Time-Series Analysis

Important Concepts, Handy Techniques, and Some Cautionary Tales

Tim Wilson
Superweek 2023

A travel tip…or Zoli as an unintentional travel agent?

Let’s think about time.

This presentation

40 minutes

DALL-E 2: “A puppy delivering a presentation that has a line chart on a slide, digital art”

Superweek

5 days

My last job

5 years

DALL-E 2: “A puppy working as marketing analyst, digital art”

Yehoshua’s intros

DALL-E 2: “A puppy with eyes that look like the infinity symbol, digital art”

“Time” is a tricky thing, but it’s at the core of what we do.

It rarely looks quite like this

It often has a weekly cycle to it

And it may have a trend to it

DALL-E 2: “A puppy running a linear regression on a computer, digital art”

Let’s think about statistics

Statistics is all about estimating a population from a sample.

Our data exists over time.

So, what is our population?

Is it the past to the present?

Maybe. Maybe not.

Maybe it’s the past, present, and future?

Or…just the future?

But…we can’t sample from the future!

So…what is our sample?

Our sample is a sample timeframe.

This is imperfect.

Because our reality is constant change.

DALL-E 2: “A room full of puppies who all have different astonished expressions on their faces, digital art”

Time-series data is often
non-stationary.

A stationary time series is one whose statistical properties do not depend on the time at which the series is observed. ¹

One Antidote to Non-Stationarity: First Differences

Are these two metrics correlated?

To the scatterplot!

R² = 0.84

DALL-E 2: “A puppy nodding its head with a speech bubble saying”YES!“, digital art”

DALL-E 2: “A puppy shaking its head with a speech bubble that has the exact text”Maybe!“, digital art”

If they’re correlated, then when one moves, the other will move similarly.

When one metric increases, the other should increase similarly.

When one metric decreases, the other should decrease similarly.

So, let’s look at the changes rather than the actual values.

This is called first differences.

Date	Orders	1st Diff: Orders
2023-01-20	9,482
2023-01-21	10,164
2023-01-22	9,503
2023-01-23	11,317
2023-01-24	9,980
2023-01-25	10,484
2023-01-26	10,458

This is called first differences.

Date	Orders	1st Diff: Orders
2023-01-20	9,482
2023-01-21	10,164
2023-01-22	9,503
2023-01-23	11,317
2023-01-24	9,980
2023-01-25	10,484
2023-01-26	10,458

This is called first differences.

Date	Orders	1st Diff: Orders
2023-01-20	9,482
2023-01-21	10,164
2023-01-22	9,503
2023-01-23	11,317	1,814
2023-01-24	9,980
2023-01-25	10,484
2023-01-26	10,458

This is called first differences.

Date	Orders	1st Diff: Orders
2023-01-20	9,482	NA
2023-01-21	10,164	682
2023-01-22	9,503	−661
2023-01-23	11,317	1,814
2023-01-24	9,980	−1,337
2023-01-25	10,484	504
2023-01-26	10,458	−26

From non-stationary to more stationary

We can calculate first differences for both metrics

Date	Orders	1st Diff: Orders	Social	1st Diff: Social
2023-01-20	9,482	NA	5,754	NA
2023-01-21	10,164	682	6,181	427
2023-01-22	9,503	−661	5,650	−531
2023-01-23	11,317	1,814	6,265	615
2023-01-24	9,980	−1,337	6,603	338
2023-01-25	10,484	504	7,114	511
2023-01-26	10,458	−26	6,522	−592