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- Time Series (`astropy.timeseries`)

# Time Series (`astropy.timeseries`)

## Introduction

From sampling a continuous variable at fixed times to counting events binned into time windows, many different areas of astrophysics require the manipulation of 1D time series data. To address this need, the `astropy.timeseries` subpackage provides classes to represent and manipulate time series.

The time series classes presented below are `QTable` subclasses that have special columns to represent times using the `Time` class. Therefore, much of the functionality described in Data Tables (astropy.table) applies here. But the main purpose of the new classes are to provide time series-specific functionality above and beyond `QTable`.

## Getting Started

In this section, we take a quick look at how to read in a time series, access the data, and carry out some basic analysis. For more details about creating and using time series, see the full documentation in Using timeseries.

The most basic time series class is `TimeSeries` — it represents a time series as a collection of values at specific points in time. If you are interested in representing time series as measurements in discrete time bins, you will likely be interested in the `BinnedTimeSeries` subclass which we show in Using timeseries).

To start off, we retrieve a FITS file containing a Kepler light curve for a source:

    >>> from astropy.utils.data import get_pkg_data_filename
    >>> filename = get_pkg_data_filename('timeseries/kplr010666592-2009131110544_slc.fits')

Note

The light curve provided here is handpicked for example purposes. For more information about the Kepler FITS format, see Section 2.3.1 of the Kepler Archive Manual. To get other light curves for science purposes using Python, see the astroquery affiliated package.

We can then use the `TimeSeries` class to read in this file:

    >>> from astropy.timeseries import TimeSeries
    >>> ts = TimeSeries.read(filename, format='kepler.fits')

Time series are specialized kinds of `Table` objects:

    >>> ts
    <TimeSeries length=14280>
              time             timecorr   ...   pos_corr1      pos_corr2
                                  d       ...      pix            pix
              Time             float32    ...    float32        float32
    ----------------------- ------------- ... -------------- --------------
    2009-05-02T00:41:40.338  6.630610e-04 ...  1.5822421e-03 -1.4463664e-03
    2009-05-02T00:42:39.188  6.630857e-04 ...  1.5743829e-03 -1.4540013e-03
    2009-05-02T00:43:38.045  6.631103e-04 ...  1.5665225e-03 -1.4616371e-03
    2009-05-02T00:44:36.894  6.631350e-04 ...  1.5586632e-03 -1.4692718e-03
    2009-05-02T00:45:35.752  6.631597e-04 ...  1.5508028e-03 -1.4769078e-03
    2009-05-02T00:46:34.601  6.631844e-04 ...  1.5429436e-03 -1.4845425e-03
    2009-05-02T00:47:33.451  6.632091e-04 ...  1.5350844e-03 -1.4921773e-03
    2009-05-02T00:48:32.291  6.632337e-04 ...  1.5272264e-03 -1.4998110e-03
    2009-05-02T00:49:31.149  6.632584e-04 ...  1.5193661e-03 -1.5074468e-03
                        ...           ... ...            ...            ...
    2009-05-11T17:58:22.526  1.014493e-03 ...  3.6121816e-03  3.1950327e-03
    2009-05-11T17:59:21.376  1.014518e-03 ...  3.6102540e-03  3.1872767e-03
    2009-05-11T18:00:20.225  1.014542e-03 ...  3.6083264e-03  3.1795206e-03
    2009-05-11T18:01:19.065  1.014567e-03 ...  3.6063993e-03  3.1717657e-03
    2009-05-11T18:02:17.923  1.014591e-03 ...  3.6044715e-03  3.1640085e-03
    2009-05-11T18:03:16.772  1.014615e-03 ...  3.6025438e-03  3.1562524e-03
    2009-05-11T18:04:15.630  1.014640e-03 ...  3.6006160e-03  3.1484952e-03
    2009-05-11T18:05:14.479  1.014664e-03 ...  3.5986886e-03  3.1407392e-03
    2009-05-11T18:06:13.328  1.014689e-03 ...  3.5967610e-03  3.1329831e-03
    2009-05-11T18:07:12.186  1.014713e-03 ...  3.5948332e-03  3.1252259e-03

In the same way as for `Table` objects, the various columns and rows of `TimeSeries` objects can be accessed and sliced using index notation:

    >>> ts['sap_flux']
    <Quantity [1027045.06, 1027184.44, 1027076.25, ..., 1025451.56, 1025468.5 ,
               1025930.9 ] electron / s>

