Date and Time Intervals

Definition of a Date and Time Interval

An interval is a unit of measurement that SAS counts within an elapsed period of time, such as days, months or hours. SAS determines date and time intervals based on fixed points on the calendar or clock. The starting point of an interval calculation defaults to the beginning of the period in which the beginning value falls, which might not be the actual beginning value that is specified. For example, if you are using the INTCK function to count the months between two dates, regardless of the actual day of the month that is specified by the date in the beginning value, SAS treats the beginning value as the first day of that month.

Interval Names and SAS Dates

Specific interval names are used with SAS date values, while other interval names are used with SAS time and datetime values. The interval names that are used with SAS date values are YEAR, SEMIYEAR, QTR, MONTH, SEMIMONTH, TENDAY, WEEK, WEEKDAY, and DAY. The interval names that are used with SAS time and datetime values are HOUR, MINUTE, and SECOND.
Interval names that are used with SAS date values can be prefixed with 'DT' to construct interval names for use with SAS datetime values. The interval names DTYEAR, DTSEMIYEAR, DTQTR, DTMONTH, DTSEMIMONTH, DTTENDAY, DTWEEK, DTWEEKDAY, and DTDAY are used with SAS time or datetime values.

Incrementing Dates and Times by Using Multipliers and by Shifting Intervals

SAS provides date, time, and datetime intervals for counting different periods of elapsed time. By using multipliers and shift indexes, you can create multiples of intervals and shift their starting point to construct more complex interval specifications.
The general form of an interval name is
Both the multiplier and the shift–index arguments are optional and default to 1. For example, YEAR, YEAR1, YEAR.1, and YEAR1.1 are all equivalent ways of specifying ordinary calendar years that begin in January. If you specify other values for multiplier and for shift-index, you can create multiple intervals that begin in different parts of the year. For example, the interval WEEK6.11 specifies six-week intervals starting on second Wednesdays.
For more information, see Single-Unit Intervals in SAS Language Reference: Concepts, Multi-Unit Intervals in SAS Language Reference: Concepts, and Shifted Intervals in SAS Language Reference: Concepts.

Commonly Used Time Intervals

Time intervals that do not nest within years or days are aligned relative to the SAS date or datetime value 0. SAS uses the arbitrary reference time of midnight on January 1, 1960, as the origin for non-shifted intervals. Shifted intervals are defined relative to January 1, 1960.
For example, MONTH13 defines the intervals January 1, 1960, February 1, 1961, March 1, 1962, and so on, and the intervals December 1, 1958, November 1, 1957, and so on, before the base date January 1, 1960.
As another example, the interval specification WEEK6.13 defines six-week periods starting on second Fridays. The convention of alignment relative to the period that contains January 1, 1960, determines where to start counting to determine which dates correspond to the second Fridays of six-week intervals.
The following table lists time intervals that are commonly used.
Commonly Used Intervals with Optional Multiplier and Shift Indexes
Three-day intervals
Weekly intervals starting on Sundays
Weekly intervals starting on Saturdays
Six-week intervals starting on second Fridays
Biweekly intervals starting on first Sundays
Same as WEEK
Weekly intervals starting on Mondays
Six-week intervals starting on first Tuesdays
Six-week intervals starting on second Wednesdays
Four-week intervals starting on first Sundays
Five-day work week with a Saturday-Sunday weekend
Six-day week with Sunday as a weekend day
Five-day week with Tuesday and Thursday as weekend days (W indicates that day 3 and day 5 are weekend days)
Five-day week with Friday and Saturday as weekend days
Three-weekday intervals with Saturday and Sunday as weekend days (The intervals are aligned with respect to Jan. 1, 1960. For intervals that nest within a year, it is not necessary to go back to Jan. 1, 1960 to determine the alignment.)
Four ten-day periods starting at the second TENDAY period
Intervals from the sixteenth of one month through the fifteenth of the next month
February–March, April–May, June–July, August–September, October–November, and December–January of the following year
January–February, March–April, May–June, July–August, September–October, November–December
Nine-month intervals starting on February 1, 1960, November 1, 1960, August 1, 1961, May 1, 1962, and so on.
Six-month intervals, March–August and September–February
Fiscal years starting in October
Biennial intervals starting in July of even years
Biennial intervals starting in July of odd years
Four-year intervals starting in November of leap years (frequency of U.S. presidential elections)
Four-year intervals starting in November of even years between leap years (frequency of U.S. midterm elections)
Thirteen-month intervals starting at midnight of January 1, 1960, such as November 1, 1957, December 1, 1958, January 1, 1960, February 1, 1961, and March 1, 1962
Eight-hour intervals starting at 6 a.m., 2 p.m., and 10 p.m. (might be used for work shifts)
For a complete list of the valid values for interval, see Intervals Used with Date and Time Functions in SAS Language Reference: Concepts.

