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<p><b>New page</b></p><div>[[File:fanchart-mathachieve-0912-en.gif|thumb]] '''Fan chart (statistics)''' is a graphical method used to display historical data and future projections in time series analysis. The term "fan chart" was popularized by the [[Bank of England]] to present its inflation projections. The chart is named for its fan-like appearance, where the width of the fan increases over time, reflecting the growing uncertainty about future outcomes as one moves further into the future.<br />
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==Overview==<br />
A fan chart typically starts with a solid line representing historical data. This line is then surrounded by shaded areas or "fans" that represent the probability distribution of future outcomes. These shaded areas often use different colors or shades to indicate different levels of probability or confidence intervals, such as the 10th and 90th percentiles, thereby providing a visual representation of the uncertainty or risk associated with future projections.<br />
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==Usage==<br />
Fan charts are widely used in [[economics]], particularly in monetary policy and inflation forecasting, where they help communicate the uncertainty inherent in economic forecasts. They are also used in other fields such as [[meteorology]], [[engineering]], and [[project management]] for similar purposes.<br />
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==Construction==<br />
To construct a fan chart, one must first have a time series of historical data and a model to generate future projections. The uncertainty in these projections is typically quantified using statistical methods, such as [[Monte Carlo simulations]] or [[Bayesian statistics]], to generate a range of possible outcomes. These outcomes are then grouped into percentiles, which are used to create the fan's layers, each representing a different level of confidence or probability.<br />
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==Interpretation==<br />
Interpreting a fan chart involves understanding the historical data, the assumptions made in the projections, and the meaning of the different layers of the fan. The central projection (often the median or mean forecast) is the most likely outcome based on the model used. The surrounding layers provide context on the range of possible outcomes, with outer layers representing less likely scenarios. A wider fan indicates greater uncertainty about future values.<br />
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==Advantages and Limitations==<br />
Fan charts are praised for their ability to visually communicate the uncertainty in forecasts, making them a valuable tool for decision-makers. However, their effectiveness depends on the accuracy of the underlying model and the assumptions about the distribution of future outcomes. Misinterpretation can occur if the audience does not fully understand how to read the chart or if the chart's design is not clear.<br />
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==See Also==<br />
* [[Time series]]<br />
* [[Forecasting]]<br />
* [[Probability distribution]]<br />
* [[Confidence interval]]<br />
* [[Monte Carlo simulation]]<br />
* [[Bayesian statistics]]<br />
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[[Category:Statistical charts and diagrams]]<br />
[[Category:Time series analysis]]<br />
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