Time Series of the World, Unite!

The R ecosystem knows a ridiculous number of time series classes. So, I decided to create a new universal standard that finally covers everyone’s use case… Ok, just kidding!

tsbox, now freshly on CRAN, provides a set of tools that are agnostic towards existing time series classes. It is built around a set of converters, which convert time series stored as ts, xts, data.frame, data.table, tibble, zoo, tsibble or timeSeries to each other.

To install the stable version from CRAN:


To get an idea how easy it is to switch from one class to another, consider this:

x.ts <- ts_c(mdeaths, fdeaths)
x.xts <- ts_xts(x.ts)
x.df <- ts_df(x.xts)
x.tbl <- ts_tbl(x.df)
x.dt <- ts_tbl(x.tbl)
x.zoo <- ts_zoo(x.dt)
x.tsibble <- ts_tsibble(x.zoo)
x.timeSeries <- ts_timeSeries(x.tsibble)

We jump form good old ts objects toxts, store our time series in various data frames and convert them to some highly specialized time series formats.

tsbox is class-agnostic

Because these converters work nicely, we can use them to make functions class-agnostic. If a class-agnostic function works for one class, it works for all:


ts_scale normalizes one or multiple series, by subtracting the mean and dividing by the standard deviation. It works like a ‘generic’ function: You can apply it on any time series object, and it will return an object of the same class as its input.

So, whether we want to smooth, scale, differentiate, chain-link, forecast, regularize or seasonally adjust a series, we can use the same commands to whatever time series at hand. tsbox offers a comprehensive toolkit for the basics of time series manipulation. Here are some additional operations:

ts_pc(x.ts)                 # percentage change rates 
ts_forecast(x.xts)          # forecast, by exponential smoothing
ts_seas(x.df)               # seasonal adjustment, by X-13
ts_frequency(x.dt, "year")  # convert to annual frequency
ts_span(x.tbl, "-1 year")   # limit time span to final year

tsbox is frequency-agnostic

There are many more. Because they all start with ts_, you can use auto-complete to see what’s around. Most conveniently, there is a time series plot function that works for all classes and frequencies:

  `Airline Passengers` = AirPassengers, 
  `Lynx trappings` = ts_df(lynx), 
  `Deaths from Lung Diseases` = ts_xts(fdeaths),
  title = "Airlines, trappings, and deaths",
  subtitle = "Monthly passengers, annual trappings, monthly deaths"


There is also a version that uses ggplot2 and has the same syntax.

Time series in data frames

You may have wondered why we treated data frames as a time series class. The spread of dplyr and data.table has given data frames a boost and made them one of the most popular data structures in R. So, storing time series in a data frame is an obvious consequence. And even if you don’t intend to keep time series in data frames, this is still the format in which you import and export your data. tsbox makes it easy to switch from data frames to time series and back.

Make existing functions class-agnostic

tsbox includes tools to make existing functions class-agnostic. To do so, the ts_ function can be used to wrap any function that works with time series. For a function that works on "ts" objects, this is as simple as that:

ts_rowsums <- ts_(rowSums)
ts_rowsums(ts_c(mdeaths, fdeaths))

Note that ts_ returns a function, which can be used with or without a name.

In case you are wondering, tsbox uses data.table as a backend, and makes use of its incredibly efficient reshaping facilities, its joins and rolling joins. And thanks to anytime, tsbox will be able to recongnize almost any date format without manual intervention.

So, enjoy some relieve in R’s time series class struggle.

Website: www.tsbox.help

Forecasting GDP with R and dataseries.org

The website dataseries.org aims to be Switzerland’s FRED - a free comprehensive database of Swiss time series. Powered by R and written in Shiny (also using a bit of JavaScript) it allows you to quickly search and explore a large number of data series.


Switzerland’s time series in one place

Similarly to the United States, public data in Switzerland is produced by a large number of different offices, which makes it hard to find any particular series. dataseries.org provides a structured and automatically updated collection of most of these data. We are still working on the data input, but are pretty much complete in the field of Economics.

