# Introduction to aion

## N. Frerebeau

### 2026-06-23

    library(aion)

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.

# 1 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")
    #> Ère commune (è. c.): Années grégoriennes comptées à partir de 0

Or by using the shortcuts:

    ## Common Era (Gregorian)
    CE()
    #> Ère commune (è. c.): Années grégoriennes comptées à partir de 0

    ## Before Present (Gregorian)
    BP()
    #> Avant le présent (BP): Années grégoriennes comptées à rebours à partir de 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 with `set_calendar()`, or on a per-function basis.

    ## Get default calendar
    get_calendar()
    #> Ère commune (è. c.): Années grégoriennes comptées à partir de 0

    ## Change default calendar to BP
    set_calendar("BP")
    get_calendar()
    #> Avant le présent (BP): Années grégoriennes comptées à rebours à partir de 1950

    ## Set it back to Gregorian Common Era
    set_calendar("CE")
    get_calendar()
    #> Ère commune (è. c.): Années grégoriennes comptées à partir de 0

# 2 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)1.

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 : nombre de jours depuis le 01-01-01 (grégorien)
    #> [1] 730179

    ## If days and months are missing, decimal years are expected
    fixed(2000.161, calendar = calendar("CE"))
    #> Rata die : nombre de jours depuis le 01-01-01 (grégorien)
    #> [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 = 2000, by = -20, length.out = 10))
    #>  [1] 2000 1980 1960 1940 1920 1900 1880 1860 1840 1820

    ## Convert years to rata die
    (rd <- fixed(years, calendar = calendar("BP")))
    #> Rata die : nombre de jours depuis le 01-01-01 (grégorien)
    #>  [1] -18627 -11322  -4017   3288  10593  17898  25203  32508  39812  47117

    ## Convert back to Gregorian years
    as_year(rd, calendar = calendar("CE"))  # Common Era
    #>  [1] -50 -30 -10  10  30  50  70  90 110 130
    as_year(rd, calendar = calendar("BP"))  # Before Present
    #>  [1] 2000 1980 1960 1940 1920 1900 1880 1860 1840 1820
    as_year(rd, calendar = calendar("b2k")) # Before 2000
    #>  [1] 2050 2030 2010 1990 1970 1950 1930 1910 1890 1870

Rata die can be represented as (nicely formated) character vectors:

    format(rd) # Default calendar (Gregorian Common Era)
    #>  [1] "-50 è. c." "-30 è. c." "-10 è. c." "10 è. c."  "30 è. c."  "50 è. c."
    #>  [7] "70 è. c."  "90 è. c."  "110 è. c." "130 è. c."
    format(rd, prefix = "ka", calendar = calendar("BP"))
    #>  [1] "2 ka BP"    "1.98 ka BP" "1.96 ka BP" "1.94 ka BP" "1.92 ka BP"
    #>  [6] "1.9 ka BP"  "1.88 ka BP" "1.86 ka BP" "1.84 ka BP" "1.82 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).

# 3 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`.

    ## Get ceramic counts (data from Husi 2022)
    data("loire", package = "folio")

    ## Keep only variables whose total is at least 600
    keep <- c("01f", "01k", "01L", "08e", "08t", "09b", "15i", "15q")

    ## Get time midpoints
    mid <- rowMeans(loire[, c("lower", "upper")])

    ## Create time-series
    (X <- series(
      object = loire[, keep],
      time = mid,
      calendar = calendar("AD")
    ))
    #> 332 x 8 x 1 séries chronologiques observées entre 450 è. c. et 1812.5 è. c.

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] 497642
    span(X, calendar = CE())
    #> [1] 1362.5

    ## Time of first observation
    start(X) # Default: rata die
    #> [1] 163995
    start(X, calendar = CE())
    #> [1] 450

    ## Time of last observation
    end(X) # Default: rata die
    #> [1] 661637
    end(X, calendar = CE())
    #> [1] 1812.5

