How does Data Buffet frequency conversion work, mathematically? When is it appropriate to use? What are the caveats and drawbacks?
Introduction
A time series consists of data points (observations) measured at a regular frequency or periodicity. For example, daily temperatures (seven times a week, 365 times a year), business-daily stock market closings (five times a week, 260 times a year), monthly employment numbers, or quarterly financial reports. To compare series, you will often want to convert them to a common frequency.
Converting from a low frequency to high (e.g., quarterly to monthly) is a process of interpolation, and the reverse (e.g., weekly to quarterly) is a process of compaction or reduction. Interpolation draws a curve between points of a series and picks new points at regular intervals; compaction condenses points by summing, averaging, or discarding. The two processes are sometimes called up-conversion and down-conversion, respectively.
Data Buffet contains time series at many different native frequencies, and provides controls to convert in the View, Basket, Chart, and Map modules; you can also construct explicit formulas. The underlying computation has caveats, and may not produce sensible results in all circumstances.
The mathematics of up-conversion
How does it work? In short, interpolation. The points of the input series are used to construct a curve (a continuous time representation), and the points of the output series are extracted from that curve. The shape of the output curve is dictated by the input curve, by the technique (Cubic, Linear or Constant), and by the observed attribute of the input series.
By default, the Cubic technique is used, unless there are fewer than four observations, which dictates the Linear technique, Or, use our controls to select one of the three techniques:
In the Constant technique, a step function is created. When plotted, it is a series of horizontal plateaus passing through the input values.
In the Linear technique, a linear spline is created. A linear spline is piecewise linear (y=ax+b) between joining points, called knots. (That is, the equations are constrained to pass through the knots.) The knots are the input observations. When plotted, a linear spline is jagged.
In the Cubic technique, a piecewise cubic spline consists of cubic curves (y=ax^3+bx^2+cx+d) joined at the knots. In addition to this first constraint, the pieces must have the same slope and curvature at the knots (i.e., the curve is seamless). (In calculus terms, the value of the function and its first two derivatives must match.) The coefficients (a, b, c, d) are determined by the values of the input series and the observed attribute; the three constraints at the knots dictate an equal number of equations and unknowns; and solving this system of equations gives you the coefficients. When plotted, the curve is so smooth you cannot see the knots.
The controls are located at:
- menu:Settings » New basket defaults » File options » Conversion method
- Basket » Settings » Output » Conversion method
Can I get more information? The specific algorithm is proprietary and additional information is not available from Moody's Analytics. However, the theory of cubic splines has extensive literature (see References below).
Caveats
Frequency conversion is a blind mathematical process and cannot guarantee that the output preserves essential properties of the input. Apply your own judgment before using the output.
Irreversibility. Down-conversion smooths the data, which destroys short-term temporal detail. You cannot then reconstitute the original curve by running an inverse up-conversion, i.e., you cannot "unscramble the egg."
Anomalous values. If the time series is volatile (i.e., repeatedly reverses direction over short intervals), the output may have a very different shape, or may "fall off a cliff" to a physically nonsensical value (e.g., less than zero). This is especially likely at the ends of the curve.
If there are gaps, activate "ignore missing values". Some time series contain gaps ("nd", missing value, null), caused by national holidays, trading holidays, or suppressed values. By default, during down-conversion Data Buffet will omit any output period that contains gapped input periods, which will impede interpretation and charting. To override, activate this option:
- menu:Settings » New basket defaults » File options » Other » Ignore missing values
- Basket » Settings » Output » Ignore missing values
- Chart » Settings » Output » Data » Ignore missing values
- Map » Settings » Output » Ignore missing values
Applied to Moody's Analytics forecasts
The Moody's Analytics forecast models are built around gross domestic product, an inherently quarterly concept; hence, the majority of the series produced by the models have a quarterly native frequency. All caveats described above apply. In particular, be mindful of these situations:
When forecasting down-converts the drivers. For example, quarterly forecast FLBR.IUSA is driven by monthly historical data LBR.IUSA. The monthly values ("original" or "actual") cannot be recovered from the quarterly series. You can convert LBR.IUSA to quarterly to match against the historical segment of FLBR.IUSA (because you have repeated our process), but not the reverse; at best, you will obtain an approximation to LBR.IUSA.
When converting alternative scenarios. In a sheaf of alternative scenarios in a single vintage, the historical segment is shared but the future values differ. With cubic spline interpolation, the shape of the entire output curve depends on past and future input values. Hence, upon converting the sheaf, the historical segments will be forced out of alignment.
Beyond conversion
Frequency conversion cannot produce "better" information from a vacuum, i.e., the interpolated points are guesses, not measurements. A time series with superior measurements may exist, but you will have to search for it manually.
Sources may publish the same indicator at multiple frequencies. Different sources or surveys may produce distinct indicators that are suitable substitutes. Moody's Analytics produces historical estimates at consistent frequencies. As a general rule, it's not possible to predict the concept code of such alternates, but if alternates exist, they will be cataloged nearby.
References
See also
Updates
- Jul 2015 - Initial version of article
- Dec 2019 - References replaced, updated GUI paths