Hierarchical Time Series with hts

This is just a quick reproduction of the items discussed in the hts package. This allows for hierarchical time series which is an important feature when looking at data that take a hierarchical format like counties within a state or precincts within counties within states.

Michael DeWitt https://michaeldewittjr.com
10-28-2018

Mission

The mission is to reproduce the figures in the following article:

https://cran.r-project.org/web/packages/hts/vignettes/hts.pdf

``````
library(hts)``````

Note on Formatting Data

This is important to understand in regard to how to format the data.

``````
# bts is a time series matrix containing the bottom-level series
# The first three series belong to one group, and the last two
# series belong to a different group
# nodes is a list containing the number of child nodes at each level.
bts <- ts(5 + matrix(sort(rnorm(500)), ncol=5, nrow=100))

y <- hts(bts, nodes=list(2, c(3, 2)))``````

The Data

``````
infantgts``````
``````
Grouped Time Series
4 Levels
Number of groups at each level: 1 2 8 16
Total number of series: 27
Number of observations per series: 71
Top level series:
Time Series:
Start = 1933
End = 2003
Frequency = 1
[1] 4426 4795 4501 4813 4572 4627 4726 4897 5367 5435 5458 4819 4741
[14] 5143 5231 4978 4621 4672 4910 4823 4743 4546 4571 4630 4751 4586
[27] 4915 4667 4700 4861 4652 4403 4124 4065 4205 4293 4507 4620 4809
[40] 4465 4088 3974 3341 3161 2834 2732 2557 2438 2365 2485 2349 2184
[53] 2473 2162 2131 2143 2018 2149 1851 1848 1598 1524 1466 1467 1352
[66] 1261 1413 1292 1313 1271 1207``````

Use a bottomâ€™s up forcasting method. There are several options from which to choose:

• comb optimal combination
• bu bottomâ€™s up
• mo middle out forecast
• tdgsa Top-down forecasts based on the average historical proportions (Gross-Sohl method A)
• tdgsf same as above but with averages
• tdfp top down forecast using proportions
``````
# Forecast 10-step-ahead using the bottom-up method
infantforecast <- forecast(infantgts, h=10, method="bu")``````

Now we can plot them:

``````
# plot the forecasts including the last ten historical years
plot(infantforecast, include=2)``````

``````
allts_infant <- aggts(infantgts)
allf <- matrix(nrow=10, ncol=ncol(allts_infant))
# Users can select their preferred time-series forecasting method
# for each time series
for(i in 1:ncol(allts_infant)){
allf[,i] <- forecast(auto.arima(allts_infant[,i]), h=10, PI=FALSE)\$mean
}

allf <- ts(allf, start=2004)
# combine the forecasts with the group matrix to get a gts object
g <- matrix(c(rep(1, 8), rep(2, 8), rep(1:8, 2)), nrow = 2, byrow = T)
y.f <- combinef(allf, groups = g)``````
``````
# set up the training sample and testing sample
data <- window(infantgts, start=1933, end=1993)
test <- window(infantgts, start=1994, end=2003)
forecast <- forecast(data, h=10, method="bu")
# calculate ME, RMSE, MAE, MAPE, MPE and MASE
accuracy.gts(forecast, test)``````
``````
Total  Sex/female    Sex/male   State/NSW   State/VIC
ME   -229.976631 -51.6732083 -178.303422 -61.6997671 -52.3224384
RMSE  239.316716  54.8648206  186.952910  72.0726053  55.6797769
MAE   229.976631  51.6732083  178.303422  61.6997671  52.3224384
MAPE   17.383377   8.8573610   24.108196  14.8044550  17.2578539
MPE   -17.383377  -8.8573610  -24.108196 -14.8044550 -17.2578539
MASE    1.192825   0.5536415    1.634811   0.6922188   0.7123545
State/QLD    State/SA  State/WA  State/NT  State/ACT  State/TAS
ME   -54.247885 -27.9688770 -34.22604 2.4214262 -10.200366  8.2673186
RMSE  58.364656  31.4104773  37.80624 4.4008195  12.277985 14.1318898
MAE   54.247885  28.3351016  34.22604 3.8128557  10.200366 11.2456064
MAPE  19.807669  35.8611517  30.49142 9.3990903  58.625236 25.6532905
MPE  -19.807669 -35.5481392 -30.49142 5.5716727 -58.625236 16.2664231
MASE   1.170397   0.9229675   1.18361 0.3087333   1.577376  0.4954012
NSW female  VIC female QLD female   SA female   WA female
ME   18.1060219 -19.2448216 -30.927587 -11.8395741  -9.4619072
RMSE 29.4705103  22.4856212  34.825359  12.7759741  12.2693801
MAE  22.6345181  19.2448216  30.927587  11.8395741  11.0295258
MAPE 11.8532079  15.1713621  27.492021  34.9177563  23.1348356
MPE   9.1030614 -15.1713621 -27.492021 -34.9177563 -20.8629247
MASE  0.5199353   0.5338369   1.059769   0.6720666   0.6308594
NT female  ACT female TAS female   NSW male    VIC male
ME    -3.6619739   1.2229746  4.1336593 -79.805789 -33.0776168
RMSE   5.4356560   4.3972340  7.0659449  85.657539  35.4311830
MAE    4.1036140   3.8000000  5.6228032  79.805789  33.0776168
MAPE  31.0793050  49.8490801 25.6532905  34.527431  19.3380825
MPE  -29.2280894 -15.2907568 16.2664231 -34.527431 -19.3380825
MASE   0.5766202   0.9047619  0.4954012   1.431922   0.7569249
QLD male     SA male    WA male   NT male    ACT male
ME   -23.3202978 -16.1293029 -24.764134  6.083400  -11.423341
RMSE  27.7367318  20.5563716  28.118008  8.673554   12.089644
MAE   23.3202978  17.9634424  25.771308  7.729126   11.423341
MAPE  15.3395187  43.6968568  42.005272 34.820043  106.448479
MPE  -15.3395187 -41.2835155 -40.987925 22.160616 -106.448479
MASE   0.9676472   0.9396744   1.577835  1.120163    2.269538
TAS male
ME    4.1336593
RMSE  7.0659449
MAE   5.6228032
MAPE 25.6532905
MPE  16.2664231
MASE  0.4954012``````
``````
fcasts <- forecast(htseg1, h = 10, method = "comb", fmethod = "arima",
weights = "sd", keep.fitted = TRUE, parallel = TRUE)``````

Corrections

If you see mistakes or want to suggest changes, please create an issue on the source repository.

Reuse

Text and figures are licensed under Creative Commons Attribution CC BY 4.0. Source code is available at https://github.com/medewitt/medewitt.github.io, unless otherwise noted. The figures that have been reused from other sources don't fall under this license and can be recognized by a note in their caption: "Figure from ...".

Citation

`DeWitt (2018, Oct. 28). Michael DeWitt: Hierarchical Time Series with hts. Retrieved from https://michaeldewittjr.com/programming/2018-10-28-hierarchical-time-series-with-hts/`
```@misc{dewitt2018hierarchical,