Which branch of statistics and mathematics deals with extrapolations?

[Cinitiator]

Which branch of statistics and mathematics deals with extrapolations and trend analysis? That is, where one can estimate various trends (be they exponential, linear, etc.) that apply to our data and draw a trend which could extrapolate the future variation.

Am I referring to the time series analysis branch of statistics? Which precise branches of mathematics and statistics should I take to be able to estimate trends and extrapolate various data?

 

[Stephen Tashi]

Which precise branches of mathematics and statistics should I take to be able to estimate trends and extrapolate various data?

The term "trend" doesn't have a unique meaning in mathematics. You are expressing a desire to predict the future of various pheonomena. Particular mathematical models apply to particular phenomena. You'd get better advice if you describe the particular things you wish to predict. Those things could be related to particular mathematical models and particular branches of math.

Someone might make you a laundry list of all mathematical fields that deal with models used to forecast the future of anything. Is that what you want?

 

[Mute]

If you have a set of data that you want to find the trends of, then typically one either uses various curve-fitting techniques (which can range from basic linear-regression style methods to more advanced methods) or time series analysis, yes.

To extrapolate from fitted or observed trends, however, is going to require a mathematical model. Sometimes the model is quite simple: you observe that some data is fit well by an exponentially increasing distribution, for example, so you assume that future data will follow the same trend and be described by the same exponential you fit the past data with. The predictive power of this approach is going to depend on whether or not the conditions under which the past data was observed change. If conditions stay the same, you might expect your fit prediction to remain valid. However, if conditions start to change for some reason or another, then at some point your prediction will cease to be valid.

In such cases, it helps if you build an actual independent mathematical model based on what processes you think will cause the observed, rather than just fitting the data itself (although fitting the data can help you choose values for your model parameters). If you get the processes which drive the data correct, then your model can have much more predictive power than simply fitting a function to the observed data and arguing that the trend should continue. On the other hand, if you get the processes wrong, your model may break down in the future as well.

This said, if your university has courses on mathematical modelling, I would look into those. Courses on statistical analysis of quantitative data are also good to look into. Looking at my own university's undergrad courses, some course titles are "applied regression and design", "time series analysis", "advanced data analysis", "topics in applied statistics", "statistical data management". Some courses in probability theory would also be good.

 

[Cinitiator]

Thank you all for your help.
Which techniques excluding regression lines are usually used for curve fitting?

 

[chiro]

Hey Cinitiator.

In addition to the comments above, you might want to look at the topics, research, and applications in data mining since this is exactly what they try and look at under the umbrella of many different fields working together like probability and statistics, computer science, and applied mathematics amongst others.