time series In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. E ...

analysis, a fan chart is a chart that joins a simple

line chart A line chart or line graph or curve chart is a type of chart which displays information as a series of data points called 'markers' connected by straight line segments. It is a basic type of chart common in many fields. It is similar to a s ...

for observed past data, by showing ranges for possible values of future data together with a line showing a central estimate or most likely value for the future outcomes. As predictions become increasingly uncertain the further into the future one goes, these forecast ranges spread out, creating distinctive wedge or "fan" shapes, hence the term. Alternative forms of the chart can also include uncertainty for past data, such as preliminary data that is subject to revision. The term "fan chart" was coined by the Bank of England, which has been using these charts and this term since 1997 in its "Inflation Report" to describe its best prevision of future

inflation In economics, inflation is an increase in the general price level of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reductio ...

to the general public. Fan charts have been used extensively in finance and

monetary policy Monetary policy is the policy adopted by the monetary authority of a nation to control either the interest rate payable for very short-term borrowing (borrowing by banks from each other to meet their short-term needs) or the money supply, often ...

, for instance to represent forecasts of

Implementation

Predicted future values can be diagrammed in various ways; most simply, by a single predicted value, and an upper and lower range around that (three lines total), or by various future intervals, depicted by varying degrees of shading (darkest near the center of the range, fainter near the ends of the range). There are several ways to represent the forecast density depending on the shape of the forecasting distribution. *If the forecast density is symmetric (

normal Normal(s) or The Normal(s) may refer to: Film and television * ''Normal'' (2003 film), starring Jessica Lange and Tom Wilkinson * ''Normal'' (2007 film), starring Carrie-Anne Moss, Kevin Zegers, Callum Keith Rennie, and Andrew Airlie * ''Norma ...

Student's t In probability and statistics, Student's ''t''-distribution (or simply the ''t''-distribution) is any member of a family of continuous probability distributions that arise when estimating the mean of a normally distributed population in situa ...

, for instance), the fan centers at the mean (which coincides with the mode and median) forecast, and the ranges expand like

confidence interval In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated ''confidence level''; the 95% confidence level is most common, but other levels, such as ...

s by adding and subtracting multiples of the forecasting standard error to the mean forecast. These ranges are known as equal-tail ranges and centre at the mean forecast. Low resolution charts may add and subtract one, two and three forecasting standard errors for approximate coverages of 68%, 95% and 99.7%. These charts can easily be built through standard Excel graphs. *If the forecast density is non-symmetric, centering the fan at the median and using equal tail ranges might not be appropriate as it would overstate the forecast uncertainty. In this case it is better to center the fan at the more likely forecast (the mode) and use Highest Probability Density (HPD) ranges. HPDs are by definition the shortest ranges covering a given probability, say 50%, and are centered at the mode. In this case it is usual to include increasing probability ranges of 10%, 20%, ..., 90%, for instance. In the Bank of England's implementation it is assumed that the forecast distribution is a two piece normal or split normal density. This density results from joining the two-halves of corresponding normal densities with the same mode but different variances. As a result, the split normal density is non-symmetric and uni-modal. In this case, inflation forecast fan charts are usually accompanied with the balance of risks, the probability that the future inflation falls below its modal forecast. In this way, central banks that employ

inflation targeting In macroeconomics, inflation targeting is a monetary policy where a central bank follows an explicit target for the inflation rate for the medium-term and announces this inflation target to the public. The assumption is that the best that monet ...

report to the general public not only the more likely forecasts of the inflation rate ''but also its balance of risks''! The split normal density is completely characterized by three parameters, the mode, variance and skewness. Therefore, the fan chart ranges depend on these parameters only. and In a central bank that employs

, the three moments of the inflation forecast distribution are determined as follows: * The mode. Modal forecasts are derived from the suite of models of the central bank. * The variance. Standard errors of forecasts might be derived from appropriately formulated forecasting models but it is advisable to derive them from historical forecasting errors instead. * The skewness. A mapping from the skewness (or balances of risks) of factors that affect the inflation rate along the forecast horizon to the skewness of the inflation forecast distribution has to be specified.

References

External links

Inflation Report Fan Charts
, Bank of England
Fan chart
MATLAB Central, by Marco B., 23 May 2010

CRAN R Package by Guy J. Abel, 9 April 2013 {{DEFAULTSORT:Fan Chart (Time Series) Statistical charts and diagrams Statistical forecasting