Assume we have a time series of $N$ different points $(t_i,y_i)$, for $i \in \{1,..N\}$. The number $N$ is "small" (let's say $3<N<10$, just to give an idea), so you may want to make good use of all the information in the data.
Define now a cumulative time series, namely
$$(t_1,y_1),(t_2,y_1+y_2),\ldots ,(t_N,y_1+y_2+\cdots +y_N).$$
I would like to estimate the slope of this "cumulated" series of data (and the uncertainty on this slope), which can be naively estimated as
$$\dfrac{y_2+\cdots +y_N}{t_N-t_1} \qquad \text{or}\qquad \dfrac{y_1+\cdots +y_{N-1}}{t_N-t_1} $$
However, apart from not knowing which of the two options is a better estimator of the slope (they both look legit), we also have no idea of the associated uncertainty. One option is to make a linear regression on the points of the cumulative. However, in this way, the information provided by $y_1$ (or $y_N$) is lost!
Which is the best (or standard) way to perform a linear regression in this case (or to estimate the slope of the cumulated data set)? Moreover: is it even possible to use the usual least mean squares method? (I guess not, since the cumulated data do not have the homoscedasticity property).
Answer to the question: This question is closely related to How to infer the average speed of a frog?. After some research, I concluded that a satisfying answer can be found in Fitting a Straight Line to Certain Types of Cumulative Data (1957), Parameter Estimation with Cumulative Errors (1974) and the methods described in Statistical estimates of the pulsar glitch activity (2021).
This really should be a comment, but don't have enough reputation. Try Holt's method (double exponential smoothing).
The formulation looks like it'll fit your problem domain. In the absence of a trend, even exponential smoothing will work pretty well. A lot of statistical packages have built-in methods for this.