The Lancaster Lectures

class: center, middle

.maintitle[Three methods for time series analysis: Fourier spectra, wavelets, and stochastic modeling]


  
  
.author[Jonathan Lilly] 
.institution[NorthWest Research Associates, Seattle] 
  
  
.date[March 6 & 7, 2018] 
.note[Sponsored by the [{STOR-i}](http://www.lancaster.ac.uk/stor-i/) program at Lancaster University] 
.footnote[Created with [{Remark.js}](http://remarkjs.com/) using [{Markdown}](https://daringfireball.net/projects/markdown/) + [{MathJax}](https://www.mathjax.org/)]

---
name: toc
class: left, .toc[[✧](index.html#toc)]

#Table of Contents
  
1. [Front Matter](#frontmatter)  [{pdf version}](./pdfs/index.pdf)
1. [Motivation](motivation.html)  [{pdf version}](./pdfs/motivation.pdf)
1. [Look at the Data](lookatthedata.html)  [{pdf version}](./pdfs/lookatthedata.pdf)
1. [Time Domain Basics](thetimedomain.html)  [{pdf version}](./pdfs/thetimedomain.pdf)
1. [Frequency Domain Basics](fourierbasics.html)  [{pdf version}](./pdfs/fourierbasics.pdf)
1. [Linking Time and Frequency](timevsfrequency.html)  [{pdf version}](./pdfs/timevsfrequency.pdf)
1. [The Discrete Fourier Transform](discretefourier.html)  [{pdf version}](./pdfs/discretefourier.pdf) 
1. [The Analytic Signal](theanalyticsignal.html)  [{pdf version}](./pdfs/theanalyticsignal.pdf)
1. [Wavelet Analysis](waveletanalysis.html)  [{pdf version}](./pdfs/waveletanalysis.pdf)
1. [Spectral Analysis](spectralanalysis.html)  [{pdf version}](./pdfs/spectralanalysis.pdf)
1. [Stochastic Modeling](matern.html) [{pdf version}](./pdfs/matern.pdf)
1. [Qualities of Scientific Thought](sixthinkinghats.html)  [{pdf version}](./pdfs/sixthinkinghats.pdf)

---
name: frontmatter
class: center,middle .toc[[✧](index.html#toc)]
 
<a rel="license" href="http://creativecommons.org/licenses/by-nc/4.0/"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-nc/4.0/88x31.png" /></a> “Three methods for time series analysis: Fourier spectra, wavelets, and stochastic modeling” by <a xmlns:cc="http://creativecommons.org/ns#" href="http://www.jmlilly.net" property="cc:attributionName" rel="cc:attributionURL">J. M. Lilly</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc/4.0/">Creative Commons Attribution-NonCommercial 4.0 International License</a>, based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="http://www.jmlilly.net/talks/lancaster/index.html" rel="dct:source">http://www.jmlilly.net/talks/lancaster/index.html</a>.

Please send comments, questions, any error reports, and feedback to <a href="mailto:eponym@jmlilly.net">eponym@jmlilly.net</a>.
 

 
Acknowledge in scientific publications as: 
 
Lilly, J. M. (2018), Three methods for time series analysis: Fourier spectra, wavelets, and stochastic modeling, http://www.jmlilly.net/talks/lancaster/index.html.
---
class: left .toc[[✧](index.html#toc)]
#A Note on the Format

These lecture are written using a system called [{Remark.js}](http://remarkjs.com/) by Ole Petter Bang. It renders very simple source code as if it were individual presentation slides through clever use of Javascript. 
 
In my experience, [{Remark.js}](http://remarkjs.com/) works well in different browsers and different systems. However, there are a few things to be aware of.
 
Because this format uses a lot of auxiliary files, it is not readily made portable. You'll have to be online to read it. PDF versions of the lectures are provided for offline reading.
 
If a line of text may fall off the end of the page, try reducing the browser font side or else switching to another browser.
 
In some browsers the controls for the animations may be difficult to find. If you don't see them upon hovering, try to resize the browser window and this may make them appear. 
 
Finally, the little gray compass in the lower left-hand corner will take you to the table of contents if you click on it. 
---
class: left .toc[[✧](#toc)]
#About this Course

These notes are from a series of lectures given at the invitation of Centre for Doctoral Training (CDT) in Statistics and Operational Research in partnership with Industry (STOR-i) at Lancaster University, March 6 & 7, 2018. The course ran from 10 AM until noon and from 2–4 PM with roughly 40 students in attendance. 
 
<img style="width:100%" src="../../figures/lancaster18-photo.jpg">

<!--class: left, .toc[[✧](#toc)]
#Group Photo

.caption[From left to right: Rebekka J. Steene, Svenja Ryan, Kristin Burmeister, Kjersti Opstad Strand, Ailin Brakstad, Stefanie Semper, Jessica Kern, Omar El Guernaoui, Mia Sophie Specht, Regina-Maria Keller, Joost Hemmen, Katriina Juva, Anna Wünsche, Kristoffer Aalstad, Stephan Kral, Jonathan Lilly, Marta Trodahl, Kristian Agasøster Haaga, Morven Muilwijk, Line Båserud, Johannes Sandanger Dugstad, Knut Ola Dølven, and Philip Kreussler. Not pictured: Jing Sun and Pingyang Li.]-->
 
---
name: overview
class: left, .toc[[✧](index.html#toc)]
# Course Overview
 
Over the next two days we're going to study three state-of-the-art methods for analyzing time series. 

 
Because time is short, an emphasis will be on theoretical understanding, rather than on practical applications.
 
The first day will provide a motivation and overview, followed by a review of the necessary mathematical foundation. The second day we will look at the methods themselves. 
 
This emphasis on fundamentals allows the course content to be fairly self-contained. 
 
These lectures are an abridged and condensed version of a weeklong course I have taught in Oslo the past two years. 
 
More details, homework assignments, and extensive demo files in Matlab may be found in the Oslo course notes at <a xmlns:dct="http://purl.org/dc/terms/" href="http://www.jmlilly.net/talks/oslo/v2/index.html" rel="dct:source">http://www.jmlilly.net/talks/oslo/v2/index.html</a>.

<!---name: overview
class: left, .toc[[✧](index.html#toc)]
# Evaluation

Please help me make the course better! Let me know your opinions on the following:
 
1. The balance of theory vs. practice.
1. The balance of low-tech methods vs. high-tech methods
1. The balance of depth (time on topic) vs. breadth (number of topics).
1. The balance of lectures vs. lab (or demo) time.
1. The balance of individual vs. group activities.
1. The balance of method vs. physical interpretation.
1. The balance of applied assignments vs. those for understanding concepts.
1. What topics do you think will be most useful to you in the future? The least?
1. What was your favorite thing about the course? Your least favorite?
1. Any other comments or feedback that could help me improve the course?--->