    >>> ts['time', 'sap_flux']
    <TimeSeries length=14280>
              time             sap_flux
                             electron / s
              Time             float32
    ----------------------- --------------
    2009-05-02T00:41:40.338  1.0270451e+06
    2009-05-02T00:42:39.188  1.0271844e+06
    2009-05-02T00:43:38.045  1.0270762e+06
    2009-05-02T00:44:36.894  1.0271414e+06
    2009-05-02T00:45:35.752  1.0271569e+06
    2009-05-02T00:46:34.601  1.0272296e+06
    2009-05-02T00:47:33.451  1.0273199e+06
    2009-05-02T00:48:32.291  1.0271497e+06
    2009-05-02T00:49:31.149  1.0271755e+06
                        ...            ...
    2009-05-11T17:58:22.526  1.0234769e+06
    2009-05-11T17:59:21.376  1.0234574e+06
    2009-05-11T18:00:20.225  1.0238128e+06
    2009-05-11T18:01:19.065  1.0243234e+06
    2009-05-11T18:02:17.923  1.0244257e+06
    2009-05-11T18:03:16.772  1.0248654e+06
    2009-05-11T18:04:15.630  1.0250156e+06
    2009-05-11T18:05:14.479  1.0254516e+06
    2009-05-11T18:06:13.328  1.0254685e+06
    2009-05-11T18:07:12.186  1.0259309e+06

    >>> ts[0:4]
    <TimeSeries length=4>
              time             timecorr   ...   pos_corr1      pos_corr2
                                  d       ...      pix            pix
              Time             float32    ...    float32        float32
    ----------------------- ------------- ... -------------- --------------
    2009-05-02T00:41:40.338  6.630610e-04 ...  1.5822421e-03 -1.4463664e-03
    2009-05-02T00:42:39.188  6.630857e-04 ...  1.5743829e-03 -1.4540013e-03
    2009-05-02T00:43:38.045  6.631103e-04 ...  1.5665225e-03 -1.4616371e-03
    2009-05-02T00:44:36.894  6.631350e-04 ...  1.5586632e-03 -1.4692718e-03

As seen in the previous examples, `TimeSeries` objects have a `time` column, which is always the first column. This column can also be accessed using the `.time` attribute:

    >>> ts.time
    <Time object: scale='tdb' format='isot' value=['2009-05-02T00:41:40.338' '2009-05-02T00:42:39.188'
      '2009-05-02T00:43:38.045' ... '2009-05-11T18:05:14.479'
      '2009-05-11T18:06:13.328' '2009-05-11T18:07:12.186']>

The first column is always a `Time` object (see Times and Dates), which therefore supports the ability to convert to different time scales and formats:

    >>> ts.time.mjd
    array([54953.0289391 , 54953.02962023, 54953.03030145, ...,
           54962.7536398 , 54962.75432093, 54962.75500215])

    >>> ts.time.unix
    array([1.24122483e+09, 1.24122489e+09, 1.24122495e+09, ...,
           1.24206505e+09, 1.24206511e+09, 1.24206517e+09])

We can also check what time scale the time is defined on:

    >>> ts.time.scale
    'tdb'

This is the Barycentric Dynamical Time scale (see Time and Dates (astropy.time) for more details). We can use what we have seen so far to make a plot:

    import matplotlib.pyplot as plt
    plt.plot(ts.time.jd, ts['sap_flux'], 'k.', markersize=1)
    plt.xlabel('Julian Date')
    plt.ylabel('SAP Flux (e-/s)')

(png, svg, pdf)

It looks like there are a few transits! We can use the `BoxLeastSquares` class to estimate the period, using the “box least squares” (BLS) algorithm:

    >>> import numpy as np
    >>> from astropy import units as u
    >>> from astropy.timeseries import BoxLeastSquares
    >>> periodogram = BoxLeastSquares.from_timeseries(ts, 'sap_flux')

To run the periodogram analysis, we use a box with a duration of 0.2 days:

    >>> results = periodogram.autopower(0.2 * u.day)
    >>> best = np.argmax(results.power)
    >>> period = results.period[best]
    >>> period
    <Quantity 2.20551724 d>
    >>> transit_time = results.transit_time[best]
    >>> transit_time
    <Time object: scale='tdb' format='isot' value=2009-05-02T20:51:16.338>

For more information on available periodogram algorithms, see Periodogram Algorithms.

We can now fold the time series using the period we found above using the `fold()` method:

    >>> ts_folded = ts.fold(period=period, epoch_time=transit_time)

Now we can take a look at the folded time series:

    plt.plot(ts_folded.time.jd, ts_folded['sap_flux'], 'k.', markersize=1)
    plt.xlabel('Time (days)')
    plt.ylabel('SAP Flux (e-/s)')

(png, svg, pdf)

Using the Astrostatistics Tools (astropy.stats) module, we can normalize the flux by sigma-clipping the data to determine the baseline flux:

    >>> from astropy.stats import sigma_clipped_stats
    >>> mean, median, stddev = sigma_clipped_stats(ts_folded['sap_flux'])
    >>> ts_folded['sap_flux_norm'] = ts_folded['sap_flux'] / median

And we can downsample the time series by binning the points into bins of equal time — this returns a `BinnedTimeSeries`:

