D3 Foresight is a d3 based library for visualizing time series forecasts interactively. At a time point, a general time series model trying to predict a single variable series (like temperature) makes forecasts for some time points in the future with some uncertainty described by probability distributions. Other than these predictions, it might also provide an estimate of peak and some onset/outbreak point (as defined by a baseline). The visualizations in this library try to cover these cases. See reichlab/flusight for a demo.

Setting up

The library requires d3 and momentjs as external dependencies. To build foresight itself, use npm compile (for ./dist/d3-foresight.js) or npm build (for ./dist/d3-foresight.min.js). The library is also available on npm as d3-foresight. For browser, include these in your html:

<script src="https://d3js.org/d3.v4.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/moment.js/2.18.1/moment.min.js"></script>
<script src="./dist/d3-foresight.min.js"></script>
;; Or use the unpkg url
<script src="https://unpkg.com/d3-foresight"></script>


Additionally, a few icons (in the legend) have an icon font dependency. The css for that can be added using:

<link rel="stylesheet" href="./assets/fontello/fontello.css" />


TimeChart

A TimeChart displays the time series to be predicted and the models' predictions. Beyond the very minimal plots involving only model forecasts, it can show the following items:

• The actual time series to be predicted.
• The observed time series. This might be different from the actual series if the truth is revised (e.g. due to reporting delays in the incident count for certain disease).
• Baseline value for the year/season.
• History of the series over some past years/seasons.
• Additional prediction information from models like
• Confidence intervals
• Peak and onset prediction

Basic plot

In this section, we will create a very basic visualization involving one model providing random numbers as forecasts for a year.

Configuration

Time in foresight is represented using timePoints which is an array mapping to discrete date/time values. As of now, foresight supports the following three types of time points:

1. week
2. mmwr-week based on MMWR definitions
3. biweek denoting a unit of two weeks
4. month denoting a month

All points can be represented using either standard JS Date objects, a string readable by momentjs (like YYYYMMDD) or using simple objects like shown:

{
week: 20, // biweek/month
year: 2016
}


Lets work on mmwr weeks for the year 2016. Our week choice can be passed to foresight charts using a config object which is the following in our case:

let config = {
pointType: 'mmwr-week', // Default is week
axes: {
y: {
title: 'Random numbers' // Title for the y axis
}
}
}


Data

At minimum, TimeChart expects an array of time points and an array of model data. The time points in our case go from week 1 to week 52 of 2016 and can be represented as:

let timePoints = [...Array(51).keys()].map(w => {
return { week: w + 1, year: 2016 }
})


At each time point, our model provides predictions for the next 10 time points. These predictions are represented in an array of same size as the time points. For when the model has no predictions, we put in null.

// Random sequence generator
function rseq (n) {
let seq = [Math.random()]
for (let i = 1; i < n; i++) {
seq.push(Math.random() * (1 + seq[i - 1]))
}
return seq
}

// Predictions look like [{ series: [{ point: 0.5 }, { point: 1.2 } ...] }, ..., null, null]
let predictions = timePoints.map(tp => {
if (tp.week > 30) {
// We only predict upto week 30
return null
} else {
// Provide 10 week ahead predictions
return {
series: rseq(10).map(r => { return { point: r } })
}
}
})


Finally we put everything together in a single object. Notice the extra metadata involved in putting together the values for the model:

let data = {
timePoints,
models: [
{
id: 'mod',
meta: {
name: 'Name',
description: 'Model description here',
url: 'http://github.com'
},
pinned: false, // Setting true shows the model in top section of the legend
// In case of absence of pinned key (or false), the model
// goes in the bottom section
predictions,
style: { // Optional parameter for applying custom css on svg elements
color: '#4682b4', // Defaults to values from the internal palette
point: {
// Style for the dots in prediction
},
area: {
// Style for the confidence area (shaded region around the line)
},
line: {
// Style for the main line
}
}
}
]
}


Plotting

The life cycle of TimeChart involves the following stages:

1. Initialization
2. Plotting
3. Updating
// 1. Initialize
// Setup the id of div where we are going to plot
// Also pass in config options
let timeChart = new d3Foresight.TimeChart('#timechart', config)

// 2. Plot
// Provide the data for the complete year
timeChart.plot(data)

// 3. Update
// Move to the given index in the set of timePoints
timeChart.update(10)
// Or simply use
// timeChart.moveForward()
// timeChart.moveBackward()

// Lets also save the timechart object in global namespace
window.timeChart = timeChart


If you are able to see the plot above (which you should be, else file an issue), you should be able to move around by clicking the arrow buttons in legend or clicking on the chart itself. These mouse click events can trigger user defined functions too. See the section on Hooks for more description.