You can download the data as spreadsheets or graphs, or embed interactive widgets in your website. Alternatively, you can import the data directly into R, using the dataseries package. Install the package from CRAN:


and run the ds function with the id argument that you find on the website:

plot(dataseries::ds("GDP.PBRTT.A.R", "ts"), 
     ylab = "mio CHF, at 2010 prices, s. adj.", main = "Gross Domestic Product")

This will give you an R plot of Switzerland’s GDP. (The data is cached, so calling the function again will not re-download until you restart the R session.)

Live Import of Series to R

In the following, I will use data from dataseries.org to produce a live forecast of Switzerland’s GDP. Each day the model is run, it will be ensured that the latest data is used. That way it is possible to produce a transparent and up-to-date forecast. For the following exercise, I will only use tools from R base, but it is of course possible to use the same data in a more advanced modeling framework.

In order to produce a reasonable forecast, we want to track early information on the business cycle, which is mostly survey data. We will use a question on from the SECO Consumer Confidence Survey on current economic performance, the Credit Suisse / Procure Purchasing Managers’ Index and the ETHZ KOF Barometer.

Transforming the data

Getting these indicators from dataseries.org directly into R is easy. Because these data are measured at different frequencies, we need to convert them to the same quarterly frequency as GDP. There are many packages that offer functions for that (e.g., our tempdisagg package has functions to move both to higher or lower frequencies), but I will stick to basic R here:

# Aggregating months to quarters (post updated on May 6, 2017)
to_quarterly <- function(x){
  aggregate(x, nfrequency = 4, FUN = mean)

pmi <- to_quarterly(dataseries::ds("PMI.SA.PM", "ts"))
kof <- to_quarterly(dataseries::ds("KOF.KFBR", "ts"))
csent <- dataseries::ds("CCI.GEPC", "ts")

A plot of these series shows the common trend in these variables and gives you an indication of the business cycle, which may have turned upward in recent months.

plot(cbind(pmi, kof, csent), main = "Business Cycle Indicators")

Since these series are stationary, our left hand side variable should be stationary as well. This is accomplished by calculating percentage change rates of GDP:

gdp.level <- dataseries::ds("GDP.PBRTT.A.R", "ts")
gdp <- (gdp.level / lag(gdp.level, -1)) - 1   

ARIMA modelling

R’s workhorse for time series modeling is the arima function, which allows you to construct a univariate or multivariate model of GDP growth. Since the data is seasonally adjusted, a simple autoregressive process (AR1) offers a good benchmark:

# AR1
m0 <- arima(gdp, order = c(1, 0, 0))
fct0 <- predict(m0, n.ahead = 1)$pred
# GDP Growth Q1: +0.3 

If you need advice on which ARIMA model to choose, the information criterions, accessed by the R functions AIC or BIC, can help you to choose a model. Simply take the model with lowest information criterion. The auto.arima function from the forecast package also allows you to do the selection automatically.

We can include our series individually or jointly and estimate a range of different models. A good model (in terms of the AIC information criterion) is the following, which uses PMI and KOF data (but not consumer sentiment data):

dta <- window(cbind(pmi, kof), start = start(pmi), end = end(pmi))
m1 <- arima(window(gdp, start = start(dta)), 
            xreg = window(dta, end = end(gdp)))
fct1 <- predict(m1, n.ahead = 1, 
                newxreg = window(dta, start = tsp(gdp)[2] + 0.25,
                                 end = tsp(gdp)[2] + 0.25)
# GDP Growth Q1: +0.7 

The model’s forecast for the first quarter of 2017 is 0.7 - a value that hasn’t been reached for more than two years.

A factor model

If you have multiple indicators at hand, a common problem is multicollinearity, the fact that indicators are correlated, and therefore too many indicators deteriorate the quality of the model estimation.

An easy fix is to use a factor model, where the indicators are summarized in a few factors, which can be calculated by principal components (see Stock and Watson 2002):

# PMI, KOF, Consumer Sentiment, first Principal Component
pca <- prcomp(window(cbind(pmi, kof, csent), start = start(pmi), 
                     end = tsp(gdp)[2] + 0.25),
              scale. = TRUE)
dta.pca <- ts(pca$x[, 'PC1'], start = start(pmi), frequency = 4)

m2 <- arima(window(gdp, start = start(dta)), 
            xreg = window(dta.pca, end = end(gdp)))
fct2 <- predict(m2, n.ahead = 1, 
                newxreg = window(dta.pca, start = tsp(gdp)[2] + 0.25)
# GDP Growth Q1: +0.7 

