0.25827029 0.1825465 0.2222157 0.15189449 0.15854924
2019-01-01 0.3562984 0.28744854 0.1726661 0.2381863 0.15497530 0.16970100
2019-02-01 0.3596556 0.29504905 0.2190216 0.2532990 0.16528823 0.17614880
2019-03-01 0.3676633 0.30941445 0.2663822 0.3146126 0.19225333 0.19722699
2019-04-01 0.3471219 0.32011859 0.3318789 0.3620176 0.21693162 0.21269362
2019-05-01 0.3391499 0.33623537 0.3498372 0.3514615 0.22655705 0.21467237
2019-06-01 0.2134116 0.23256447 0.3097683 0.2937520 0.20671346 0.18182811
2019-07-01 0.1947303 0.25061919 0.3017159 0.2840877 0.16773642 0.12524420
2019-08-01 0.1676979 0.23042951 0.2933951 0.2741012 0.17294869 0.14598469
2019-09-01 0.1574564 0.20590697 0.2507077 0.2448338 0.16662829 0.14514487
2019-10-01 0.1670441 0.21569649 0.2239352 0.2349953 0.15196066 0.14107334
2019-11-01 0.2314212 0.23944840 0.1962703 0.2248290 0.16566737 0.18157745
2019-12-01 0.2937217 0.26243412 0.2524490 0.2844418 0.17893194 0.22077498
2020-01-01 0.3023854 0.28244002 0.2816947 0.3094329 0.16686343 0.22517501
2020-02-01 0.3511840 0.30870934 0.3109404 0.3344240 0.15479491 0.22957504
2020-03-01 0.3968343 0.33328386 0.3382992 0.3578028 0.14350501 0.23369119
2020-04-01 0.3745884 0.34262505 0.3675449 0.3827939 0.19862225 0.23809122
2020-05-01 0.3530601 0.35166492 0.3709603 0.3476905 0.25196152 0.24234931
2020-06-01 0.2282214 0.20867654 0.3517663 0.3336991 0.24879937 0.22456414
2020-07-01 0.2057477 0.21648387 0.3331914 0.3201591 0.20879761 0.18008671
2020-08-01 0.2000177 0.19419089 0.3040352 0.2979807 0.19359850 0.16924703
2020-09-01 0.1848961 0.19882785 0.2737280 0.2814912 0.17682968 0.15218477
2020-10-01 0.3177567 0.22982973 0.2646506 0.2804482 0.20588015 0.20085790
2020-11-01 0.3710144 0.28390520 0.2552706 0.2793703 0.18294126 0.15860050
2020-12-01 0.3783443 0.27966508 0.2316715 0.2586552 0.17646898 0.17848388
2021-01-01 0.3458173 0.25866979 0.2361880 0.2659490 0.17908497 0.18354894
2021-02-01 0.3604397 0.27641854 0.2407045 0.2732429 0.19147607 0.18462597
2021-03-01 0.3736471 0.29244967 0.2685608 0.2918238 0.20266803 0.18559877
2021-04-01 0.3581235 0.31151629 0.3729554 0.3619925 0.22856252 0.20997657
2021-05-01 0.3513976 0.34056181 0.4269086 0.4071241 0.26643216 0.24394560
2021-06-01 0.2306971 0.29087504 0.3798922 0.2053191 0.25745857 0.23557143
2021-07-01 0.2577626 0.26011944 0.3343924 0.3452438 0.21910554 0.19516812

I have tried to approch the issue with an xts format

projsxts <- xts(x= projs_2017Jul_t, order.by = projs_2017Jul_time)
plot(projsxts,  main="NDVI values for oak projects with ESR (fitted values)", xlab="Time", ylab="NDVI")

[Xts timeseries plot][1] [1]: https://i.stack.imgur.com/M46YQ.png

And also the normal ts approach, using "mts" as class for a multiple time series:

projs_2017Jul_ts1 <- ts(projs_2017Jul_t, frequency = 12, start=c(2017,8), end = c(2021,8), class = "mts", names = names2017)
print(projs_2017Jul_ts1)

I can obtain a summary, but when I try to use "decompose" I have the errors that "time series has no or less than 2 periods", although it has 48 months.

If I try to "stl", it says its only allowed in univariate series.

describe2017 <- summary.matrix(projs_2017Jul_ts1) #########gives Min, Median, Mean, Max (...) Values per column

projs_2017Jul_ts1 <- decompose(projs_2017Jul_ts1)
*"Error in decompose(projs_2017Jul_ts1) :   time series has no or less than 2 periods"*

decompose_ts <- stl(projs_2017Jul_ts1)
*Error in stl(projs_2017Jul_ts1) : only univariate series are allowed*

Any advice/suggestion on how to do this, please? Thank you !

Answer 1

You basic approach is correct (create a time-series object, then use methods to decompose the time-series). I was able to reproduce your error, which is good. The stl function only takes a single (univariate time-series), but when you feed a single time-series into stl , it gives the same error as you got using the decompose function. I think your data are not long enough for the algorithm to decompose. Typically, you need two full periods of data, in this case, the period is likely supra-annual, and five years is not long enough for the algorithm to identify the periodicity of the series.

see this post: error in stl, series has less than two periods (erroneous?)

## code I used to get your data into R
x <- readClipboard()
ts.data <- read.table(text = x, header = TRUE)

## code to create a timeseies object for 287
ts1 <- xts::xts(ts.data[,"X287"], order.by = as.Date(row.names(ts.data)))

## check the plot
plot(ts1)

plot of ts for 287

## use stl - Cleveland et al 1990 method  for decomposing timeseries into seasonal, trend and remainder  
stl.ts1 <-  stl(ts1)

Error in stl(as.ts(ts1)): series is not periodic or has less than two period