Baseline

A baseline is a horizontal line specifying some sort of baseline. To plot it, pass a baseline item in data. Optionally, set a label for the baseline by providing it in the config.

let tcBaseline = new d3Foresight.TimeChart('#tc-baseline', Object.assign(copy(config), {
baseline: {
text: 'Baseline', // To show multiline text, pass an array of strings,
description: 'This is a sample baseline',
url: 'https://github.com'
}
}))
tcBaseline.plot(Object.assign(copy(data), {
baseline: 0.3
}))
tcBaseline.update(10)


Actual

Another important component to show is the actual line that we are trying to predict. The actual series is an array of the same length as the timePoints and can be something like this

// Suppose we have actual data for 20 time steps only. We give null for other points
let actual = rseq(20).concat(timePoints.slice(20).map(tp => null))

let tcActual = new d3Foresight.TimeChart('#tc-actual', config)
tcActual.plot(Object.assign(copy(data), { actual: actual }))
tcActual.update(10)


Observed

Observed data series refers to the time series as observed at a certain time point. Observed lines are useful (only) when there are updates in actual data, resulting in different versions based on when the data was released.

We formalize these versions using lags. When we are at a time point $$t$$ what we get as truth (the value that creates the actual series) is a lag $$0$$ truth, $$l_0(t)$$. At the same time, we also get $$l_1(t - 1)$$ truth for time point $$t - 1$$, $$l_2(t - 2)$$ truth for $$t - 2$$ and so on. In this case, even if we have higher lag truths for time $$t$$, the observed series at time $$t$$ will be made up of the series $$[l_i(t - i), \forall i \in [t - 1, t - 2, \ldots 0]]$$

To display the observe data thus we need to provide the required lag truths for a time point. We do this by providing a list of lists. The outer list is over all the time points. The inner lists represent decreasing lag values (like { lag: 2, value: 0.2}) for that time point.

A simple example follows. Notice that the third time point is the latest one and so we only have lag 0 value for that.

// Assume there are 3 timepoints
let observedExample = [
[ { lag: 2, value: 0.88 }, { lag: 1, value: 0.88 }, { lag: 0, value: 0.93 }],
[ { lag: 1, value: 1.11 }, { lag: 0, value: 1.32 } ],
[ { lag: 0, value: 1.13 } ]
]


The next snippet generates some random data programmatically for demoing purpose.

// Lets only show 20 time steps.
let observed = rseq(20).map((r, idx) => {
let delta = 0.05
let lags = []
for (let l = 20; l >= 0; l--) {
lags.push({ lag: l, value: r + (delta * (20 - l)) })
}
return lags
})

// Add [] for other points
observed = observed.concat(timePoints.slice(20).map(tp => []))

let tcObserved = new d3Foresight.TimeChart('#tc-observed', config)
tcObserved.plot(Object.assign(copy(data), { observed: observed }))
tcObserved.update(10)


History

Historical data lines (similar to actual series) can be shown by passing an array of historical actual series like the following:

let historicalData = [
{
id: 'some-past-series',
actual: rseq(51)
},
{
id: 'another-past-series',
actual: rseq(51)
}
]

let tcHistory = new d3Foresight.TimeChart('#tc-history', config)
tcHistory.plot(Object.assign(copy(data), { history: historicalData }))
tcHistory.update(10)


One possible issue with showing history is that the number of time units might not line up perfectly. For example, the current year might have 52 weeks but some older year might have had 53 weeks. Since we expect all the actual series passed as history to have the same length, the user is supposed to pad/clip all the series to match the current season's length.

