Applied Time Series Analysis

DATA 330 | Spring 2021

  • Join Slack, GroupMe or both
  • Join GitHub team
  • Review syllabus
  • Listen to a little philosophy

Questions?

Why Time Series?

Why do we care about time series in data science?

  1. Data science is the field that finds patterns in data.
  2. A time series is a special type of data.
  3. We use special tools to find patterns in time series.

But why?

Modeling.

Why?

I can think of two cases:

First, there’s big data.

Big data
any collection of data that is too big to be held in the memory of your computer

“Resolution” or “number of samples” are not “big data.”

The four V’s of big data.

  • Volume
  • Velocity
  • Variety
  • Veracity

Focus on the “hows” and “whys”
and not the results to explain what we depict.

For example:

“Massive Dataset Analysis for Geoscience Data”

“One approach is to reduce data in a way that preserves spatial, temporal, and inter-scale structures via discrete probability distribution estimates associated with cells of space-time grids at different resolutions. It is then possible to study relationships between cells at different scales. Data are stratified […] to form subsets. Each subset is reduced using a clustering algorithm […]. The clusters’ centroids and populations define a set of discrete probability distributions, which become the fundamental units for data analysis.” – AJ Braverman, Jet Propulsion Laboratory, CA

We see evidence of time series + data science.

Imagine having only to store data models
in place of big data.

There’s a popular belief that all data is a mixture of parametric structures and stochastic noise.

When the shared sample space for the stochastic process is time,
we refer to this data as a time series.

Which brings us to my second case …

forecasting.

If there truly are patterns in data and we know what happened in the past, can we predict the future?

What’s so great about predictions?

π

Restate my assumptions:

  1. Mathematics is the language of nature.
  2. Everything around us can be represented and
    understood through numbers.
  3. If you graph the number of any system patterns emerge;
    therefore, there are patterns everywhere in nature.

Evidence:

  • The cycling of disease epidemics.
  • The wax and wane of caribou populations.
  • Sunspot cycles.
  • The rise and fall of the Nile.

So what about the stock market?

We’re not there yet.

Over the next 15 weeks, I’d like to

  • Discuss and examine the fundamentals of time series data
  • Look at some challenges in real world time series data
  • Introduce modeling and forecasting of times series data

WARNING: There’s a lot of math in our textbook.

We’ll have opportunities for discussions.

Sorry about the pacing. It’s going to be off.

Okay. Let’s begin.