17 October 2013

Calculating Values within a Rolling Window in Transact SQL

Before the SQL Window functions were implemented, it was tricky to calculate rolling totals or moving averages efficiently in SQL Server. There are now a number of techniques, but which has the best performance? Dwain Camps gets out the metaphorical stopwatch.

Calculating Values within a Rolling Window in SQL

Any time that you need to combine values across several rows in SQL, the problem can be challenging, particularly when it comes to performance.  We will focus upon the rolling twelve-month totals problem, but our methods can be applied to any time window (e.g., 3 months) or to averages and other aggregations across those time windows as well.

A rolling total for a month is the total for that month plus the previous months within the time window, or NULL if you don’t have the values for all the previous months within the time window .

In previous versions of SQL Server, you had to jump through a few hoops to come up with a method that performs well, but SQL 2012 offers some new features that make it simpler.  In either case, there are several valid solutions.  Which is fastest and most efficient?  We’ll try to answer this question  in this article.

We will be working in SQL 2012.  If you would like to follow along, you can use the Sample Queries.sql resource you’ll find attached.

Data Setup and Statement of the Business Problem

Often times you’ll find yourself with many transactions within a month, but in our case we’ll assume you’ve already grouped your transactions for each month.  We’ll assign our PRIMARY KEY to a DATE data type, and include some values over which we want to accumulate rolling twelve month totals.

Since a valid, rolling twelve month total can’t occur until you have at least twelve months of data in your set, we seek to generate a NULL value for our rolling total column for the first 11 rows in the returned results.  It is only in the 12th month of 2011 that we will have twelve months of data in which to calculate the rolling total.  With our sample data, we can calculate that total as 7776 (or we can run the query below if manual calculations aren’t your thing).

Calculating a rolling twelve month total is akin to calculating a running total from all prior rows, with just a few calculation tricks we’ll show a little later on.

Solutions That Work in SQL Server 2005 Onwards

Solution #1: Using A Tally Table

Hopefully you’ll know what a Tally table is, but to make a long story short it is simply a table that has one integer column that is a sequential number from 1 to n, n being the number of rows you need.  Since we know that each monthly row in our test table must be summed into exactly 12 other rows (ignoring end points), perhaps we can use a simple zero-based Tally table to do this.  Let’s give it a try.

This query returns 12 rows where the GroupingDate column represents the period we want to sum the 2011-01-01 row into.  It is then a relatively simple matter to create the sum over the grouping like this.

When we examine the results of this query, we find that there are a couple of issues:

  • The first 11 rows do not show NULL as we’d like.
  • The last 11 rows represent dates that are outside of our data range, namely they are later than 2012-12-01.

The first issue can be taken care of with a ROW_NUMBER(), while the second issue is resolved with a HAVING clause.    Since we must reference our GroupingDate column in multiple places, we’ll put that calculation into a CROSS APPLY so we only need to do it once.

For reference and comparison against later queries, here are the final (correct) results.

Solution #2: A More Traditional Approach

Even though the first solution is able to do a single Index scan of our table, our suspicions are that using a Tally table may not be the optimal way to solve this problem.  This is mainly because of the second issue we saw, specifically the extra rows that were generated with dates past the end point of our input data set.  Let’s look at a couple of more traditional approaches, the first being an INNER JOIN.

Clearly the above is a much simpler query than our solution using a Tally table, but still suffers from the first issue of having to force NULLs into the first 11 rows by using ROW_NUMBER().  A quick check of the execution plan indicates that it is making full use of the clustered index that is available (one scan and one seek).  We can get away with using a BETWEEN on our dates because we’re looking at closed end points (normal best practice is to use >= start point and < end point).

I’ve never liked queries that JOIN a table onto itself; so we are still left wondering how well this will perform because of what I’d classify as a semi-triangular join, which as the linked article points out is simply SQL Row-by-Agonizing-Row (RBAR) in disguise.

If you haven’t already guessed from the other articles I’ve written, I love the CROSS APPLY construct in SQL.  So let’s see if we can do something similar to the INNER JOIN approach to get to our twelve month rolling totals.

