This week my research group discussed Adrian Raftery’s recent paper on “Use and Communication of Probabilistic Forecasts” which provides a fascinating but brief survey of some of his work on modelling and communicating uncertain futures. Coincidentally, today I was also sent a copy of David Spiegelhalter’s paper on “Visualizing Uncertainty About the Future”. Both are well-worth reading.
It made me think about my own efforts to communicate future uncertainty through graphics. Of course, for time series forecasts I normally show prediction intervals. I prefer to use more than one interval at a time because it helps convey a little more information. The default in the forecast package for R is to show both an 80% and a 95% interval like this: Continue reading →
I get questions about this almost every week. Here is an example from a recent comment on this blog:
I have two large time series data. One is separated by seconds intervals and the other by minutes. The length of each time series is 180 days. I’m using R (3.1.1) for forecasting the data. I’d like to know the value of the “frequency” argument in the ts() function in R, for each data set. Since most of the examples and cases I’ve seen so far are for months or days at the most, it is quite confusing for me when dealing with equally separated seconds or minutes. According to my understanding, the “frequency” argument is the number of observations per season. So what is the “season” in the case of seconds/minutes? My guess is that since there are 86,400 seconds and 1440 minutes a day, these should be the values for the “freq” argument. Is that correct?
Continue reading →
Since my last post on the seasonal adjustment problems at the Australian Bureau of Statistics, I’ve been working closely with people within the ABS to help them resolve the problems in time for tomorrow’s release of the October unemployment figures.
Now that the ABS has put out a statement about the problem, I thought it would be useful to explain the underlying methodology for those who are interested. Continue reading →
I do not normally post job adverts, but this was very specifically targeted to “applied time series candidates” so I thought it might be of sufficient interest to readers of this blog. Continue reading →
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 →
Although the Guardian claimed yesterday that I had explained “what went wrong” in the July and August unemployment figures, I made no attempt to do so as I had no information about the problems. Instead, I just explained a little about the purpose of seasonal adjustment.
However, today I learned a little more about the ABS unemployment data problems, including what may be the explanation for the fluctuations. This explanation was offered by Westpac’s chief economist, Bill Evans (see here for a video of him explaining the issue). Continue reading →
It’s not every day that seasonal adjustment makes the front page of the newspapers, but it has today with the ABS saying that the recent seasonally adjusted unemployment data would be revised.
I was interviewed about the underlying concepts for the Guardian in this piece.
Further comment from me about users paying for the ABS data is here.
I keep telling students that there are lots of jobs in data science (including statistics), and they often tell me they can’t find them advertised. As usual, you do have to do some networking, and one of the best ways of doing it is via a Data Science Meetup. Many cities now have them including Melbourne, Sydney, London, etc. It is the perfect opportunity to meet with local employers, many of which are hiring due to the huge expansion in the use of data analysis in business (aka business analytics).
At the end of each Melbourne meetup, some employers have been advertising their current analytic job openings to the audience.
Now the local organizers are going to extend the opportunity to allow job-searchers to give a 90 second pitch to employers. Details are provided on the message board.
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, seasonal.periods=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.