Problems with cross-validation for time-ordered data Let's assume a simple scenario: You want to forecast the house prices of various properties. The dataset is cross-sectional in nature, as you only observe each property once. However, you also have a timestamp of the observation (month/year).
In a sense, this means that the data is intrinsically time-ordered. In general, I know that with time series data, the use of e.g., k-fold cross-validation can be problematic. However, I don't have real time series data (multiple obs. for one house), but time-ordered data across houses. It is also clear that for time series data, there are other approaches such as rolling estimation.
In particular, I would like to understand theoretically from a statistical/econometric perspective why this might be problematic rather than just intuitively. Does anyone have a theoretical guide to this topic or know of relevant literature to delve deeper into this topic?
EDIT: Based on @Björn's answer, it seems useful to provide more information about the goal here. The goal is actually to predict future prices based on the trained model.

One critical issue is the cage of covariance includes time varying effects, which can impose and unrecognised pattern on the data if not handled appropriately. There will be a general trends across house prices depending on the general economic situation evolving over time. more complex patterns such as evolving fashions and functional requirements will impose addition layers of complexity.
It is related to the Moiré effect. Here's a figure I've created recently that shows how hidden patterns in the data can affect CV, using an extreme example for demonstration purposes. Moiré patterns can be extremely complex and hard to detect if you don't look for them intentionally. If the periodicity of the sampling is a multiplicative factor of the periodicity of the underlying trend then you may under-sample underlying effects in the modelling set that mostly get held out for the test set (or vice versa).

Visualisation of experimental factor distribution in the simulated structured dataset. The color is created by red channel for time interval, green channel to indicate dose exposure, blue channel to indicate experimental group membership. Selection to hold out group indicated 1/3 reduction in intensity. a-c) Week of study as x-axis, dose group (sub-divided by experimental group) as Y-axis. a) is the basic experimental design matrix. b) black pixels indicate samples selected by sequential block selection for K-fold c) black pixels indicate samples selected using Monte-Carlo d) the average properties of the train and test sets with each selection method.
