In a previous blog post, I had exported biking distance, running distance and daily step counts from my iPhone. I then tried to detect a possible change in step count, using pymc3 to model two different distributions. While this achieves the goal of detecting a single changepoint, there is a lot more we can do with that iPhone data. For example, my biking is presumably a stationary process and possibly could have some periodicity, we can try to model these using time-series tools. Relevant R code is found in my timeseries_analysis.R.

This blog post is not about mobile health. You definitely can do a seriously deep dive, where you extract the raw accelerometer events from your device through, for example, Apple’s CoreMotion API, then process it using something like GGIR. Apple also provides CoreML so you can potentially do on-device analyses.

Instead, I want to use my iPhone as a (very limited) source for time-series data, as you can see below.

The R time-series analysis ecosystem

You can clean your raw data with lubridate, aggregate with dplyr, then convert it into one of the relevant data structures: base R’s ts (time-series), xts (extended time-series) and zoo. For those interested in quantitative finance, there is tidyquant, which speaks xts and zoo in the Tidyverse syntax while interoperating with other domain-specific packages (quantmod, PerformanceAnalytics, etc..).

Exploratory analysis

This is where we test for stationarity by looking at autocorrelation and partial autocorrelation, look for spurious correlation with other variables in the dataset or external factors. You may also need to perform smoothing using Kalman filter.

Decomposing data into seasonal, trend, and irregular components

We can start with base R’s stl (Seasonal Decomposition of Time Series by Loess). If your data isn’t seasonal (or seasonal enough), stl() will fail with an informative message, which I think is better than trying to find an answer anyway. After removing seasonal and trend components, we can start looking at detecting anomalies. STL can also perform forecasting (see below).

Detecting anomalies

Timeseries anomalies are generally divided into outliers, which are local temporary data points, and changepoints, which represents a shift to a fundamentally state in the data.

You can use stl() itself to detect outliers. As I mentioned above, outliers is what remains in the data once seasonal and trend components have been removed. However, when decomposing data where the trend is less dominant than the seasonal component, the loess smoother tends to perform worse, as described here by the authors of the anomalize package. You can simply use IQR to flag outliers. Twitter, who has access to tons of seasonal data, created the AnomalyDetection package, which uses a refined version of the Generalized ESD test.

For detecting changepoints, I used the changepoint package, which implements different algorithms, including Binary Segmentation, At Most One Change (AMOC), and the newer Prune Exact Linear Time (PELT). Besides being much faster than my previous pymc3 approach, these methods are also more robust. For instance, I could detect multiple change points in my steps data without fully specifying distributions for them. The particular function you call in changepoint depend on whether the data’s mean, variance, or both have changed. You then need to specify penalties for calculating the changepoint(s), or have the algorithms calculate them for you. A nice walkthrough of the package is found here.

Modeling & forecasting

Time series data can be modeled in different ways: Hidden Markov Models(HMMs), linear Gaussian models with the Kalman filter applied, or Bayesian structures, each having its own strengths and weaknesses.

For forecasting, extensions to STL could be used (eg. STLM, STLF), or depending on application you can use Exponential Smoothing (ETS), Autoregressive Integrated Moving Average (ARIMA), or Box-Cox transform, ARMA errors, Trend, and Seasonal (BATS/TBATS). Many of these algorithms are implemented in the forecast package.

Time-series data sources

Since my personal datasets are tiny, it’s good to know sources for larger, richer datasets. Along with the well-known Kaggle time-series datasets, the US Centers for Disease Control sponsors a competition to forecast flu spread at FluSight, providing ground truth using actual flu surveillance data along with test sets.

Reference

Since the field has been around a while, there are many, many books on time-series analysis. A recent one I find interesting is Aileen Nielsen’s Practical Time Series Analysis. The writing is very accessible, there are plenty of references, and Nielsen alternated code examples between R and python. I can see this style becoming a little disorienting for some readers, but I actually liked it, since it forces you to focus on the concepts rather than implementation details while giving a good survey of available tools.

The author of the forecast R package Rob Hyndman has published extensively on forecasting, including the book “Forecasting: Principles and Practice”, which is freely accessible online.