Again, we get a forecast value of 0.7. Overall, survey data indicates that the economy is well on track. Let’s do a graphical comparison of our forecasts:

# skeletons to include forecasts 
gdp.fct0  <- window(gdp, extend = TRUE, end = tsp(gdp)[2] + 0.25)
gdp.fct1 <- gdp.fct2 <- gdp.fct0

# plug forecasts into skeletons
window(gdp.fct0, start = end(gdp.fct0)) <- fct0
window(gdp.fct1, start = end(gdp.fct1)) <- fct1
window(gdp.fct2, start = end(gdp.fct2)) <- fct2

ts.plot(window(cbind(gdp, gdp.fct0, gdp.fct1, gdp.fct2), start = 2010), 
        col = 1:4, ylab = "quarterly growth rates, s. adj.", 
        main = "GDP Forecasts")
       legend = c("GDP Growth Rate", "AR 1 Forecast", 
                  "PMI, KOF", "Principal Component"), 
       lty = 1, col = 1:4, bty = "n")

Publication of first quarter GDP is on June 1, 2017. See you in a month!

seasonal 1.3: A Better Way to Seasonal Adjustment Diagnostics

The R package seasonal makes it easy to use X-13ARIMA-SEATS, the seasonal adjustment software by the United States Census Bureau. Thanks to the x13binary package, installing it from CRAN is now as easy as installing any other R package:


The latest version 1.3 comes with a new udg function and a customizable summary method, which give power users of X-13 a convenient way to check the statistics that are of their interest. For a full list of changes, see the package NEWS.

A generalized way to access diagnostics

Version 1.3 offers a generalized way to access diagnostic statistics. In seasonal, it was always possible to use all options of X-13 and access all output series. Now it is easy to access all diagnostics as well.

The main new function is udg, named after the X-13 output file which it is reading. Let us start with a simple call to seas (the main function of the seasonal package) that uses the X-11 seasonal adjustment method:

m <- seas(AirPassengers, x11 = "")

The udg function returns a list containing 357 named diagnostics. They are properly type-converted, so they can be directly used for further analysis within R.

If we ask for a specific statistic, such as the popular X-11 M statistics, the result will be simplified to a numeric vector (see ?udg for additional options):

udg(m, c("f3.m01", "f3.m02", "f3.m03", "f3.m04"))

## f3.m01 f3.m02 f3.m03 f3.m04 
##  0.041  0.042  0.000  0.283

There are also some new wrappers for commonly used statistics, such as AIC, BIC, logLik or qs, which use the udg function.

A customizable summary

The new functionality paves the way for a customizable summary method for seas objects. For example, if we want to add the M statistics for X-11 adjustments to the summary, we can write:

summary(m, stats = c("f3.m01", "f3.m02", "f3.m03", "f3.m04"))

## Call:
## seas(x = AirPassengers, x11 = "")
## Coefficients:
##                     Estimate Std. Error z value Pr(>|z|)    
## Weekday           -0.0029497  0.0005232  -5.638 1.72e-08 ***
## Easter[1]          0.0177674  0.0071580   2.482   0.0131 *  
## AO1951.May         0.1001558  0.0204387   4.900 9.57e-07 ***
## MA-Nonseasonal-01  0.1156204  0.0858588   1.347   0.1781    
## MA-Seasonal-12     0.4973600  0.0774677   6.420 1.36e-10 ***
## ---
## Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
## X11 adj.  ARIMA: (0 1 1)(0 1 1)  Obs.: 144  Transform: log
## AICc: 947.3, BIC: 963.9  QS (no seasonality in final):    0  
## Box-Ljung (no autocorr.): 26.65   Shapiro (normality): 0.9908  
## f3.m01: 0.041  f3.m02: 0.042  f3.m03: 0  f3.m04: 0.283 

Note the new line at the end, which shows the M statistics.

If we want to routinely consider these statistics in our summary, we can set the seas.stats option accordingly:

options(seas.stats = c("f3.m01", "f3.m02", "f3.m03", "f3.m04"))

This will change the default behavior, and


will return the same output as above. To restore the default behavior, set the option back to NULL.

options(seas.stats = NULL)
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