How to create and analyze a time series with variable test frequency in R - r

Question

Here is a short description of the problem I am trying to solve: I have test data for multiple variables (weight, thickness, absorption, etc.) that are taken at varying intervals over time - no set schedule, sometimes a test a day, sometimes days might go between tests. I want to detect trends in each of these and alert stake holders when any parameter is trending up/down more than a certain amount. I first did a linear model between each variable's raw data and test time (I converted the test time to days or weeks since a fixed date) and create a table with slopes for each variable - so the stake holders can view one table for all variables and quickly see if any of them is raising concern. The issue was that the data for most variables is very noisy. Someone suggested using time series functions, separating noise and seasonality from the trends, and studying the trend component for a cleaner analysis. I started to look into this and see a couple concerns/questions already:
Time series analysis seems to require specifying a frequency - how do you handle this if your test data is not taken at regular intervals
If one gets over the issue in #1 above, decomposes the data, and gets the trend separated out (ie. take out particularly the random variation/noise), how would you then get a slope metric from that? Namely, if I wanted to then fit a linear model to the trend component of the raw data (after decomposing), what would be the x (independent) variable? Is there a way to connect the trend component of the ts-decompose function with the original data's x-axis data (in this case the actual test date/times, say converted to weeks or days from a fixed date)?
Finally, is there a better way of accomplishing what I explained above? I am only looking for general trends over time - say over 3 months of data, not day to day trends.

Answer 1

Time series are generally used to see if previous observations of a variable have influence on future observations. You would model under the assumption that the previous observations are able to predict the future observations. That is the reason for that most (not all) time series models require evenly spaced instances of training data. If your data is not only very noisy, but also not collected on a regular basis, then you should seriously consider if time series is the appropriate choice of modelling.
Time series analysis seems to require specifying a frequency - how do you handle this if your test data is not taken at regular intervals.
What you can do, is creating an aggregate by increasing the time bucket (shift from daily data to a weekly average for instance) such that every unit of time has an instance of training data. Following your final comment, you could create the average of the observations of the last 3 months of data instead from the observations.
If one gets over the issue in #1 above, decomposes the data, and gets the trend separated out (ie. take out particularly the random variation/noise), how would you then get a slope metric from that? Namely, if I wanted to then fit a linear model to the trend component of the raw data (after decomposing), what would be the x (independent) variable?
In the simplest case of a linear model, the independent variable is the unit of time corresponding to the prediction you are trying to make. However this is not always regarded a time series model.
In the case of an autoregressive model, this would be the previous observation of what you are trying to predict, something similar to y(t) = x(t-1), for instance multiplied by a smoothing factor. I encourage you to read Forecasting: principles and practice which is an excellent book on the matter.
Is there a way to connect the trend component of the ts-decompose function with the original data's x-axis data (in this case the actual test date/times, say converted to weeks or days from a fixed date)?
The function decompose.ts returns a list which includes trend. Trend is a vector of the estimated trend components corresponding to it's respective time value.
Let's create an example time series with linear trend
df <- data.frame(
date = seq(from = as.Date("2021-01-01"), to = as.Date("2021-01-10"), by=1)
)
df$value <- jitter(seq(from = 1, to = nrow(df), by=1))
time_series <- ts(df$value, frequency = 5)
df$trend <- decompose(time_series)$trend
> df
date value trend
1 2021-01-01 0.9170296 NA
2 2021-01-02 1.8899565 NA
3 2021-01-03 3.0816892 2.992256
4 2021-01-04 4.0075589 4.042486
5 2021-01-05 5.0650478 5.046874
6 2021-01-06 6.1681775 6.051641
7 2021-01-07 6.9118942 7.074260
8 2021-01-08 8.1055282 8.041628
9 2021-01-09 9.1206522 NA
10 2021-01-10 9.9018900 NA
As you see, the trend component already is an estimate of the dependent variable at the corresponding time. In decompose the estimate of trend is based on a moving average.