Confidence Intervals

Confidence intervals show a region of uncertainty around the model predictions (peak, onset and the regular time step predictions). These involve users to specify:

1. Label for the confidence intervals to be shown in legend. For example 90% etc.
2. Additional low and high values along with point values in predictions.

The legend label can be specified in the main chart option by passing the following key/value pair (say we want to show 90% and 50% CIs):

...
confidenceIntervals: ['90%', '50%']
...


Corresponding to the values specified above (and in the same order), we now attach a list of low and high values as shown below:

// Predictions now look like [{ series: [
// { point: 0.5, low: [0.3, 0.4], high: [0.7, 0.6] },
// { point: 1.2, low: [1.0, 1.1], high: [1.4, 1.3] }
// ...] }, ..., null, null]
let predictionsWithCI = timePoints.map(tp => {
if (tp.week > 30) {
// We only predict upto week 30
return null
} else {
// Provide 10 week ahead predictions adding a dummy 0.2 and 0.1 spacing
// to show the confidence interval
return {
series: rseq(10).map(r => {
return {
point: r,
low: [Math.max(0, r - 0.2), Math.max(0, r - 0.1)],
high: [r + 0.2, r + 0.1]
}
})
}
}
})


Putting everything together now:

let dataWithCI = {
timePoints,
models: [
{
id: 'mod',
meta: {
name: 'Name',
description: 'Model description here',
url: 'https://github.com'
},
predictions: predictionsWithCI
}
]
}

let configCI = Object.assign(copy(config), { confidenceIntervals: ['90%', '50%'] })
let tcCI = new d3Foresight.TimeChart('#tc-ci', configCI)
tcCI.plot(dataWithCI)
tcCI.update(10)


Peak and Onset

Just like a series key in predictions, we can also add onsetTime, peakTime and peakValue keys to show the respective predictions. Each of these have a mandatory point key and can have low and high ranges to show confidence intervals. Here is an example for a model's prediction at a certain timepoint with the onset and peak values specified (along with a confidence interval):

// Consider the confidence intervals ['90%', '50%']
{
onsetTime: {
high: [15, 17],
low: [9, 11],
point: 13
},
peakTime: {
high: [25, 27],
low: [19, 21],
point: 23
},
peakValue: {
high: [3.6, 3.8],
low: [3.0, 3.2],
point: 3.4
},
series: [
{
high: [1.4, 1.6],
low: [0.8, 1.0],
point: 1.2
},
...
]
}


Note that the values for peakTime and onsetTime are indices for the time points instead of actual week values. For example, suppose the time points actually refer to weeks from 5 to 15 (inclusive) for a year. An onsetTime value of 3 will now refer to week 9 (0 based index starting at 5).

By not using the actual week value here, we localize the meaning of time point in a single place, the series timePoints itself.

Lets recreate the season data now with added peak and onset predictions. We will not be adding confidence intervals here to keep things simple.

let predictionsWithPeakOnset = timePoints.map(tp => {
if (tp.week > 30) {
// We only predict upto week 30
return null
} else {
return {
series: rseq(10).map(r => { return { point: r } }),
peakTime: { point: 12 + getRandomInt(5) },
onsetTime: { point: 8 + getRandomInt(5) },
peakValue: { point: Math.random() }
}
}
})



For showing the onset value, we also need to pass a config option { onset: true } to the timeChart so that the onset panel is displayed just above the x axis.

let dataWithPeakOnset = {
timePoints,
models: [
{
id: 'mod',
meta: {
name: 'Name',
description: 'Model description here',
url: 'https://github.com'
},
predictions: predictionsWithPeakOnset
}
]
}

let configOnset = Object.assign(copy(config), { onset: true })
let tcPeakOnset = new d3Foresight.TimeChart('#tc-peak-onset', configOnset)
tcPeakOnset.plot(dataWithPeakOnset)
tcPeakOnset.update(10)


Starting from v0.10.0, you can add extra lines to be shown in the plot. To keep the library backward compatible, you need to provide the extra data as another key in the data object that you send to the plot function. Here is an example and specification of the structure that we expect:

let tcAdditional = new d3Foresight.TimeChart('#timechart-additional', config)

