20236 Time Series Analysis
Time Series Analysis代写 In this project, you are free to choose the data and problem of your interest. Alternatively, we provide the activity
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:
- Describethe data, also providing the source;
- explainwhat you would like to investigate for this data,
- describeyour analysis and comment Time Series Analysis代写
Instructions: if you are using your own dataset, you can setup your final 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 Time Series Analysis代写
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.Time Series Analysis代写
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. Intuitively:
- heartrate and speed are positively related if elevation is constant,
- speedand elevation gains are negatively related if heart rate is constant,Time Series Analysis代写
- heartrate is positively related to elevation increases if speed is maintained constant,
- elevationgains/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.
HMMTime Series Analysis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 fit.
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. Use a DLM for this goal. Hint: again, you may use your answer from Assignment 3 here with changes (if any) as you see fit.
DLM, part 2 (new)Time Series Analysis代写
As we have mentioned, the activity tracking data can be used for different kinds of analysis, depending on the goal. You can now make your own analysis, following these steps:
- Outlineyour question and explain your goals;
- Motivate and write the model you will use to answer your question, explaining how you will interpret itsparameters;
- Userelevant plots and tables to briefly report your analysis and interpret the
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.1 For this reason, the elevation profile 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 effort 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.Time Series Analysis代写
Different models could be compared in terms of their relative performance and potential for interpretation across different 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 moretracks have similar behavior: can we borrow information from one track, in predicting another, similar, track? Time Series Analysis代写How do regression results change if one borrows information from related regressions? There are countlessquestions you may want to answer! Set a goal, think of a model, compare with alternatives, show your results.
1See e.g. http://www.naviki.org