ASP 460 2.0 Data VisualizationDr Thiyanga TalagalaVisualizing Time Series Data1 / 30

Individual Time Series: Points

library(mozzie)
library(ggplot2)
data(mozzie)
colombo.dengue <- mozzie[, 1:4]
ggplot(colombo.dengue, aes(x=ID, y=Colombo))+
  geom_point()+xlab("Time")+
  ylab("Number of dengue cases")

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Individual Time Series: Points

library(mozzie)
library(ggplot2)
data(mozzie)
colombo.dengue <- mozzie[, 1:4]
ggplot(colombo.dengue, aes(x=ID, y=Colombo))+
  geom_point()+xlab("Time")+
  ylab("Number of dengue cases")

This is NOT a scatter plot. Why?

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Individual Time Series: Points

This is NOT a scatter plot. Why?

the points are spaced equally along the x-axis.
there is a order among points.

To emphasize time dependent relationship we can connect neighboring points with lines.

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Individual Time Series: Points and Lines

library(mozzie)
library(ggplot2)
data(mozzie)
colombo.dengue <- mozzie[, 1:4]
ggplot(colombo.dengue, aes(x=ID, y=Colombo))+
  geom_point()+
   geom_line()+
  xlab("Time")+
  ylab("Number of dengue cases")

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Individual Time Series: Points and Lines

Lines do not represent observed data. Lines are meant as a guide to the eye.
If few observed values a far apart or unevenly spaced, it is not suitable to connect points with lines.

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Individual Time Series: Lines only

ggplot(colombo.dengue, aes(x=ID, y=Colombo))+
   geom_line()+
  xlab("Time")+
  ylab("Number of dengue cases")

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Individual Time Series: Lines only

Without points more emphasis is given on the overall trend and less on individual values.
In general, when there are too many points it is better to plot without points.

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Individual time series: Fill the area under the curve

ggplot(colombo.dengue, aes(x=ID, y=Colombo))+
   geom_area()+
  xlab("Time")+
  ylab("Number of dengue cases")

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Visually separates the area above and below the curve.
More emphasis is given to the overarching trend in the series.
This visualization is only valid if the y axis starts at zero.

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Visualising multiple time series

Difficult to read.

By connecting points with lines we help the reader to follow the paths of each individual time series.

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Smoothing

library(gapminder)
head(gapminder)

## # A tibble: 6 x 6
##   country     continent  year lifeExp      pop gdpPercap
##   <fct>       <fct>     <int>   <dbl>    <int>     <dbl>
## 1 Afghanistan Asia       1952    28.8  8425333      779.
## 2 Afghanistan Asia       1957    30.3  9240934      821.
## 3 Afghanistan Asia       1962    32.0 10267083      853.
## 4 Afghanistan Asia       1967    34.0 11537966      836.
## 5 Afghanistan Asia       1972    36.1 13079460      740.
## 6 Afghanistan Asia       1977    38.4 14880372      786.

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Smoothing

library(tidyverse)
gapminder_af <- gapminder %>%
  filter(continent == "Africa")
ggplot(gapminder_af, aes(x=year, y=lifeExp))+
  geom_point()+
  geom_line()+
  facet_wrap(~country)

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Smoothing

gapminder_af <- gapminder %>%
  filter(continent == "Africa")
ggplot(gapminder_af, aes(x=year, y=lifeExp))+
  geom_line()+
  facet_wrap(~country)+
  theme(axis.text.x = element_text(angle = 90, hjust = 1))

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Smoothing

library(tidyverse)
gapminder_af <- gapminder %>%
  filter(continent == "Africa")
ggplot(gapminder_af, aes(x=year, y=lifeExp))+geom_smooth()+facet_wrap(~country)+
  theme(axis.text.x = element_text(angle = 90, hjust = 1))

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Time series plots

library(forecast)
library(fpp2)
mozcol <- ts(mozzie$Colombo, frequency = 52, start = c(2008, 52))
autoplot(mozcol) +
  ggtitle("Dengue Count - Colombo") +
  ylab("Count") +
  xlab("Year")

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Seasonal plots

ggseasonplot(mozcol, year.labels=TRUE, year.labels.left=TRUE) +
  ylab("Count") +
  ggtitle("Seasonal plot: Dengue Count - Colombo")

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Polar seasonal plot

ggseasonplot(mozcol, polar=TRUE) +
  ylab("Count") +
  ggtitle("Polar seasonal plot: Dengue Count - Colombo")

