Base R ships with a lot of functionality useful for time series, in
particular in the stats package. However, these
features are not adapted to most archaeological time series. These are
indeed defined for a given calendar era, they can involve dates very far
in the past and the sampling of the observation time is (in most cases)
not constant. aion provides a system of classes and
methods to represent and work with such time-series.
Calendars
aion currently supports both Julian and Gregorian
calendars (with the most common eras for the latter, e.g. Before
Present, Common Era…). A calendar can be defined using the
calendar() function:
## Create a calendar object
## (Gregorian Common Era)
calendar("CE")
#> Common Era (CE): Gregorian years counted forwards from 0.
Or by using the shortcuts:
## Common Era (Gregorian)
CE()
#> Common Era (CE): Gregorian years counted forwards from 0.
## Before Present (Gregorian)
BP()
#> Before Present (BP): Gregorian years counted backwards from 1950.
When creating date vectors or time series, you must specify
the calendar corresponding to your data (see below). This allows to
select the correct method for converting dates to rata die.
Outputs generated by aion are expressed in rata die
by default (this can be modified on a per-function basis). The
only two exceptions are the plot() and
format() functions, which default to the calendar specified
in the package options (see below). You can change the default calendar
to be used throughout the package by modifying the
aion.calendar option, or on a per-function basis.
## Get default calendar
getOption("aion.calendar")
#> Common Era (CE): Gregorian years counted forwards from 0.
## Change default calendar to BP
options(aion.calendar = BP())
getOption("aion.calendar")
#> Before Present (BP): Gregorian years counted backwards from 1950.
## Set it back to Gregorian Common Era
options(aion.calendar = CE())
getOption("aion.calendar")
#> Common Era (CE): Gregorian years counted forwards from 0.
Vectors of dates
In base R, dates are represented by default as the number of days
since 1970-01-01 (Gregorian), with negative values for earlier dates
(see help(Date)). aion uses a different
approach: it allows to create date vectors represented as rata
die (Reingold and Dershowitz 2018),
i.e. as number of days since 01-01-01 (Gregorian).
This makes it possible to get rid of a specific calendar and to make
calculations easier. It is then possible to convert a vector of rata
die into dates or (decimal) years of any calendar.
The fixed() function allows to create a vector of
rata die from dates belonging to a specific calendar:
## Convert 2000-02-29 (Gregorian) to rata die
fixed(2000, 02, 29, calendar = calendar("CE"))
#> Rata die: number of days since 01-01-01 (Gregorian).
#> [1] 730179
## If days and months are missing, decimal years are expected
fixed(2000.161, calendar = calendar("CE"))
#> Rata die: number of days since 01-01-01 (Gregorian).
#> [1] 730179
A rata die vector can be converted into dates (or years) of
a particular calendar:
## Create a vector of 10 years BP (Gregorian)
## (every 20 years starting from 2000 BP)
(years <- seq(from = 20000, by = -20, length.out = 10))
#> [1] 20000 19980 19960 19940 19920 19900 19880 19860 19840 19820
## Convert years to rata die
(rd <- fixed(years, calendar = calendar("BP")))
#> Rata die: number of days since 01-01-01 (Gregorian).
#> [1] -6592992 -6585687 -6578382 -6571077 -6563772 -6556467 -6549162 -6541857
#> [9] -6534553 -6527248
## Convert back to Gregorian years
as_year(rd, calendar = calendar("CE")) # Common Era
#> [1] -18050 -18030 -18010 -17990 -17970 -17950 -17930 -17910 -17890 -17870
as_year(rd, calendar = calendar("BP")) # Before Present
#> [1] 20000 19980 19960 19940 19920 19900 19880 19860 19840 19820
as_year(rd, calendar = calendar("b2k")) # Before 2000
#> [1] 20050 20030 20010 19990 19970 19950 19930 19910 19890 19870
Rata die can be represented as (nicely formated) character
vectors:
format(rd) # Default calendar (Gregorian Common Era)
#> [1] "-18050 CE" "-18030 CE" "-18010 CE" "-17990 CE" "-17970 CE" "-17950 CE"
#> [7] "-17930 CE" "-17910 CE" "-17890 CE" "-17870 CE"
format(rd, prefix = "ka", calendar = calendar("BP"))
#> [1] "20 ka BP" "19.98 ka BP" "19.96 ka BP" "19.94 ka BP" "19.92 ka BP"
#> [6] "19.9 ka BP" "19.88 ka BP" "19.86 ka BP" "19.84 ka BP" "19.82 ka BP"
The rata die vector provides the internal time
representation of the aion time-series (if you want to
work with numeric vectors that represent year-based time scales, you may
be interested in the era
package).
Time series
A time series is a sequence of observation time and value pairs with
strictly increasing observation times.
A time series object is an \(n \times m
\times p\) array, with \(n\)
being the number of observations, \(m\)
being the number of series and with the \(p\) columns of the third dimension
containing extra variables for each series. It can be created from a
numeric vector, matrix or
array.
## Set seed for reproductibility
set.seed(12345)
## 6 x 50 observations...
obs <- matrix(rnorm(300), nrow = 50, ncol = 6)
## ...sampled every two years starting from 2000 BP
spl <- seq(from = 2000, by = -2, length.out = 50)
## Create time series
(X <- series(object = obs, time = spl, calendar = BP()))
#> 50 x 6 x 1 time series observed between -18627 and 17167 r.d.
Time series terminal and sampling times can be retrieved and
expressed according to different calendars (remember that
outputs are expressed in rata die by default):
## Time series duration
span(X) # Default: rata die
#> [1] 35794
span(X, calendar = CE())
#> [1] 98.99726
## Time of first observation
start(X) # Default: rata die
#> [1] -18627
start(X, calendar = CE())
#> [1] -50
## Time of last observation
end(X) # Default: rata die
#> [1] 17167
end(X, calendar = CE())
#> [1] 48
## Sampling times
time(X, calendar = BP())
#> [1] 2000 1998 1996 1994 1992 1990 1988 1986 1984 1982 1980 1978 1976 1974 1972
#> [16] 1970 1968 1966 1964 1962 1960 1958 1956 1954 1952 1950 1948 1946 1944 1942
#> [31] 1940 1938 1936 1934 1932 1930 1928 1926 1924 1922 1920 1918 1916 1914 1912
#> [46] 1910 1908 1906 1904 1902
Plot one or more time series:
## Multiple plot
plot(X) # Default calendar
## Extract the first series
Y <- X[, 1, ]
## Plot a single series
plot(
Y,
calendar = b2k(), # b2k time scale
panel.first = graphics::grid() # Add a grid
)
year_axis(side = 3, calendar = CE()) # Add a secondary time axis
mtext(format(CE()), side = 3, line = 3) # Add secondary axis title
Note that aion uses the astronomical notation for
Gregorian years (there is a year 0).