Primer: Seasonally Adjusting An Inflation Forecast

One practice that oftentimes needs to endure done either past times fixed income analysts is to generate a forecast inflation series. For an economist, such forecasts are oftentimes business office of the task description. For a fixed income analyst, fifty-fifty if they are non attempting to forecast inflation themselves, they volition demand to generate the forecast serial to calculate cash flows. For example, nosotros demand to calculate an implied inflation forecast to build upward a fitted inflation breakeven curve. One thing to move past times along inwards heed is that nosotros demand a forecast serial that is non seasonally adjusted to endure useful for inflation-linked bond analytics, but it is oftentimes easier to generate a seasonally adjusted series.


(Note: This brusk primer is an unedited draft from my upcoming mass on breakeven inflation analysis. The text is essentially complete, but I am alone targeting publication inwards September/October. I've been distracted past times a major domicile renovation project, hence my writing output has been depression recently. That projection is straightaway winding down, hence I should endure able to ramp upward my writing again.)

Extracting the seasonal designing is an of import analytical exercise. Purists mightiness endure tempted to seasonally accommodate the information themselves, but that poses a risk. If you lot produce it yourself, you lot volition destination upward working amongst your ain information set, in addition to you lot could hence into arguments almost the information amongst others (who volition invariably operate the seasonally adjusted serial supplied past times the national statistical agency). Using the official information eliminates 1 of the many potential sources of analytical friction. Meanwhile, this is too the easiest solution: you lot larn the seasonal designing past times dividing the non-seasonally adjusted serial past times the seasonally adjusted one, equally shown below.

The figure to a higher house shows the designing created past times dividing the non-seasonally adjusted (NSA) serial past times the seasonally adjusted (SA) series. The concluding betoken shown is for Jan 2017, in addition to is equal to 0.9946 (rounded). This agency that the non-seasonally adjusted serial is 99.46% of the seasonally adjusted serial at that date. We run across that at that topographic point is a dip closed to Dec each year, in addition to a peak inwards the summertime closed to June. In 2016, the peak was inwards June, at 1.0046, in addition to the depression was inwards Dec at 0.9943 (both numbers rounded). The ratio betwixt those 2 factors is 0.9896, which implies that at that topographic point is a 1.05% drib from June to Dec – 105 solid set down points, non-annualised.

As seen above, the seasonal adjustment designing for the USA CPI has been relatively stable over fourth dimension (which is expected based on the structure method). It would endure relatively reasonable shortcut to extrapolate the concluding year’s factors going forward. This allows us to accept seasonally adjusted CPI forecasts (which are presumably easier to generate), in addition to operate them to generate non-seasonally adjusted forecasts.

The methodology tin hence endure summarised.

1. Take the official CPI serial for the past times year, in addition to split the non-seasonally adjusted serial past times the seasonally adjusted series. Preserve the concluding 12 months of data.
2. Generate a seasonally adjusted CPI forecast (somehow).
3. Multiply the forecast serial past times a serial created past times repeating the 12-month designing of seasonal adjustments calculated inwards stride (1).

I would await that this technique appears extremely obvious for many readers. However, I spelled out the procedure, equally it was non genuinely obvious to me when I showtime had to produce the operation. My work was that when I started inwards finance, I was a freshly minted applied mathematics Ph.D.; I wanted to uncovering the most “rigorous” solution. This led me on a blind path: I wanted to piece of work amongst the official seasonal adjustment algorithm. The work is that the seasonal adjustment algorithm is described equally mapping a non-seasonally adjusted serial to a seasonally-adjusted one; inverting that mapping is non-trivial. However, given the incertitude of an inflation forecast inwards the showtime place, who cares almost getting the inverse mapping precisely correct? Approximations are your friend; you lot only demand to know when precision matters (e.g., getting banknote prices in addition to marketplace quotes correct).

(c) Brian Romanchuk 2018