    >>> from astropy.timeseries import aggregate_downsample
    >>> ts_binned = aggregate_downsample(ts_folded, time_bin_size=0.03 * u.day)
    >>> ts_binned
    <BinnedTimeSeries length=74>
       time_bin_start   time_bin_size ...        pos_corr2          sap_flux_norm
                              d       ...           pix
         TimeDelta         float64    ...         float64              float64
    ------------------- ------------- ... ----------------------- ------------------
    -1.1022116370482966          0.03 ...  0.00031207725987769663 0.9998741745948792
    -1.0722116370482966          0.03 ...  0.00041217938996851444 0.9999074339866638
    -1.0422116370482966          0.03 ...  0.00039273229776881635  0.999972939491272
    -1.0122116370482965          0.03 ...   0.0002928022004198283 1.0000077486038208
    -0.9822116370482965          0.03 ...   0.0003891147789545357 0.9999921917915344
    -0.9522116370482965          0.03 ...   0.0003491091774776578 1.0000101327896118
    -0.9222116370482966          0.03 ...   0.0002824827388394624 1.0000121593475342
    -0.8922116370482965          0.03 ...  0.00016335179680027068 0.9999905228614807
    -0.8622116370482965          0.03 ...   0.0001397567830281332 1.0000263452529907
                    ...           ... ...                     ...                ...
      0.817788362951705          0.03 ... -2.2798192730988376e-05 1.0000624656677246
      0.847788362951705          0.03 ...  0.00022221534163691103 1.0000633001327515
      0.877788362951705          0.03 ...  0.00019213277846574783 1.0000433921813965
     0.9077883629517051          0.03 ...   0.0002187517675338313  1.000024676322937
     0.9377883629517049          0.03 ...  0.00016979355132207274 1.0000224113464355
     0.9677883629517047          0.03 ...  0.00014231358363758773 1.0000698566436768
     0.9977883629517045          0.03 ...   0.0001224415173055604 0.9999606013298035
     1.0277883629517042          0.03 ...  0.00027701034559868276 0.9999635815620422
      1.057788362951704          0.03 ...   0.0003093520936090499 0.9999105930328369
     1.0877883629517038          0.03 ...  0.00022884277859702706 0.9998687505722046

Now we can take a look at the final result:

    plt.plot(ts_folded.time.jd, ts_folded['sap_flux_norm'], 'k.', markersize=1)
    plt.plot(ts_binned.time_bin_start.jd, ts_binned['sap_flux_norm'], 'r-', drawstyle='steps-post')
    plt.xlabel('Time (days)')
    plt.ylabel('Normalized flux')

(png, svg, pdf)

To learn more about the capabilities in the `astropy.timeseries` module, you can find links to the full documentation in the next section.

## Using `timeseries`

The details of using `astropy.timeseries` are provided in the following sections:

### Initializing and Reading in Time Series

- Creating Time Series
  - Initializing a Time Series
  - Initializing a Binned Time Series
  - Adding Data to the Time Series
- Reading and Writing Time Series
  - Built-in Readers
  - Reading Common Light Curve Formats

### Accessing Data and Manipulating Time Series

- Accessing Data in Time Series
  - Accessing Data
  - Accessing Times
  - Extracting a Subset of Columns
  - Extracting a Subset of Rows
- Converting between Different Time Representations
  - Converting Times
  - Formatting Times
  - Times Relative to Other Times
- Manipulation and Analysis of Time Series
  - Combining Time Series
  - Sorting Time Series
  - Resampling
  - Folding
  - Arithmetic
- Masking Values in Time Series
  - Example
- Interfacing with the Pandas Package
  - Example

### Periodogram Algorithms

- Lomb-Scargle Periodograms
  - Basic Usage
  - Periodogram Normalizations
  - Peak Significance and False Alarm Probabilities
  - Periodogram Algorithms
  - RR Lyrae Example
  - Literature References
- Box Least Squares (BLS) Periodogram
  - Mathematical Background
  - Basic Usage
  - Objectives
  - Period Grid
  - Peak Statistics
  - Literature References

## Reference/API

### astropy.timeseries Package

This subpackage contains classes and functions for work with time series.

#### Functions

`aggregate_downsample`(time_series, *[, ...]) | Downsample a time series by binning values into bins with a fixed size or custom sizes, using a single function to combine the values in the bin.
`autocheck_required_columns`(cls) | This is a decorator that ensures that the table contains specific methods indicated by the _required_columns attribute.

#### Classes

`BasePeriodogram`(t, y[, dy]) |
`BaseTimeSeries`([data, masked, names, dtype, ...]) |
`BinnedTimeSeries`([data, time_bin_start, ...]) | A class to represent binned time series data in tabular form.
`BoxLeastSquares`(t, y[, dy]) | Compute the box least squares periodogram
`BoxLeastSquaresResults`(*args) | The results of a BoxLeastSquares search
`LombScargle`(t, y[, dy, fit_mean, ...]) | Compute the Lomb-Scargle Periodogram.
`TimeSeries`([data, time, time_start, ...]) | A class to represent time series data in tabular form.

#### Class Inheritance Diagram

### astropy.timeseries.io Package

#### Functions

`kepler_fits_reader`(filename) | This serves as the FITS reader for KEPLER or TESS files within astropy-timeseries.