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https://github.com/adrigrillo/trend-identification

Comparison of different trend detection and estimation methods in time series
https://github.com/adrigrillo/trend-identification

comparison detection estimation time-series trends

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Comparison of different trend detection and estimation methods in time series

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README 

        
## Trend identification and estimation in time series



Student(s): Grillo, A., Hanrieder, M., Mauranen, H., Mikos, M., Wiezorek, J.  

Supervisor(s): Bonizzi, P.  

Semester: 2018-2019



![Fig 1. - How a trend can affect the

interpretation](website/images/Components.png)



#### Background



This project should help to analyse time series data, which is a special

type of data with a time-value, such as seconds or timestamp, as x-value

and any observed value as y-value. The y-value can then be a measured

value like temperature or stock exchange data. In a mathematical sense

this kind of data consists of several components. One component is the

so-called noise which describes random events or measurement errors.

Another component is the season, such as time of year in weather data.

In general the season component describes repetitive behaviour during

the observation period. Furthermore, data can contain a trend, which

describes how the data will develop beyond the measurement period. In

Fig. 1 a synthetic time series data was generated with these three

different components, a trend, random noise and seasonality.



A main topic of this project is to find trends, which can be split in

two parts. The first part is the identification, which means finding out

if a trend exists, while the second part is to estimate this trend. An

estimation of a trend can be an equation like *x+5* or just a list of

points. This depends on the method that is used. Trends can have

different shapes such as just a straight increasing or decreasing line

or more complex curves like simple polynomials. An overview about the

considered types of trend can be found in Fig 2. Different methods can

either identify or estimate a trend, or do both.



![Fig 2. - Performance analysis on monotonic trend](website/images/Rplot.png)



#### Problem statement and motivation



It is very useful to separate the trend and season from the time series.

For instance, scientists investigating global warming are interested in

the overall changes, or trend, in temperature and not so much in the

seasonal changes. Another example application is medicine, where

electrocardiograms suffer from patient's breathing and baseline wander,

that cause the heartbeats to be shifted away. There it is more useful to

consider the series without the long-term changes. The quality of the

separation for each component allows easier analysis on the time series.



There are multiple ways to take apart time series recordings. However,

none of them are considered the standard way and little research exists

to compare the methods for different types of time series. Our goal is

to systematically compare the different approaches to find the best one

or to be able to give the best method for specific type of time series.



#### Methods



A lot of methods are able to detect or approximate a trend, but these

methods perform differently depending on the influences of the trend,

the seasonal component and the noise. Mostly common methods, such as

regression, are covered with a couple more complex methods. An overview

and a brief description of them can be found in the report. All of the

methods are applied to each trend individually. This allows determining

the best method for a trend type. These results are compared to find

either the best overall method or a group of trends where specific

methods perform well.



An example analysis of the estimation methods on two different trends

can be found in Fig 3 and Fig 4, in the bar chart on the right the

distance to the original trend is measured, so the smaller the value,

the better the performance. On the mixed polynomial trend most methods

perform very well, but the Theil-Sen estimator performs very bad. While

on the monotonic trend all methods performs comparable except for the

discrete wavelet spectrum which performs worse.



![Fig 3. - Performance analysis on mixed polynomial

trend](website/images/methods_1.png)



![Fig 4. - Performance analysis on monotonic

trend](website/images/methods_2.png)



#### Research questions



  - What are the best and most versatile approaches for trend

    identification and estimation in time series data?

  - What are the strengths and weak points of the different methods

    tested?

  - Is it possible to automatically select the best approach(es) for

    trend identification and estimation, based on the

    (statistical/frequency/etc.) properties of a time series and the

    specific problem domain and application?



#### Main outcome



The research results in the comparison of strengths and weaknesses of

different methods for trend detection and estimation.



#### Downloads:



[Final report](”???”) [Final presentation](”???”)