In the following sections we introduce basic operations for time series analysis. We disuses the following topics:

As mentioned in the previous section there exist many different R-packages to work with time series. Please be aware that basic operations on time series are implemented in most of them. Hence, it is very important to be aware of the object class and respectively, the data representation. This representation dictates which functions will be available for loading, processing, analyzing, printing, and plotting the time series data.


Loading the sample data

For the purpose of demonstration we load the monthly (ts.FUB.monthly) and daily (ts.FUB.daily) time series data for the weather station Berlin-Dahlem (FU) into R. We can do that by using the load() function. Check out the previous section on Data sets used to remind yourself how we processed the data.

library(xts)
load(url("https://userpage.fu-berlin.de/soga/300/30100_data_sets/DWD_FUB.RData"))

First, we check to object classes for the two data sets.

class(ts.FUB.monthly)
## [1] "xts" "zoo"
class(ts.FUB.daily)
## [1] "xts" "zoo"

Perfect, both data sets are of class xts and zoo. Note that xts is just an extension of the zoo class. Visit the vignettes for these both packages to refresh your knowledge on these type of data representation. Type vignette('zoo') and vignette('xts') into your console to open the vignettes.

For the sake of this tutorial we transform the monthly data set (ts.FUB.monthly) into a ts object, but keep the object type (xts) for the daily data set. Therefore, we apply the ts() function, which converts a vector into a time series. The ts object class is less flexible compared to the zoo or xts object classes, however, this object class is widely used and thus, it is important to know how to interact with that particular object class.

The ts function needs as least these arguments:

In order to extract the vector with data (x) from the xts object, in our case the ts.FUB.monthly object, we apply the coredata() function on it.

x <- coredata(ts.FUB.monthly)
head(x)
##      [,1]
## [1,]  2.8
## [2,]  1.1
## [3,]  5.2
## [4,]  9.0
## [5,] 15.1
## [6,] 19.0

Further, to extract the start argument we apply the index() function on of the ts.FUB.monthly object and combine it with the year() and month() function. The start argument is either a single number or a vector of two integers, which specify a natural time unit.

library(lubridate)
start <- c(year(index(ts.FUB.monthly)[01]),
           month(index(ts.FUB.monthly)[01]))
start      
## [1] 1719    1

As we are dealing with monthly data we set the argument frequency = 12.

Putting it all together gives

ts.FUB.monthly = ts(x,
                    start = start, 
                    frequency = 12)
str(ts.FUB.monthly)
##  Time-Series [1:3576, 1] from 1719 to 2017: 2.8 1.1 5.2 9 15.1 19 21.4 18.8 13.9 9 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : NULL
##   ..$ : chr "Series 1"

The ts.FUB.monthly contains a time series of monthly mean temperatures from January 1719 to December 2016.

Let us plot the ts object with the generic plot() function.

plot(ts.FUB.monthly)

We could as well have used the autoplot() function from the ggplot2 package. Let us now visualize the data set ts.FUB.daily using the autoplot() function. However, first we inspect the data set with the str() function.

str(ts.FUB.daily)
## An 'xts' object on 1950-01-01/2016-12-31 containing:
##   Data: num [1:24472, 1:2] -3.2 1 2.8 -0.1 -2.8 2.6 5.7 7 5.8 -2.4 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : NULL
##   ..$ : chr [1:2] "Temp" "Rain"
##   Indexed by objects of class: [Date] TZ: UTC
##   xts Attributes:  
##  NULL

We see that the ts.FUB.daily time series ranges from 1950-01-01 to 2016-12-31. Further, we realize that the xts object ts.FUB.daily stores two time series: one for temperatures (Temp) and one for rainfall (Rain).

library(ggplot2)
autoplot(ts.FUB.daily)