Autocorrelation Analysis

   

The command MAKE/ACF produces an autocovariance/autocorrelation function from data contained either in a list of BDTs or in a single PET. The input data are divided in stretches (maximum length 8192) and an ACF for a single stretch is produced. The output ACF (segmented ACF) is the average (lag by lag) of the single ones. Different choices are available for the normalization of the single ACFs, namely:

1. Plain autocovariance function R
2. Plain autocorrelation function (autocovariance normalized to the variance)
3. Partially unbiased autocovariance function
4. Partially unbiased autocorrelation function

For the definition of partially unbiased autocovariance/autocorrelation function see [Sutherland et al.1978]

In the BDT case the input tables do not have to be necessarily contiguous, but the same bin size is required. Any detected gap in the data will close the current stretch and a new one will be started. If one of the input BDTs is not found, the program is closed at that time. All the parameters for the analysis (filenames included) are contained in the parameter file. Different options are available: rebinning of the input light curve (BDT only), windowing, choice of the length of the single data stretches (maximum length 8192 bins), number of time lags in the output ACF and normalization selection (see above). A parameter is available to select the minimum percentage exposure allowed to accept a bin; it is also possible to compute the ACF of the percentage exposure only (window function).

The syntax of the command is:

MAKE/ACF parfil

where parfil is the name of the parameter file which can be generated using the EXSAS command CREATE/PARFIL ACF. The parameter file entries are shown in Table 7.13.

  
Table 7.13: Parameter file entries for MAKE/ACF

The meaning of the parameters is as follows:

• MODE is the accumulation mode. It can be:
  • BINNED: the input data are in BDT format. Up to 9 different tables can be in input.
  • UNBINNED: the input data are in PET format. only one table can be in input.
• N_OF_FILES is the number of input tables to be read in for the analysis in the BINNED case. The maximum number allowed is 9. Default is 1. In the UNBINNED case this parameter is unnecessary, because only one table can be in input.
• FILENAME_n is the n-th input table name. Default extension is TBL. There is no default.
• WINDOW_FILENAME is the name of the ASCII file containing the start-end times of the periods accepted for the analysis. The default filename for the window file is dummy.win. If the window file is not found, all times will be accepted. The default extension for window files is WIN.
• STRETCH_LENGTH is the length (in bins) of the single time stretch for the ACF evaluation. The maximum value allowed (as well as the default) is 8192 ( ).
• LABEL label for the output. This string will be written to the output table (and optional image) in the descriptor ACF_COMMENT.
• MAXIMUM_LAG is the maximum lag for the ACF production (i.e. the length of the output ACF minus one). The default value is 50.
• OUTPUT_FILENAME is the filename of the output table containing the ACF. The default extension is TBL.
• NORMALIZATION_MODE choice for the normalization of the output ACF. It can assume the values:
  1. Plain autocovariance function R
  2. Plain autocorrelation function (autocovariance normalized to the variance)
  3. Partially unbiased autocovariance function
  4. Partially unbiased autocorrelation function
• BIN_SIZE is the bin size for the light curve accumulation. It is required only in the UNBINNED case. There is no default.
• START_TIME it is the start time for the time series to be accepted for the analysis. This value is used only if no window file is specified. The default value is 0.0.
• REBIN_FACTOR is the rebin factor for the input data, used only in the BINNED case. By means of this parameter it is possible to rebin the data before the analysis. Default value is 1 (no rebinning). The rebinning is done internally and does not affect the data in the input BDTs.
• EXPOSURE_FRACTION is the minimum exposure fraction allowed for a bin to be selected as a ``good'' bin. If this parameter is set to 1.0 (the default) only fully exposed bins will be accepted. If it is set to 0.0, even complete gaps will be accepted as empty bins. All the intermediate values are of course allowed.
• WINDOW_PS_FLAG is the flag for the production of the ACF of the window function only. If it is set to 0 (the default), the normal ACF of the data will be computed. If it is set to 1, the ACF of the window function will be computed: this means that each selected bin will contain the percentage exposure of that bin rather than the detected counts. This option makes sense only if the parameter EXPOSURE_FRACTION is set to a value less than 1.0.
• Format of the input: the files input to this command are:
  • PARAMETER FILE: Its general format is shown in table  
  • DATA TABLE(S): they are BDTs as produced by the EXSAS projection package. Their format is described in section 7.2.2.
  • WINDOW FILE: it is a standard ASCII file. Each line of the file contains the start and end time of an accepted time interval. No comment lines are allowed.
• Format of the output: the files in output from this command are:
  • ACF: it is in the format of a MIDAS table with 4 columns, respectively: lag, error on lag, ACF and error on ACF. The descriptors of the main EXSAS header are copied from the first input table to the output table. Some new descriptors are created: the descriptor ACF_NUMBER (I*4) contains the total number of ACFs averaged, the descriptor WINDOW_NAME (C*80) contains the window file name and the descriptor ACF_COMMENT (C*80) contains the LABEL parameter read in from the parameter file.
  • LOGFILE: it is an ASCII file containing a copy of the output to terminal. The useful parameters read in from the parameter file are reported. The status of the window file opening and reading is displayed. For each single ACF is displayed a line containing: the index number of the ACF, the average count rate and the ACF value for the first two lags. Any data file opening is reported. The logfile has the standard name ac_seg.log