The ts Format
If you save the data in the special format ts, the plotting function plot.ts can produce a better-looking x-axis automatically. The ts format adds attributes to your data, such as the beginning and end times and frequency. This section shows how you can convert a usual vector to the ts format, then plot it.
Reading Time Series Data
The first thing that you will want to do to analyse your time series data will be to read it into R, and to plot the time series. You can read data into R using the scan() function, which assumes that your data for successive time points is in a simple text file with one column.
For example, the file http://robjhyndman.com/tsdldata/misc/kings.dat contains data on the age of death of successive kings of England, starting with William the Conqueror (original source: Hipel and Mcleod, 1994).
The data set looks like this:
Age of Death of Successive Kings of England #starting with William the Conqueror #Source: McNeill, "Interactive Data Analysis" 60 43 67 50 56 42 50 65 68 43 65 34 ...
Only the first few lines of the file have been shown. The first three lines contain some comment on the data, and we want to ignore this when we read the data into R. We can use this by using the “skip” parameter of the scan() function, which specifies how many lines at the top of the file to ignore. To read the file into R, ignoring the first three lines, we type:
> kings <- scan("http://robjhyndman.com/tsdldata/misc/kings.dat",skip=3) Read 42 items > kings [1] 60 43 67 50 56 42 50 65 68 43 65 34 47 34 49 41 13 35 53 56 16 43 69 59 48 [26] 59 86 55 68 51 33 49 67 77 81 67 71 81 68 70 77 56
In this case the age of death of 42 successive kings of England has been read into the variable 'kings'.
Once you have read the time series data into R, the next step is to store the data in a time series object in R, so that you can use R's many functions for analysing time series data. To store the data in a time series object, we use the ts() function in R. For example, to store the data in the variable 'kings' as a time series object in R, we type:
> kingstimeseries <- ts(kings) > kingstimeseries Time Series: Start = 1 End = 42 Frequency = 1 [1] 60 43 67 50 56 42 50 65 68 43 65 34 47 34 49 41 13 35 53 56 16 43 69 59 48 [26] 59 86 55 68 51 33 49 67 77 81 67 71 81 68 70 77 56
Sometimes the time series data set that you have may have been collected at regular intervals that were less than one year, for example, monthly or quarterly. In this case, you can specify the number of times that data was collected per year by using the 'frequency' parameter in the ts() function. For monthly time series data, you set frequency=12, while for quarterly time series data, you set frequency=4.
You can also specify the first year that the data was collected, and the first interval in that year by using the 'start' parameter in the ts() function. For example, if the first data point corresponds to the second quarter of 1986, you would set start=c(1986,2).
An example is a data set of the number of births per month in New York city, from January 1946 to December 1959 (originally collected by Newton). This data is available in the file http://robjhyndman.com/tsdldata/data/nybirths.dat We can read the data into R, and store it as a time series object, by typing:
> births <- scan("http://robjhyndman.com/tsdldata/data/nybirths.dat") Read 168 items > birthstimeseries <- ts(births, frequency=12, start=c(1946,1)) > birthstimeseries Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1946 26.663 23.598 26.931 24.740 25.806 24.364 24.477 23.901 23.175 23.227 21.672 21.870 1947 21.439 21.089 23.709 21.669 21.752 20.761 23.479 23.824 23.105 23.110 21.759 22.073 1948 21.937 20.035 23.590 21.672 22.222 22.123 23.950 23.504 22.238 23.142 21.059 21.573 1949 21.548 20.000 22.424 20.615 21.761 22.874 24.104 23.748 23.262 22.907 21.519 22.025 1950 22.604 20.894 24.677 23.673 25.320 23.583 24.671 24.454 24.122 24.252 22.084 22.991 1951 23.287 23.049 25.076 24.037 24.430 24.667 26.451 25.618 25.014 25.110 22.964 23.981 1952 23.798 22.270 24.775 22.646 23.988 24.737 26.276 25.816 25.210 25.199 23.162 