Solution #3: Using TOP and CROSS APPLY

Here we calculate the sum of the prior 11 rows in the CROSS APPLY, then add this to the current row.  Examination of the query plan for this solution compared to the INNER JOIN method shows some differences, so it is possible the performance characteristics will also be different.  Unfortunately we still had to NULL out the first 11 rows with our ROW_NUMBER() as before, but you should convince yourself that the final results are the same.

Solution #4: Using a Correlated Sub-query

From the prior method, we can extract the summed Value result from within the CROSS APPLY and put it into a correlated sub-query instead.

This also produces a slight different query plan so we’ll be interested to see how its performance results compare to other solutions proposed so far.

So much for traditional solutions, and my apologies if I happened to overlook one of your favorites, but feel free to code it up and add it to the performance test harness we’ll present later to see how it fares.

Solution #5: Using a Quirky Update

If you’ve never heard of the Quirky Update (QU) and how it can be applied to problems such as running totals, I strongly recommend you have a read of this outstanding article by SQL MVP Jeff Moden, entitled Solving the Running Total and Ordinal Rank Problems

Before we continue, we should note that there are those that insist the QU method represents an undocumented behavior of SQL Server and so is not to be trusted.  We can say that the syntax is clearly described by the MS Books On Line entry for the UPDATE statement for SQL versions 2005, 2008 and 2012.  In fact it goes back further than that. I have successfully used it in SQL Server 2000 but it was inherited from Sybase and was in the first SQL Server version ever released.  To the naysayers I’ll say that the “undocumented” behavior is at least consistent across all versions and there is probably little reason to suspect that it will be deprecated or change in future versions of MS SQL.  Consider yourself warned!

If you ever consider using a QU to solve any problem, you need to take careful note of the many rules that apply (also included in the referenced article by Jeff).  The main ones, which I’ve handled in this query, can be summarized as:

  • The table must have a clustered index that indicates the ordering of the source rows by the period as you wish it to be traversed.
  • The table must have a column into which you can place the aggregated running total.
  • When you perform the update, you need to lock the table using the TABLOCKX query hint to make sure nobody else gets in any INSERTs, DELETEs or UPDATEs before you’re through.
  • You must prevent SQL from trying to parallelize the query using the OPTION (MAXDOP 1) hint.

Since a rolling twelve month average is simply a running total in disguise, we can add a column to our table and apply a QU query to do our calculation.

I must confess that this does look a little messy, with all of the variables you need to DECLARE.  Basically what we are doing is to keep track of the last twelve (lagging) values, in order to remove the 12th one (where the Rolling12Months column is assigned) from what is otherwise a QU running total as described in Jeff’s article.  We have high hopes for its speed given that it is known to be the fastest method for solving the running totals problem.

Once again, you should convince yourself that the results are consistent with prior solutions, and yes this solution still behaves the same in SQL 2012.  If you’re with me so far, you may also be asking yourself “what happens if I need to calculate multiple running twelve month totals across different partitions?”  This is relatively simple for all the other solutions presented but does propose a bit of a challenge using the QU.  The answer to this can be found in the attached resource file: Quirky Update Partitioned.sql.

SQL 2012 Solutions

Until now, everything we have done will work in SQL 2008.  The only thing we’ve done that is not supported in SQL 2005 is the initializations of the variables we DECLAREd in the QU approach.  Now let’s see what new features SQL 2012 has that can be applied to this problem.

Solution #6: Using a Window Frame

Our first SQL 2012 solution (#6) shows how to use a window frame that starts 11 rows prior to the current row, up through the current row to SUM our desired results.

We still need to handle the NULLs for the first 11 rows specially, but otherwise this solution is quite neat and concise.

Solution #7: Using the LAG Analytic Function

SQL 2012 also offers a new analytic function: LAG, which can be used to solve this problem.  LAG returns information from a prior row, offset by the number passed as its second argument.  The main benefit seems to be that there’s no need for special handling on the initial 11 rows.

