I have/will update this post as I expanded the fanplot package.

My fanplot package has gone up on CRAN. Below is a online version of the package vignette…

Visualising Time Series Model Results

The fanplot package can also be used to display uncertainty in estimates from time series models. To illustrate, the packages `th.mcmc`

data frame object contains posterior density distributions of the estimated volatility of daily returns from the Pound/Dollar exchange rate from 02/10/1981 to 28/6/1985. These distributions are from a MCMC simulation from a stochastic volatility model given in Meyer and Yu (2002) where it assumed;

The latent volatilities , which are unknown states in a state-space model terminology, are assumed to follow a Markovian transition over time given by the state equations:

with .

The `th.mcmc`

object consists of (1000) rows corresponding to MCMC simulations and (945) columns corresponding to each . A fan chart of the evolution of the distribution of can be visualised using the fanplot package via,

library("fanplot")
# empty plot
plot(NULL, main="Percentiles", xlim = c(1, 965), ylim = c(-2.5, 1.5))
# add fan
fan(data = th.mcmc)

The `fan`

function calculates the values of 100 equally spaced percentiles of each future distribution when the default `data.type = "simulations"`

is set. This allows 50 fans to be plotted from the `heat.colours`

colour palette, providing a fine level of shading. In addition, lines and labels are provided along each decile.

Prediction Intervals

When argument `type = "interval"`

is set, the `probs`

argument corresponds to prediction intervals. Consequently, the fan chart comprises of 3 different shades, running from the darkest shade for the 50th prediction interval to the lightest for the 95th prediction interval.

# empty plot
plot(NULL, main="Prediction Intervals",
xlim = c(-20, 965), ylim = c(-2.5, 1.5))
# add fan
fan(data = th.mcmc, type = "interval", llab=TRUE, rcex=0.6)

Contour lines are overlayed for the upper and lower bounds of each prediction intervals, as set using the `ln`

command. A further line is plotted along the median of , which is controlled by the `med.ln`

argument (set to `TRUE`

by default when `type="interval"`

). The default labels on the right hand side correspond to the upper and lower bounds of each plotted line. The left labels are added by setting `llab = TRUE`

. Note, some extra room is created for the labels by setting the `xlim = c(-20, 965)`

argument of plotting area to a wider range than the original data (945 observations). The text size of the right labels are controlled using the `rcex`

argument. The left labels, by default, take the same text size as `rcex`

although they can be separately controlled using the `lcex`

argument.

Alternative Colours

Alternative colour schemes to the default `heat.colors`

, can be obtained by supplying a `colorRampPalette`

to the `fan.col`

argument. For example, a new palette running from blue to white, via grey can be passed using;

# empty plot
plot(NULL, main="Alternative Colour Scheme",
xlim = c(-20, 965), ylim = c(-2.5, 1.5))
# add fan
fan(data = th.mcmc, rlab=seq(20,80,15), llab=c(10,50,90),
fan.col=colorRampPalette(c("royalblue", "grey", "white")))

Alternative labels are specified using the `rlab`

and `llab`

arguments.

Spaghetti Plots

Spaghetti plots can be used to represent uncertainty shown by a range of possible future trajectories or past estimates. For example using the `th.mcmc`

object, 20 random sets of can be plotted when setting the argument `style = "spaghetti"`

;

# empty plot
plot(NULL, main="Spaghetti Plot", xlim = c(-20, 965), ylim = range(th.mcmc))
# transparent fan with visible lines
fan(th.mcmc, ln=c(5, 50, 95), llab=TRUE, alpha=0, ln.col="orange")
# spaghetti lines
fan(th.mcmc, style="spaghetti", n.spag=20)

The spaghetti lines are superimposed on a fan chart in order to illustrate some underlying probabilities. The initial fan chart is completely transparent from setting the transparency argument `alpha`

to 0. In order for the percentile lines to be visible a non-transparent colour is used for the `ln.col`

argument.

Forecast Fans

The fanplot package can also be used to illustrate probabilistic forecasts. For example, using the `auto.arima`

function in the forecast package a model for the time series for net migration to the United Kingdom (contained in the `ips`

data frame of the fanplot package) can be fitted.

#create time series
net <- ts(ips$net, start=1975)
#fit model
library("forecast")
m <- auto.arima(net)
m
Series: net
ARIMA(1,1,2) with drift
Coefficients:
ar1 ma1 ma2 drift
-0.2301 -0.0851 -0.6734 6.7625
s.e. 0.3715 0.3620 0.1924 1.4154
sigma^2 estimated as 1231: log likelihood=-179.3
AIC=368.6 AICc=370.54 BIC=376.66

We may then simulate 1000 values from the selected model using the `simulate.Arima`

function, and plot the results.

mm <- matrix(NA, nrow=1000, ncol=5)
for(i in 1:1000)
mm[i,] &lt;- simulate(m, nsim=5)
# empty plot
plot(net, main="UK Net Migration", xlim=c(1975,2020), ylim=c(-100,300))
# add fan
fan(mm, start=2013)

Users might want to connect the fan with the past data. This can be achieved by providing the last value to the anchor argument.

# empty plot
plot(net, main="UK Net Migration",
xlim=c(1975,2020), ylim=c(-100,300))
# add fan
fan(mm, start=2013, anchor=net[time(net)==2012],
type="interval", probs=seq(5, 95, 5), ln=c(50, 80))

More shades for the fan are added to the plot (over the default 3 used for a interval fans) by supplying a sequence to the `probs`

argument. Alternative contour lines (from the default median, 50th, 80th and 95th percentiles for interval fans) are added using the `ln`

argument.

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