Retail Calendar Intervals: ISO 8601 Compliant

The retail industry often accounts for its data by dividing the yearly calendar into four 13-week periods, based on one of the following formats: 4-4-5, 4-5-4, or 5-4-4. The first, second, and third numbers specify the number of weeks in the first, second, and third months of each period, respectively.
The intervals that are created from the formats can be used in any of the following functions: INTCINDEX, INTCK, INTCYCLE, INTFIT, INTFMT, INTGET, INTINDEX, INTNX, INTSEAS, INTSHIFT, and INTTEST.
For more information, see Retail Calendar Intervals: ISO 8601 Compliant in SAS Language Reference: Concepts.

Custom Time Intervals

Reasons for Using Custom Time Intervals

Standard time intervals (for example, QTR, MONTH, WEEK, and so on) do not always fit the data. Additionally, some time series are measured at standard intervals where there are gaps in the data. For example, you might want to use fiscal months that begin on the 10th day of each month. In this case, using the MONTH interval is not appropriate because the MONTH interval begins on the 1st day of each month. You can use a custom interval to model data at a frequency that is familiar to the business and to eliminate gaps in the data by compressing the data. The intervals must be listed in ascending order. There cannot be gaps between intervals, and intervals cannot overlap.
As another example, you might want to collect data hourly for a business that is closed at night. In this case, using the DTHOUR interval results in gaps in the data that can cause problems in standard time series analysis. You might also want to calculate the number of business days between dates, excluding holidays and weekends, but holidays are counted when you use the INTCK function with the WEEKDAY interval. These are cases in which custom intervals can be used effectively.

Using Custom Time Intervals in a SAS Program

You can define custom intervals in a data set within a SAS program. Using a custom interval requires that you follow two steps for each interval:
  1. Associate a data set name with a custom interval name by using the INTERVALDS= system option in an OPTIONS statement.
    Here is an example of the arguments in an INTERVALDS= system option. The example associates the data set StoreHoursDS with the custom interval StoreHours:
    options intervalds=(StoreHours, StoreHoursDS); 
    For more information, see INTERVALDS= System Option in SAS System Options: Reference.
  2. Create a data set that describes the custom interval.
    The data set must contain the begin variable; it can also contain end and season variables. In your SAS program, include a FORMAT statement that is associated with the begin variable that specifies a SAS date, datetime, or numeric format that matches the begin variable data. If an end variable is present, include it in the FORMAT statement. A numeric format that is not a SAS date or SAS datetime format indicates that the values are observation numbers. If the end variable is not present, the implied value of end at each observation is one less than the value of begin at the next observation.
    Include in the span of the custom interval data set any dates or times that are necessary for performing calculations on the time series, including backcasting, forecasting, and other operations that might extend beyond the series.
After you define custom intervals by using the preceding steps, the custom interval can be specified in SAS procedures and functions in places where a standard time interval can be specified.