    ## Sampling times
    time(X, calendar = BP())
    #>   [1] 1500.0 1475.0 1475.0 1463.5 1450.0 1450.0 1450.0 1450.0 1438.5 1438.5
    #>  [11] 1438.5 1425.0 1413.5 1400.0 1400.0 1400.0 1400.0 1400.0 1400.0 1400.0
    #>  [21] 1400.0 1400.0 1400.0 1400.0 1400.0 1400.0 1400.0 1400.0 1400.0 1400.0
    #>  [31] 1388.5 1375.0 1375.0 1375.0 1363.5 1350.0 1350.0 1350.0 1350.0 1350.0
    #>  [41] 1350.0 1350.0 1350.0 1325.0 1313.5 1313.5 1300.0 1300.0 1300.0 1300.0
    #>  [51] 1275.0 1275.0 1275.0 1275.0 1263.5 1250.0 1250.0 1250.0 1250.0 1250.0
    #>  [61] 1250.0 1250.0 1250.0 1250.0 1238.5 1238.5 1238.5 1225.0 1225.0 1225.0
    #>  [71] 1213.5 1213.5 1213.5 1213.5 1200.0 1200.0 1200.0 1200.0 1188.5 1188.5
    #>  [81] 1188.5 1188.5 1175.0 1175.0 1175.0 1175.0 1163.5 1163.5 1150.0 1150.0
    #>  [91] 1150.0 1150.0 1150.0 1150.0 1150.0 1150.0 1150.0 1150.0 1150.0 1150.0
    #> [101] 1150.0 1150.0 1150.0 1150.0 1150.0 1150.0 1150.0 1150.0 1150.0 1150.0
    #> [111] 1150.0 1150.0 1150.0 1150.0 1138.5 1138.5 1138.5 1138.5 1125.0 1125.0
    #> [121] 1125.0 1125.0 1125.0 1125.0 1113.5 1113.5 1113.5 1100.0 1100.0 1100.0
    #> [131] 1100.0 1100.0 1100.0 1100.0 1100.0 1100.0 1100.0 1100.0 1100.0 1088.5
    #> [141] 1088.5 1075.0 1075.0 1075.0 1050.0 1050.0 1050.0 1050.0 1050.0 1050.0
    #> [151] 1050.0 1050.0 1050.0 1050.0 1050.0 1050.0 1050.0 1050.0 1050.0 1050.0
    #> [161] 1050.0 1038.5 1038.5 1038.5 1038.5 1038.5 1038.5 1025.0 1025.0 1025.0
    #> [171] 1025.0 1025.0 1025.0 1025.0 1013.5 1013.5 1013.5 1013.5 1013.5 1013.5
    #> [181] 1013.5 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0
    #> [191] 1000.0 1000.0 1000.0  988.5  963.5  963.5  963.5  950.0  950.0  950.0
    #> [201]  950.0  950.0  950.0  950.0  950.0  950.0  950.0  950.0  950.0  950.0
    #> [211]  950.0  950.0  950.0  950.0  950.0  938.5  925.0  925.0  925.0  925.0
    #> [221]  925.0  925.0  925.0  913.5  913.5  900.0  900.0  900.0  900.0  900.0
    #> [231]  900.0  900.0  900.0  900.0  900.0  875.0  875.0  875.0  863.5  850.0
    #> [241]  850.0  850.0  850.0  850.0  850.0  850.0  838.5  825.0  825.0  813.5
    #> [251]  813.5  800.0  788.5  775.0  763.5  750.0  725.0  725.0  725.0  713.5
    #> [261]  713.5  713.5  700.0  700.0  700.0  700.0  688.5  688.5  675.0  675.0
    #> [271]  675.0  663.5  663.5  663.5  663.5  650.0  650.0  650.0  650.0  638.5
    #> [281]  638.5  638.5  638.5  625.0  625.0  613.5  613.5  600.0  600.0  600.0
    #> [291]  600.0  588.5  575.0  575.0  575.0  538.5  525.0  525.0  525.0  513.5
    #> [301]  513.5  500.0  500.0  500.0  475.0  475.0  475.0  475.0  475.0  463.5
    #> [311]  450.0  450.0  450.0  425.0  425.0  425.0  425.0  425.0  413.5  363.5
    #> [321]  338.5  325.0  313.5  313.5  275.0  250.0  250.0  225.0  188.5  175.0
    #> [331]  150.0  138.5

Plot one or more time series:

    ## Multiple plot (default calendar)
    plot(
      x = X,
      type = "h" # histogram like vertical lines
    )

    ## Extract the first series
    Y <- X[, 1, ]

    ## Plot a single series
    plot(
      Y,
      type = "h", # histogram like vertical lines
      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).

# References

Reingold, Edward M., and Nachum Dershowitz. 2018. Calendrical Calculations: The Ultimate Edition. 4th ed. Cambridge University Press. https://doi.org/10.1017/9781107415058.

1. Although it is intended that the rata die should be an integer value, this is not enforced in the internal representation. R’s numeric type is a double-precision floating-point that follows the IEEE 754 standard. This means that a numeric can safely represent an integer value up to `2^53 - 1`. This covers more than the age of the Universe: `fixed(13.8, calendar = CE(), scale = 10^9)`. ↩