{
id: 'Extra 1',
data: 1.53, // Scalar makes it show up as horizontal line
style: { // Optional style parameter
color: 'red',
point: {
// Optional parameter for styling the dots
},
line: {
// Style for the main line
'stroke-dasharray': '5,5'
}
},
meta: {
// Similar to what is used in models, all optional
name: 'Extra baseline',
description: 'This is an additional baseline',
url: 'https://github.com'
},
tooltip: false, // Should the value show up in tooltip (false by default or when absent)
legend: true // Should the value show up in legend (true by default or when absent)
},
{
id: 'Extra 2',
data: rseq(51), // Structure similar to like the actual array
style: {
color: '#9b59b6',
point: {
r: 0
}
},
tooltip: true
}
]



Data Version Time and Timezero

There are two possible reference times for a prediction by a particular model:

1. Timezero: The time with respect to which the forecasts are made. For example, if a model predicts 3 steps ahead values of [1.0, 1.2, 0.5] with a timezero of t, then we say that the predicted values are for time steps t + 1, t + 2, and t + 3.
2. Data Version Time: Specifies the data at a particular version (given by the time value) the model looked at while making its prediction.

In a usual prediction task, when we are a time t, our predictions are made by considering t as the timezero and the data version time. The data version time is displayed using a gray shaded region (covering all the data that the model looked at) and a boundary text 'Data as of'. The timezero line is shown as a separate dashed vertical line with text 'Timezero'.

When both times are the same, only data version time is displayed. In case the user provides data version times separately for each prediction, both times are shown since they might be different. You can also override the display of the timezero line by passing a Boolean key in either the options parameter (passed when initializing the plot) or the data parameter (passed when calling the plot function):

...
timezeroLine: true
...


Here is an example plot where user passes in additional data version. Note that the dataVersionTime values are not indices for the timePoints array but date time values themselves. We first define the function that adds dummy data version time to all the predictions.

// Lets just add 2 to the timezeros for dvds
let dvts = data.timePoints.map(tp => {
return { week: tp.week + 2, year: tp.year }
})

data.models.forEach(m => {
m.predictions.forEach((p, idx) => {
if (p) {
p.dataVersionTime = dvts[idx]
}
})
})

return data
}

let tcDvd = new d3Foresight.TimeChart('#timechart-dvt-plot', config)

tcDvd.update(10)


TODO All config and data options

Possible options to the constructor are described below:

let options = {
baseline: {
text: ['CDC', 'Baseline'], // A list of strings creates multiline text
description: Baseline ILI value as defined by CDC.
<br><br><em>Click to know more</em>,
url: 'http://www.cdc.gov/flu/weekly/overview.htm' // url is optional
},
axes: {
x: {
title: ['Epidemic', 'Week'],
description: Week of the calendar year, as measured by the CDC.
<br><br><em>Click to know more</em>,
url: 'https://wwwn.cdc.gov/nndss/document/MMWR_Week_overview.pdf'
},
y: {
title: 'Weighted ILI (%)',
description: Percentage of outpatient doctor visits for
influenza-like illness, weighted by state population.
<br><br><em>Click to know more</em>,
url: 'http://www.cdc.gov/flu/weekly/overview.htm',
domain: [0, 13] // For explicitly clipping the y values
}
},
pointType: 'mmwr-week',
confidenceIntervals: ['90%', '50%'], // List of ci labels
onset: true, // Whether to show onset panel or not
timezeroLine: false // Whether to show the timezeroLine, skipping this makes us fall back to the
// behavior based presence of data version time
}


Options for plotting go here

Hooks

Charts can call user defined functions when movement events are triggered inside (e.g. by clicking on movement buttons or clicking on the overlay). To register your functions to be called on these events, you can use addHook.

timeChart.addHook(d3Foresight.events.JUMP_TO_INDEX, index => {
// This is triggered when an event moves the
// visualization to certain index in timePoints

// Current index is timeChart.currentIdx
console.log('chart moved to ' + index)
})


addHook returns a subscription token which can then be used to revoke that hook using removeHook.

let token = timeChart.addHook(
d3Foresight.events.JUMP_TO_INDEX,
index => console.log(Now at \${index})
)
timeChart.removeHook(token)