Example 1: Creating Store Hours for a Business Using the INTNX Function

The following DATA step creates the StoreHoursDS data set for a business that is open from 9:00 AM to 6:00 PM Monday through Friday, and Saturday from 9:00 AM to 1:00 PM. The example uses the INTNX Function, which increments a date, time, or datetime value by a given time interval, and returns a date, time, or datetime value. In this example, StoreHours is the interval, and StoreHoursDS is the data set that contains user-supplied holidays:
options intervalds=(StoreHours=StoreHoursDS);
data StoreHoursDS(keep=begin end);
   start = '01JAN2009'd;
   stop  = '31DEC2009'd;
   do date = start to stop;
      dow = weekday(date);
      if dow not in (1,7) then 
         do hour = 9 to 17;
      else if dow = 7 then 
         do hour = 9 to 12;
   format begin end datetime.;
title 'Store Hours Custom Interval';

proc print data=StoreHoursDS (obs=18);
The output shows the first 18 observations of the custom interval data set.
A Custom Interval for Store Hours
A Custom Interval for Store Hours

Example 2: Creating the Fiscal Month Custom Interval Using the INTNX Function

The following DATA step creates the FMDS data set to define a custom interval, FiscalMonth, which is appropriate for a business that uses fiscal months that start on the 10th day of each month. The SAME alignment option of the INTNX function specifies that the dates that are generated by the INTNX function be the same day of the month as the date in the start variable. The MONTH function assigns the month of the begin variable to the season variable, which specifies monthly seasonality:
options intervalds=(FiscalMonth=FMDS);
data FMDS(keep=begin season);
   start = '10JAN1999'd;
   stop  = '10JAN2001'd;
   nmonths = intck('month',start,stop);
   do i=0 to nmonths;
      begin = intnx('month',start,i,'S');
      season = month(begin);
   format begin date9.;

proc print data=FMDS;
   title 'Fiscal Month Data';
Fiscal Month Data
Fiscal Month Data
The difference between the custom FiscalMonth interval and a standard interval is seen in the following example. The output from the program compares how the data is accumulated. For the FiscalMonth interval, values in the first nine days of the month are accumulated with the interval that begins in the previous month. For the standard MONTH interval, values in the first nine days of the month are accumulated with the calendar month.
data sales(keep=date sales);
   do date = '01JAN2000'd to '31DEC2000'd;
      month = MONTH(date);
      dayofmonth = DAY(date);
      sales = 0;
      if (dayofmonth lt 10) then sales= month/9;
   format date monyy.;

proc timeseries data=sales out=dataInFiscalMonths;
   id date interval=FiscalMonth accumulate=total;
   var sales;

proc timeseries data=sales out=dataInStdMonths;
   id date interval=Month accumulate=total;
   var sales;

data compare;
   merge dataInFiscalMonths(rename=(sales=FM_sales))
   by date;

title 'Standard Monthly Data and Fiscal Month Data';

proc print data=compare;
Comparison of Standard Monthly Data and Fiscal Month Data
Comparison of Standard Monthly Data and Fiscal Month Data

Example 3: Using Custom Intervals with the INTCK Function

The following example uses custom intervals in the INTCK function to omit holidays when counting business days:
options intervalds=(BankingDays=BankDayDS);
data BankDayDS(keep=begin);
   start = '15DEC1998'd;
   stop  = '15JAN2002'd;
   nwkdays = intck('weekday',start,stop);
   do i = 0 to nwkdays;
      begin = intnx('weekday',start,i);
      year = year(begin);
      if begin ne holiday('NEWYEAR',year) and 
         begin ne holiday('MLK',year) and 
         begin ne holiday('USPRESIDENTS',year) and 
         begin ne holiday('MEMORIAL',year) and 
         begin ne holiday('USINDEPENDENCE',year) and 
         begin ne holiday('LABOR',year) and 
         begin ne holiday('COLUMBUS',year) and 
         begin ne holiday('VETERANS',year) and 
         begin ne holiday('THANKSGIVING',year) and 
         begin ne holiday('CHRISTMAS',year) then
   format begin date9.;
data CountDays;
   start = '01JAN1999'd;
   stop  = '31DEC2001'd;
   ActualDays = intck('DAYS',start,stop);
   Weekdays   = intck('WEEKDAYS',start,stop);
   BankDays   = intck('BankingDays',start,stop);
   format start stop date9.;