Once again, the returned results are the same but the query plan is quite different than for the prior SQL 2012 solution; however we’re not particularly optimistic that this approach will yield a reasonably performing alternative because of the number of “look-backs” needed to make it work.

Performance Comparison of the Methods

The real test to see how multiple solutions perform is to check actual execution times in a quiescent server using a test harness with many rows.  Our test harness is shown, along with how Solution #1 and #2 have been modified (refer to comments in the code) to:

  • Insert the results into a temp table, to avoid the elapsed time impact of returning the rows to SQL Server Management Studio’s results grid.

  • Remove the DATE arithmetic, because when generating multi-million row test harnesses it is difficult to generate that many unique months, so the [Date] table column has been revised to be a BIGINT data type.

When we run our test harness at 1,000,000 rows, we get the following raw results, which would seem to eliminate Solutions #1 and #7 as contenders for the top prize in elapsed execution time.  You may want to also run this once at 4,000,000 rows (excluding solutions #1 and #7) to give SQL a chance to “learn” a “good” execution plan, prior to attempting to recreate the test results we’ll show in a moment.

For the remaining solutions (#2 – #6), we have graphed the CPU and Elapsed time results from 1M though 4M rows.



Interpreting the Results

Elapsed and CPU times seem to be consistent across the different methods with respect to their ordering.  All appear to scale in a linear fashion.

The Quirky Update, assuming you can understand it and all of its associated rules, seems to be the fastest available solution to solving this problem, even considering the new features available in SQL 2012.

In SQL 2012, the window frame approach is certainly neat, compact and elegant, but slightly trails the Quirky Update solution across the rows we tested.  These test results seem to conform to an earlier test on Running Totals in SQL “Denali” CTP3 by Microsoft Certified Master Wayne Sheffield in his blog.

If you’re stuck with an earlier version of SQL (2005 or 2008), and for some reason you can’t abide using a Quirky Update (e.g., if you don’t trust this undocumented behavior), the fastest solutions available to you are either the CROSS APPLY TOP or using a correlated sub-query, as both of those seemed to be in a close tie across the board.

It seems that the “traditional” INNER JOIN is something to be avoided.  It will probably only get worse if you need to do date arithmetic within the JOIN’s ON clause.  Likewise, using either a Tally Table or multiple LAGs (SQL 2012) certainly was not the way to go.

We did not explore CURSOR-based solutions, but you can back track to the article referenced on running totals to get an idea of how they might perform in this case.  I’ve also seen some solutions that employ a recursive Common Table Expression (rCTE), but I most certainly wouldn’t bet on their performance compared to the QU or window frame solutions.

There are many ways to calculate values within a rolling window in SQL and there are some clear performance winners among them.  We hope you found this guide to the available methods interesting and informative.

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Dwain Camps

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  • Joe Celko

    Very good!
    Great article! I was surprised that LAG() did so badly. I guess each invocation is done separately rather than factored out and optimized like a window.

  • Nic

    Great explanation!
    I agree, this is a great explanation of different ways to calculate values within a rolling window.
    If you test these examples on SQL 2012 you have to change #MyTable with #RollingTotalsExample.
    Thanks a lot, Mr. Camps!

  • Monster Maghoul

    Tally method
    Hi Dwain,

    Nice blog post.

    I noticed that your Tally table query was causing a Table Spool operator and thought you might consider making the "Tally" part of a "Dates" table like this:

    SELECT GroupingDate
    ,Value=MAX(CASE GroupingDate WHEN [Date] THEN a.Value END)
    WHEN ROW_NUMBER() OVER (ORDER BY GroupingDate) < 12
    ELSE SUM(Value)
    INTO #Results_Soln2
    FROM #RollingTotalsExample a
    — Remove the DATE arithmetic
    ) c(GroupingDate)
    GROUP BY GroupingDate
    HAVING GroupingDate <= MAX([Date])
    ORDER BY GroupingDate;

    (Apologies if formatting is bad – no preview!)

    This change still wouldn’t make it a contender, but does make a massive improvement to that query…

  • Dwain.C

    Thanks for the Comments
    Thanks Joe and Nic. I’m glad you found the article interesting.

