# Practical Time Series Forecasting – Bounding Uncertainty

“*A good forecaster is not smarter than everyone else, he merely has his ignorance better organized*.”

― **Anonymous**

Predicting the future is an exercise in probability rather than certainty. As we have mentioned several times over the course of these articles, **your forecast model will be wrong**.

** It is just a matter of how useful it might be.**

A time series model will **forecast a path** through the forecast horizon, a “point forecast.” But **this path is just one of the paths** your forecast can take based on your estimated model.

Providing a sense of the **uncertainty surrounding your forecast** is an essential part of your job as a forecaster.

### Forecast intervals

The standard approach is to provide the “**forecast interval**” for your forecast.

Typically, this is cast in terms of a 95% prediction interval. That is, 95 times out of 100, the actual value will fall within the specified range. (Note that there is a **difference between** a “confidence” interval and a “forecast” interval.)

### Sources of forecast uncertainty

There are at least **two sources** of forecast uncertainty over the forecast horizon.

The **first results from our ignorance of what the model’s error will be in the forecast horizon**. So, we must rely on how well the model did in the recalibration sample (estimation + holdout) as an estimate.

The **second source of uncertainty results from the model’s coefficients **(or parameters)** being estimates of their true values**. As estimates, they have their own “confidence” interval.

As a result, **the forecast interval can be quite large** (as shown above). And, due to error compounding over time, the **forecast interval widens** the further into the forecast horizon you go.

In our example above, during the **first month** of the forecast horizon, the forecast interval is **plus or minus 0.63%** of the forecasted value. By **month 6**, this spread widens to **plus or minus 2.95%**.

Even accounting for forecast error and parameter uncertainty, these forecast intervals may still be **too narrow**.

### What about meta forecasts?

In an **earlier article** we discussed **combining forecasts into a meta forecast**. The **challenge** in terms of a **meta prediction interval** is that it is **not a simple matter to combine the prediction intervals of the constituents’ forecasts**.

**One approach** is to simply **show the extreme upper and lower forecast paths** along with the meta forecast path, which will lie somewhere between the two extremes.

And then to **caution the consumer of your forecast** that this is just to give a sense of the possible forecast range, which **will likely be too narrow** (since the upper and lower forecast will each have their own prediction interval).

### Probability-based assessment of forecast uncertainty

Another approach is to **couch your forecast uncertainty ****in terms of a probability**.

For example, based on your SALES forecast, **what are the chances of hitting a certain level of sales by a certain date**? If you are forecasting procurement needs for a warehouse, **what is the chance of running out of inventory by a certain date**? If you are a macroeconomist forecasting GDP, **what are the chances of the economy falling into a recession by a certain date**?

**Suppose** you are tasked with forecasting daily SALES over the next year.

**Management has targeted a certain level of SALES and wants to know when that target will be hit.** You can use the forecast uncertainty produced by your model to generate the following chart:

The vertical axis is the chance of hitting the SALES target by a certain date (in this case, days into the next year). So, **160 days into the year, there is a 10% chance of hitting the sales target.**

**By day 192**, a month later, the **chance has grown to 30%**. And **by day 218, there is a 50/50 chance** the sales target will be reached.

Stating these chances in terms of odds may be an easier way to present this:

** By day 160**, the odds of hitting the target would be **9 to 1**. By **day 192** it would be a little over **2 to 1**. And by **day 218**, it would be **1 to 1…a flip of the coin.**

### Bottom line

Uncertainty is a fact of life and your forecasts will be “wrong.”

But quantifying how wrong they can be will go a long way towards making them “useful.”

**Part 1 – Practical Time Series Forecasting – Introduction**

**Part 2 – Practical Time Series Forecasting – Some Basics**

**Part 3 – Practical Time Series Forecasting – Potentially Useful Models**

**Part 4 – Practical Time Series Forecasting – Data Science Taxonomy**

**Part 5 – Practical Time Series Forecasting – Know When to Hold ’em**

**Part 6 – Practical Time Series Forecasting – What Makes a Model Useful?**

**Part 7 – Practical Time Series Forecasting – To Difference or Not to Difference**

**Part 8 – Practical Time Series Forecasting – Know When to Roll ’em**

**Part 9 – Practical Time Series Forecasting – Meta Models**