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Visualizing Uncertainty - the Fan Chart

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The Bank of England invented the first fan chart, published in February 1996. At the BoE, the Fan Chart visualizes a crucial methodological process; the fan chart portrays a probability distribution that approximates to the BoE MPC's (Monetary Policy Committee) subjective assessment of inflationary pressures evolving through time, based on a central view and the risks surrounding it[1]. To derive the MPC's forecast distribution, three parameters need to be evaluated. First, a measure of the central tendency for inflation-usually expressed as a particular projected path. Second, a view on the degree of uncertainty (the variance). Third, a view on the balance of the risks, to get a measure of the skew.

Fan Chart Inflation Example asymptotix

The fan chart always has the following features. There is an equal number of red bands on either side of the central band (eight). Each pair of bands covers 10% of the distribution but, if the risks are unbalanced, the same colour bands are not of equal width (representing unequal probability intervals). The distribution is truncated, so that there is an implicit ninth and final pair of bands, occupying the white space outside the 90% covered. The central projection is, by construction, always in the deepest red band since it is associated with the mode.

The Fan Chart is effectively a visualization of Interval and Density forecasting. It is not just a pretty picture. In this sense it is becoming a standard as the "Visualization of Uncertainty". Interval forecasts and density forecasts are being increasingly used in practical real-time forecasting. An interval forecast of a variable specifies the probability that the future outcome will fall within a stated interval; this usually uses round numbers such as 50% or 90% and states the interval boundaries as the corresponding percentiles. A density forecast is an estimate of the complete probability distribution of the possible future values of the variable. As supplements to point forecasts they each provide a description of forecast uncertainty, whereas no information about this is available if only a point forecast is presented, a practice which is being increasingly criticized in macroeconomic forecasting. Density forecasts are more directly used in decision-making in the fields of finance and risk management[2]. The Bank of England has published a density forecast of inflation in its quarterly Inflation Report since February 1996. The forecast is represented graphically as a set of prediction intervals covering 10%, 20%,...,90% of the probability distribution, of lighter shades for the outer bands. This is done for inflation forecasts one to nine quarters ahead, and since the dispersion increases and the intervals "fan out" as the forecast horizon increases, the result has become known as the "fan chart".

Fanchart GDP asymptotix

Forecasters in general, and central banks in particular, often wish to provide an accurate predictive density for a number of macroeconomic variables. The framework offers a formalized and model-consistent way to incorporate judgement into predictive densities in a model-based environment. The methodology is best suited to a forecasting process that places a great deal of emphasis on one model which, given recent improvements in the forecasting ability of DSGE models, increasingly describes the forecasting practices of several central banks.27 As policy institutions head further along the path of incorporating models into the policy process, a new and straightforward way to address judgement when generating predictive densities is available[3].

Among economic forecasters, it has become a more common practice to provide point projection with a density forecast. This realistic view acknowledges that nobody can predict future evolution of the economic outlook with absolute certainty. Interval confidence and density forecasts have thus become useful tools to describe in probability terms the uncertainty inherent to any point forecast[4].

The Fan Chart is becoming regarded by the IMF as a key best practice standard in transparency of Fiscal and Supervisory authorities worldwide[5].

 

RELATED REFERENCES

 

http://ec.europa.eu/economy_finance/db_indicators/surveys/documents/workshops/2010/ec_meeting/14_m_cornec_conditional_gdp_fan_chart.pdf

 

http://peer.ccsd.cnrs.fr/docs/00/58/19/98/PDF/PEER_stage2_10.1080%252F00036840600843947.pdf

 

http://doras.dcu.ie/14871/1/Brian_Byrne_content.pdf

 

FAN CHART CODE SNIPPITS

 

http://www.oga-lab.net/RGM2/func.php?rd_id=gamlss:centiles

 

http://www.jstatsoft.org/v27/i04/paper

 

http://www.mathworks.com/matlabcentral/fileexchange/27702-fan-chart/content/FanChart.m

 

http://rss.acs.unt.edu/Rdoc/library/vars/html/fanchart.html

 

http://www.oga-lab.net/RGM2/func.php?rd_id=vars:fanchart

 

http://had.co.nz/ggplot2/geom_smooth.html

 

http://had.co.nz/ggplot2/geom_ribbon.html

 

http://had.co.nz/ggplot2/stat_density2d.html

 

http://had.co.nz/ggplot2/stat_smooth.html

fanchart gdp2 asymptotix

 

 


[1] http://www.bankofengland.co.uk/publications/quarterlybulletin/qb980101.pdf

 

[2] http://www.ecb.eu/pub/pdf/scpwps/ecbwp083.pdf

 

[3] http://www.federalreserve.gov/pubs/feds/2006/200639/200639pap.pdf

 

[4] https://www.ciret.org/conferences/newyork_2010/papers/upload/p_75-392908.pdf

 

[5] http://www.bankofcanada.ca/wp-content/uploads/2010/09/holub.pdf

 

 

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