    Joe: I too was slightly surprised by the LAG results and it makes me wonder what the break-even point would be. Perhaps 3 months might not be as bad, but it is still difficult to believe it might be faster than the QU.

  • Dwain.C

    Tally Tables

    For some reason, I have a personal preference for in-line Tally tables, but your results are interesting if only to consider for other cases.

  • chaunc42

    Assistance with Moving Annual Total
    My first post.

    I need to calculate the Moving Annual Total for the Value above for the preceding 12 months, with this month being month 12.

    I then need to get the Moving Annual Total for the 12 months before this. With the idea being to compare MAT for this month with the corresponding month last year, and for each preceeding month. My attempt gave me this:

    With cte as
    r_Num = ROW_NUMBER() Over ( order by [Date])
    , [Date]
    , Value

    , Rolling12Months=CASE WHEN ROW_NUMBER() OVER (ORDER BY [Date]) > 11
    FROM #RollingTotalsExample
    Select *
    From cte,
    ( Select m_R_Num = max(r_Num) from cte) deMax
    Where r_Num between m_R_Num – 23 and m_R_Num

    With the ability to change the Were statement to reflect whether I want this year or the previous year.

    My real data has the date as in Integer 201409 which I think will make life easier for me as I can subtract 100 to get the previous year.

    Excellent article and any help would be appreciated.

    Thanks David

  • chaunc42

    This is my working solution (with some noise)

    — Rolling 12 months totals using SQL 2012 and a window frame

    IF OBJECT_ID(‘tempdb..#PreviousYear’) IS NOT NULL
    DROP TABLE #PreviousYear;

    With cte as
    r_Num = ROW_NUMBER() Over ( order by [Date])
    , [Date]
    , Value

    , Rolling12Months=CASE WHEN ROW_NUMBER() OVER (ORDER BY [Date]) > 11
    FROM #RollingTotalsExample
    py_Row_Num = ROW_NUMBER() Over ( order by m_R_Num)
    , *
    , sStart = m_R_Num – 24
    , eEnd = m_R_Num – 12
    into #PreviousYear
    From cte,
    ( Select m_R_Num = max(r_Num) from cte) deMax
    Where r_Num between m_R_Num – 23 and m_R_Num – 12;

    — Rolling 12 months totals using SQL 2012 and a window frame

    IF OBJECT_ID(‘tempdb..#ThisYear’) IS NOT NULL
    DROP TABLE #ThisYear;

    With cte as
    r_Num = ROW_NUMBER() Over ( order by [Date])
    , [Date]
    , Value
    , Rolling12Months=CASE WHEN ROW_NUMBER() OVER (ORDER BY [Date]) > 11
    FROM #RollingTotalsExample
    ty_Row_Num = ROW_NUMBER() Over ( order by m_R_Num)
    , *
    , sStart = m_R_Num – 11
    , eEnd = m_R_Num
    into #ThisYear
    From cte,
    ( Select m_R_Num = max(r_Num) from cte) deMax
    Where r_Num between m_R_Num – 11 and m_R_Num;

    Select *
    from #ThisYear ty
    Left Join #PreviousYear py on ty.ty_Row_Num = py.py_Row_Num

  • Yertle

    These may work
    I’m not near a comp with sql access right now so I can’t test it(there may be some typos/syntax errors).

    SELECT T.DateKey
    ,AVG(T.ValueField) OVER (
    ODER BY T.DateKey ASC
    ) AS YMA_ValueField
    FROM DataTable AS T
    ORDER BY T.DateKey ASC;

    In case AVG is one of the aggregate functions not supported with BETWEEN range(I know SUM is supported).

    SELECT T.DateKey
    ,SUM(T.ValueField) OVER (
    ODER BY T.DateKey ASC
    ) / CASE
    WHEN DATEDIFF(DAY, @StartDate, T.DateKey) < 365
    THEN DATEDIFF(DAY, @StartDate, T.DateKey)
    ELSE 365 END AS YMA_ValueField
    FROM DataTable AS T
    ORDER BY T.DateKey ASC;

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