Almost all prediction intervals from time series models are too narrow. This is a well-known phenomenon and arises because they do not account for all sources of uncertainty. In my 2002 IJF paper, we measured the size of the problem by computing the actual coverage percentage of the prediction intervals on hold-out samples. We found that for ETS models, nominal 95% intervals may only provide coverage between 71% and 87%. The difference is due to missing sources of uncertainty.
There are at least four sources of uncertainty in forecasting using time series models:
- The random error term;
- The parameter estimates;
- The choice of model for the historical data;
- The continuation of the historical data generating process into the future.
Continue reading →
The hts package for R allows for forecasting hierarchical and grouped time series data. The idea is to generate forecasts for all series at all levels of aggregation without imposing the aggregation constraints, and then to reconcile the forecasts so they satisfy the aggregation constraints. (An introduction to reconciling hierarchical and grouped time series is available in this Foresight paper.)
The base forecasts can be generated using any method, with ETS models and ARIMA models provided as options in the
forecast.gts() function. As ETS models do not allow for regressors, you will need to choose ARIMA models if you want to include regressors. Continue reading →
Souhaib Ben Taieb has been awarded his doctorate at the Université libre de Bruxelles and so he is now officially Dr Ben Taieb! Although Souhaib lives in Brussels, and was a student at the Université libre de Bruxelles, I co-supervised his doctorate (along with Professor Gianluca Bontempi). Souhaib is the 19th PhD student of mine to graduate.
His thesis was on “Machine learning strategies for multi-step-ahead time series forecasting” and is now available online. The prior research in this area has largely centred around two strategies (recursive and direct), and which one works better in certain circumstances. Recursive forecasting is the standard approach where a model is designed to predict one step ahead, and is then iterated to obtain multi-step-ahead forecasts. Direct forecasting involves using a separate forecasting model for each forecast horizon. Souhaib took a very different perspective from the prior research and has developed new strategies that are either hybrids of these two strategies, or completely different from either of them. The resulting forecasts are often significantly better than those obtained using the more traditional approaches.
Some of the papers to come out of Souhaib’s thesis are already available on his Google scholar page.
Well done Souhaib, and best wishes for the future.
The International Institute of Forecasters sponsors workshops every year, each of which focuses on a specific theme. The purpose of these workshops is to facilitate small, informal meetings where experts in a particular field of forecasting can discuss forecasting problems, research, and solutions. Over the years, our workshops have covered topics from Predicting Rare Events, ICT Forecasting, and, most recently, Singular Spectrum Analysis. Often these workshops are associated with a special issue of the International Journal of Forecasting.
If you are already hosting a workshop on a forecasting topic and need support from the IIF, or if you are interested in organising and hosting a new workshop, please contact George Athanasopoulos.
A list of past workshops and workshop guidelines are provided on the IIF website.
I’ve received a few emails about including regression variables (i.e., covariates) in TBATS models. As TBATS models are related to ETS models,
tbats() is unlikely to ever include covariates as explained here. It won’t actually complain if you include an
xreg argument, but it will ignore it.
When I want to include covariates in a time series model, I tend to use
auto.arima() with covariates included via the
xreg argument. If the time series has multiple seasonal periods, I use Fourier terms as additional covariates. See my post on forecasting daily data for some discussion of this model. Note that
fourierf() now handle
msts objects, so it is very simple to do this.
For example, if
holiday contains some dummy variables associated with public holidays and
holidayf contains the corresponding variables for the first 100 forecast periods, then the following code can be used:
y <- msts(x, frequency=c(7,365.25))
z <- fourier(y, K=c(5,5))
zf <- fourierf(y, K=c(5,5), h=100)
fit <- auto.arima(y, xreg=cbind(z,holiday), seasonal=FALSE)
fc <- forecast(fit, xreg=cbind(zf,holidayf), h=100)
The main disadvantage of the ARIMA approach is that the seasonality is forced to be periodic, whereas a TBATS model allows for dynamic seasonality.
My forecasting textbook with George Athanasopoulos is already available online (for free), and in print via Amazon (for under $40). Now we have made it available as a downloadable e-book via Google Books (for $15.55). The Google Books version is identical to the print version on Amazon (apart from a few typos that have been fixed).
To use the e-book version on an iPad or Android tablet, you need to have the Google Books app installed [iPad, Android]. You could also put it on an iPhone or Android phone, but I wouldn’t recommend it as the text will be too small to read.
You can download a free sample (up to the end of Chapter 2) if you want to check how it will look on your device.
The sales of the print and e-book versions are used to fund the running the OTexts website where all OTexts books are freely available.
The online version is continuously updated — any errors discovered are fixed immediately. The print and e-book versions will be updated approximately annually to bring them into line with the online version.
A few weeks ago I had a Skype chat with Tim Harford, the “Undercover Economist” for Britain’s Financial Times. He was working on an article for the FT on forecasting, and wanted my perspective as an academic forecaster. I mostly talked about what makes some things more predictable than others, as discussed in this blog post. In the end, his article headed in a different direction, so I don’t get quoted, but it is still a good read!
He also put out this YouTube summary, for those who don’t like to read:
The FPP resources page has recently been updated with several new additions including
- R code for all examples in the book. This was already available within each chapter, but the examples have been collected into one file per chapter to save copying and pasting the various code fragments.
- Slides from a course on Predictive Analytics from the University of Sydney.
- Slides from a course on Economic Forecasting from the University of Hawaii.
If any one using the book has other material that could be made available, please send them to me. For example, recorded lectures, slides, additional examples, assignments, exam questions, solutions, etc.
On 23–25 September, I will be running a 3-day workshop in Perth on “Forecasting: principles and practice” mostly based on my book of the same name.
Workshop participants will be assumed to be familiar with basic statistical tools such as multiple regression, but no knowledge of time series or forecasting will be assumed. Some prior experience in R is highly desirable.
Venue: The University Club, University of Western Australia, Nedlands WA.
- Day 1:
- Forecasting tools, seasonality and trends, exponential smoothing.
- Day 2:
- State space models, stationarity, transformations, differencing, ARIMA models.
- Day 3:
- Time series cross-validation, dynamic regression, hierarchical forecasting, nonlinear models.
The course will involve a mixture of lectures and practical sessions using R. Each participant must bring their own laptop with R installed, along with the fpp package and its dependencies.
For costs and enrolment details, go to