title 'Methods of Counting Days';

proc print data=CountDays;
Bank Days Custom Interval
Bank Days Custom Interval

Best Practices for Custom Interval Names

The following items list best practices to use when you are creating custom interval names:
  • Custom interval names should not conflict with existing SAS interval names. For example, if BASE is a SAS interval name, do not use the following formats for the name of a custom interval:
    • BASE
    • BASEm
    • BASEm.n
    • DTBASE
    • DTBASEm
    • DTBASEm.n
    The following paragraphs describe the variables:
    specifies an optional multiplier that sets the interval equal to a multiple of the period of the basic interval type. For example, the interval YEAR2 consists of two-year, or biennial, periods.
    specifies an optional shift index that shifts the interval to start at a specified subperiod starting point. For example, YEAR.3 specifies yearly periods that are shifted to start on the first day of March of each calendar year and end in February of the following year.
    If you define a custom interval such as CUSTBASE, then you can use CUSTBASEm.n.
    Because of these rules, do not begin a custom interval name with DT, and do not end the custom interval name with a number.
  • To ensure that custom intervals work reliably, always include one of the following formats:
    date-format with beginning and ending values
    specifies intervals that are used with SAS date values.
    datetime-format with beginning and ending values
    specifies intervals that are used with SAS datetime values.
    number-format with beginning and ending values
    specifies intervals that are used with SAS observation numbers.
  • Beginning and ending values should be of the same type. Both values should be date values, datetime values, or observation numbers.
  • Calculations for custom intervals cannot be performed before the first begin value or after the last end value. If you use the begin variable only, then the last end value that you can calculate is the last begin value –1. If you forecast or backcast the time series, be sure to include time definitions for the forecast and backcast values.
  • CUSTBASEm.2 is never able to calculate a beginning period for the first date value in a data set because, by definition, the beginning of the first interval starts before the data set begins (at the – (m– 2) th observation). For example, you might have an interval called CUSTBASE4.2 with the first interval beginning before the first observation:
    -2    Start of partial CUSTBASE4.2 interval observation:  -(4-2) = -2.
    1     End of partial CUSTBASE4.2 interval observation: This is the first 
           observation in the data set.
    2     Start of first complete CUSTBASE4.2 interval.
    5     End of first complete CUSTBASE4.2 interval.
    6     Start of 2nd CUSTBASE4.2 interval.
    If you execute the INTNX function, the result must return the date that is associated with OBS –2, which does not exist:
    INTNX('CUSTBASE4.2', date-at-obs1, 0, 'B');
  • Include a variable named season in the custom interval data set to define the seasonal index. This result is similar to the result of INTINDEX ('interval', date);
    In the following example, the data set is associated with the custom interval CUSTWEEK:
    Obs        begin                    season
        1             27DEC59          52
        2             03JAN60            1
        3             10JAN60            2
        4             17JAN60            3
        5             24JAN60            4
        6             31JAN60            5
    The following examples show the results of using custom interval functions:
    returns a value of 1.
    returns a value of 52, which is the largest value of the season.
    returns CUSTWEEK52, which is CUSTBASEmax(season).
    returns a value of 1.
    returns a value of 2.
    A new cycle begins when the season is less than the previous value of season.
  • Seasonality occurs when seasons are identified, such as season1, season2, season3, and so on. If all seasons are identified as season1, then there is no seasonality. No seasonality is also called trivial seasonality.
    Only trivial seasonality is available for intervals of the form CUSTBASEm. If season is not included in the data set, then trivial seasonality is valid.
  • If a format for the begin variable is included in a data set, then a message generated by INTFMT ('CUSTBASE', 'l') or INTFMT ('CUSTBASE', 's') appears. The message recommends a format based on the format that is specified in the data set.
  • Executing INTSHIFT ('CUSTBASE'); or INTSHIFT ('CUSTBASEm.s'); returns the value of CUSTBASE.
  • With INTNX, INTCK, and INTTEST, the intervals CUSTBASE, CUSTBASEm, and CUSTBASEm.s work as expected.