Talk:Linear trend estimation

Textbook
can anybody contribute some standart textbook about time series analysis and trend estimation?

Just moving the following suggestion off of the main page and onto the talk page [The lkoimnkj"Real data is autocorrelated" section in need of expansion: examples.] Tristanreid 22:23, 9 February 2006 (UTC)

Trend Analysis merger
Don't Merge. 13-September-2006: The term "trend analysis" is a broader issue, of which trend estimation is a procedure in statistical mathematics. Keep "trend analysis" as a separate article, to expand with information from other fields of study, beyond statistical methods. Compare gHits (Google hits) of the terms: "trend analysis" hits 2,940,000, while old "trend estimation" hits 71,300 = 41 times more webpages on "trend analysis" with no Wikipedia copycat webpages, yet; meanwhile, "trend estimation" has enough detail to warrant the separate article be kept:  the 2 terms are not synonymous. -Wikid77 08:49, 13 September 2006 (UTC)

Dubious re R-squared and significance
The section "Goodness of fit (R-squared) and trend" currently says


 * A noisy series can have a very low r^2 value but a very high significance in a test for the presence of trend.

This strikes me as dubious since the RHS variable time is unbounded and hence its variance goes up as you extend the series. Since it is unsourced I'm going to delete it in a couple days unless there are objections. If the r-squared is low, then the noise must have high variance. With high noise variance, to get a strong t-statistic you'd need a lot of data points. But with a lot of data points, for given noise variance most of the variance in the dependent variable will be variance in the deterministic trend component of the data, and all of that variance is captured given a large number of data points, giving a high r-squared. So with non-stationary RHS variable "time", you can't get a good t-statistic without also having a good r-squared. Duoduoduo (talk) 15:49, 18 November 2012 (UTC)

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Statistics
Population consist of a linear Trend 43.230.214.196 (talk) 13:15, 8 January 2023 (UTC)

Tone and scope
This article reads like a tutorial or textbook, it should adhere to encyclopedic tone.

Secondly, its scope needs to be reconsidered; as it is, it simply duplicates simple linear regression. There's already Curve fitting, covering non-rectilinear trends (formulated in a linear model or not). Then there's Line fitting, for geometrical fitting methods. Other related articles are Decomposition of time series and Seasonal adjustment

Looking at Wikipedia in other languages, the one in French Ajustement affine seems promising. fgnievinski (talk) 21:10, 20 September 2023 (UTC)