24.707 1953 24.364 22.644 25.565 24.062 25.431 24.635 27.009 26.606 26.268 26.462 25.246 25.180 1954 24.657 23.304 26.982 26.199 27.210 26.122 26.706 26.878 26.152 26.379 24.712 25.688 1955 24.990 24.239 26.721 23.475 24.767 26.219 28.361 28.599 27.914 27.784 25.693 26.881 1956 26.217 24.218 27.914 26.975 28.527 27.139 28.982 28.169 28.056 29.136 26.291 26.987 1957 26.589 24.848 27.543 26.896 28.878 27.390 28.065 28.141 29.048 28.484 26.634 27.735 1958 27.132 24.924 28.963 26.589 27.931 28.009 29.229 28.759 28.405 27.945 25.912 26.619 1959 26.076 25.286 27.660 25.951 26.398 25.565 28.865 30.000 29.261 29.012 26.992 27.897
Similarly, the file http://robjhyndman.com/tsdldata/data/fancy.dat contains monthly sales for a souvenir shop at a beach resort town in Queensland, Australia, for January 1987-December 1993 (original data from Wheelwright and Hyndman, 1998). We can read the data into R by typing:
> souvenir <- scan("http://robjhyndman.com/tsdldata/data/fancy.dat") Read 84 items > souvenirtimeseries <- ts(souvenir, frequency=12, start=c(1987,1)) > souvenirtimeseries Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1987 1664.81 2397.53 2840.71 3547.29 3752.96 3714.74 4349.61 3566.34 5021.82 6423.48 7600.60 19756.21 1988 2499.81 5198.24 7225.14 4806.03 5900.88 4951.34 6179.12 4752.15 5496.43 5835.10 12600.08 28541.72 1989 4717.02 5702.63 9957.58 5304.78 6492.43 6630.80 7349.62 8176.62 8573.17 9690.50 15151.84 34061.01 1990 5921.10 5814.58 12421.25 6369.77 7609.12 7224.75 8121.22 7979.25 8093.06 8476.70 17914.66 30114.41 1991 4826.64 6470.23 9638.77 8821.17 8722.37 10209.48 11276.55 12552.22 11637.39 13606.89 21822.11 45060.69 1992 7615.03 9849.69 14558.40 11587.33 9332.56 13082.09 16732.78 19888.61 23933.38 25391.35 36024.80 80721.71 1993 10243.24 11266.88 21826.84 17357.33 15997.79 18601.53 26155.15 28586.52 30505.41 30821.33 46634.38 104660.67
Plotting Time Series
Once you have read a time series into R, the next step is usually to make a plot of the time series data, which you can do with the plot.ts() function in R.
For example, to plot the time series of the age of death of 42 successive kings of England, we type:
> plot.ts(kingstimeseries)
We can see from the time plot that this time series could probably be described using an additive model, since the random fluctuations in the data are roughly constant in size over time.
Likewise, to plot the time series of the number of births per month in New York city, we type:
> plot.ts(birthstimeseries)
We can see from this time series that there seems to be seasonal variation in the number of births per month: there is a peak every summer, and a trough every winter. Again, it seems that this time series could probably be described using an additive model, as the seasonal fluctuations are roughly constant in size over time and do not seem to depend on the level of the time series, and the random fluctuations also seem to be roughly constant in size over time.
Similarly, to plot the time series of the monthly sales for the souvenir shop at a beach resort town in Queensland, Australia, we type:
> plot.ts(souvenirtimeseries)
In this case, it appears that an additive model is not appropriate for describing this time series, since the size of the seasonal fluctuations and random fluctuations seem to increase with the level of the time series. Thus, we may need to transform the time series in order to get a transformed time series that can be described using an additive model. For example, we can transform the time series by calculating the natural log of the original data:
> logsouvenirtimeseries <- log(souvenirtimeseries) > plot.ts(logsouvenirtimeseries)
Here we can see that the size of the seasonal fluctuations and random fluctuations in the log-transformed time series seem to be roughly constant over time, and do not depend on the level of the time series. Thus, the log-transformed time series can probably be described using an additive model.
Source: A. Coghlan, https://a-little-book-of-r-for-time-series.readthedocs.io/en/latest/src/timeseries.html#reading-time-series-data
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