20236 Time Series Analysis
In this project, you are free to choose the data and problem of your interest. Alternatively, we provide the activity tracking data below. Some general guidelines:
- Describe the data, also providing the source;
- explain what you would like to investigate for this data,
- describe your analysis and comment brieflfly.
Instructions: if you are using your own dataset, you can setup your fifinal project as you wish. You can use
the above questions to guide you. If you are using the activity tracking data, you can follow the above guide
or do your own.
Maximum 8 pages in total.
Activity tracking data
Technology today makes it possible to cheaply record and analyze data from a great variety of sources.
Activity tracking has seen a tremendous growth in popularity in recent years due to user-friendly smart
devices. This wealth of information can sometimes be accessed in its raw form and interpreted considering
the underlying physical process.
We consider a dataset made of 45 activities. Each activity corresponds to (part of) a bike ride, and is
described by average speed, elevation (elev), and heart rate (bpm) measured at regular 30-second intervals,
for a duration of 2 hours. The three time series are related by a common physical process – the bike ride.
- heart rate and speed are positively related if elevation is constant,
- speed and elevation gains are negatively related if heart rate is constant,
- heart rate is positively related to elevation increases if speed is maintained constant,
- elevation gains/losses are intuitively more important than the level
Among the possible goals of analysis, we mention: understanding the relationship among the time series
for each track; cheap real-time estimation of power output; performance prediction; scoring of each activity
based on some objective; many others.
Fin代写 Let us start with univariate analysis for these data. In particular, we focus on bpm (heart rate in beats per
minute). Model the evolution of bpm in a track as a HMM. Motivate this choice and interpret your results.
You may use your answer from Assignment 2 here with changes (if any) as you see fifit.
DLM, part 1
Next, we focus on the problem of forecasting bpm using a model that envisages minor changes of the heart
rate as opposed to abrupt changes. Fin代写 Use a DLM for this goal. Hint: again, you may use your answer from
Assignment 3 here with changes (if any) as you see fifit.
DLM, part 2 (new)
As we have mentioned, the activity tracking data can be used for difffferent kinds of analysis, depending on
the goal. You can now make your own analysis, Fin代写 following these steps:
- 1 Outline your question and explain your goals;
- Motivate and write the model you will use to answer your question, explaining how you will interpret
- Use relevant plots and tables to brieflfly report your analysis and interpret the results.
You are required to consider multiple time series in the same model.
Example. Tools exist to create GPS tracks which can be followed during an activity.
For this reason, the
elevation profifile of a track might be known in advance. Speed is also under (limited) control by the cyclist.
Therefore, given the track elevation (and its change) and a desired speed, a cyclist might be interested in
predicting bpm in order to be able to dose their effffort in time and optimize their performance. With the
goal of predicting bpm given dfelev and/or speed, one could use a regression model with constant or time
varying parameters. Difffferent models could be compared in terms of their relative performance and potential
for interpretation across difffferent activities. Does including a covariate in a regression model result in better
performance compared to a univariate local level model? One could also explore whether or not two or more
tracks have similar behavior: Fin代写 can we borrow information from one track, in predicting another, similar, track?
How do regression results change if one borrows information from related regressions? There are countless
questions you may want to answer! Set a goal, think of a model, compare with alternatives, show your results.