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.