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Time series plot

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Seasonal plot

ggseasonplot(a10, year.labels=TRUE, year.labels.left=TRUE) +
  ylab("$ million") +
  ggtitle("Seasonal plot: antidiabetic drug sales")

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Polar seasonal plot

ggseasonplot(a10, polar=TRUE) +
  ylab("$ million") +
  ggtitle("Polar seasonal plot: antidiabetic drug sales")

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Seasonal subseries plots

ggsubseriesplot(a10) +
  ylab("$ million") +
  ggtitle("Seasonal subseries plot: antidiabetic drug sales")

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a10

           Jan       Feb       Mar       Apr       May       Jun       Jul
1991                                                              3.526591
1992  5.088335  2.814520  2.985811  3.204780  3.127578  3.270523  3.737851
1993  6.192068  3.450857  3.772307  3.734303  3.905399  4.049687  4.315566
1994  6.731473  3.841278  4.394076  4.075341  4.540645  4.645615  4.752607
1995  6.749484  4.216067  4.949349  4.823045  5.194754  5.170787  5.256742
1996  8.329452  5.069796  5.262557  5.597126  6.110296  5.689161  6.486849
1997  8.524471  5.277918  5.714303  6.214529  6.411929  6.667716  7.050831
1998  8.798513  5.918261  6.534493  6.675736  7.064201  7.383381  7.813496
1999 10.391416  6.421535  8.062619  7.297739  7.936916  8.165323  8.717420
2000 12.511462  7.457199  8.591191  8.474000  9.386803  9.560399 10.834295
2001 14.497581  8.049275 10.312891  9.753358 10.850382  9.961719 11.443601
2002 16.300269  9.053485 10.002449 10.788750 12.106705 10.954101 12.844566
2003 16.828350  9.800215 10.816994 10.654223 12.512323 12.161210 12.998046
2004 18.003768 11.938030 12.997900 12.882645 13.943447 13.989472 15.339097
2005 20.778723 12.154552 13.402392 14.459239 14.795102 15.705248 15.829550
2006 23.486694 12.536987 15.467018 14.233539 17.783058 16.291602 16.980282
2007 28.038383 16.763869 19.792754 16.427305 21.000742 20.681002 21.834890
2008 29.665356 21.654285 18.264945 23.107677 22.912510 19.431740          
           Aug       Sep       Oct       Nov       Dec
1991  3.180891  3.252221  3.611003  3.565869  4.306371
1992  3.558776  3.777202  3.924490  4.386531  5.810549
1993  4.562185  4.608662  4.667851  5.093841  7.179962
1994  5.350605  5.204455  5.301651  5.773742  6.204593
1995  5.855277  5.490729  6.115293  6.088473  7.416598
1996  6.300569  6.467476  6.828629  6.649078  8.606937
1997  6.704919  7.250988  7.819733  7.398101 10.096233
1998  7.431892  8.275117  8.260441  8.596156 10.558939
1999  9.070964  9.177113  9.251887  9.933136 11.532974
2000 10.643751  9.908162 11.710041 11.340151 12.079132
2001 11.659239 10.647060 12.652134 13.674466 12.965735
2002 12.196500 12.854748 13.542004 13.287640 15.134918
2003 12.517276 13.268658 14.733622 13.669382 16.503966
2004 15.370764 16.142005 16.685754 17.636728 18.869325
2005 17.554701 18.100864 17.496668 19.347265 20.031291
2006 18.612189 16.623343 21.430241 23.575517 23.334206
2007 23.930204 22.930357 23.263340 25.250030 25.806090
2008

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Seasonal subseries plots

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Lag plots: a10

Monthly anti-diabetic drug sales in Australia from 1991 to 2008.

gglagplot(a10)

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Lag plots: mozzie

Dengue counts - Colombo

gglagplot(mozcol)

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Lag plots: ausbeer

Monthly Australian beer production: Jan 1991 – Aug 1995.

beer2 <- window(ausbeer, start=1992)
gglagplot(beer2)

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Time series features

Transform a given time series $y = {y_{1}, y_{2}, \dots, y_{n}}$ to a feature vector $F = (f_{1} (y), f_{2} (y), \dots, f_{p} (y))^{'}$ .

Examples of time series features

strength of trend
strength of seasonality
lag-1 autocorrelation
spectral entropy
proportion of zeros

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Time-domain representation

Feature-domain representation

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References

Talagala, T. S., Hyndman, R. J., & Athanasopoulos, G. (2018). Meta-learning how to forecast time series. Monash Econometrics and Business Statistics Working Papers, 6, 18.

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