Inflation has been in the news a lot recently, everybody is talking about its current level and (maybe most importantly) its forecast. The Bank of England (BoE) expects CPI inflation to increase further in coming months and peak at around 7% in April. After that, inflation is expected to decrease and to be back to the 2% target in around 2 years.

So, this week we have four data visualisation tools to helps to illustrate and understand inflation forecasts. Take a look and tell me which one is your favourite!

## Central Projection Scatter

Let’s start with the plot that you can find in the in the front page of the Monetary Policy Report – February 2022. This chart shows the historical CPI from 2004 until today as a solid line and then the “forecast” until 2025 as red diamonds. We should note that the “forecast” in this chart is a central projection (e.g. mean, median, mode), i.e. just a point on the forecasted distribution.

Point-wise predictions do not provide information on the uncertainty about this estimate. So, from this chart we can see that the peak for the inflation forecast is around 7% in April but we have no idea of how much higher inflation can go.

## Fan Chart

The next plot is a fan chart. It shows the historical CPI values from 2004 until today as a solid line and then a “fan” area showing the forecast distributions. The fan area is highlighted in grey to indicate when the forecast starts. The fan itself is formed by bands which correspond to areas between quantiles of the forecasted distribution.

In this example, the bands correspond to the quantiles: 0.05, 0.2, 0.35, 0.65, 0.8, and 0.95. So, inflation will be in the fan area with probability of 0.90. Moreover, the bands are coloured according to its distance from the median of the distribution. The central band (which corresponds to the area between the quantiles 0.35 and 0.65) is the darkest and contains the median.

This chart, as opposed to the previous one, gives us a better picture of the uncertainty of the forecast. From this plot, we can say that inflation will peak in April when it will be between 4.5% and 9% with high (0.9 exactly) probability. Moreover, we can plot the central projection on top of the fan chart as follows.

## Density Functions as Slices in 3D Plot

The next chart is a 3d plot. It shows the density functions for all the quarters for which the BoE has a forecast. In this case, we have 13 densities corresponding to the forecasts for each quarter between 2022-Q1 and 2025-Q1.

This chart allows us to see the whole shape of the forecasted distributions. This is possible because we know that the BoE uses the two-piece normal distribution to model CPI inflation. The down side is that 3d plots can be difficult to appreciate (interpret and understand) due to its geometry. For instance, it is difficult to see the densities the middle. Besides, there is no historical CPI values on this chart. This prevent us to compare the forecasts with the realised values.

## Ridgeline

The final chart is a Ridgeline plot. Like the previous one, this chart shows the forecasted densities but in a 2-dimensional setup. This facilitates visualising the changes in the shape of the distribution over time. Here we can appreciate how the density functions move towards the right first (as CPI inflation forecast peaks) and then slowly to the left in the next 12 quarters.

Note that the original Ridgeline plots show KDEs (Kernel Density Estimators) since the actual densities are unknown in general. However, this is not necessary in our case, since we know the forecasts follow two-piece normal distributions.

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