Regime switching processes
This article is about what it means when your process has sudden transitions between multiple regimes, and how to capture these.
Many processes are not stable over time but may have multiple stable states or regimes. For example, an individual can alter between healthy and depressed states over a period of time, or a couple may switch between conflict, neutral, and happy states.
If your process consists of multiple regimes it switches between, it is important to think about how to capture these different regimes and how to capture when your process switches between regimes.
In this article, you will find: 1) what constitutes a regime 2) how regime switching can take place over time with different types of mechanisms; 3) consequences of not accounting for regime switching.
1 What is a regime?
There is no clear-cut definition of what a regime is, but a regime is often referred to as a stable state. Stable states, also referred to as stable equilibria or attractors, are a central concept in [dynamical systems theory], where they represent conditions toward which a system tends to return to over time after perturbations (Richardson et al., 2013).
During a regime, the characteristics of your process do not change over time. Typically, a regime is characterized by certain (statistical) properties, such as a set of parameter values (e.g., a mean and a variance).
Your process may have multiple regimes, each characterized by distinct equilibria. For example, regimes could have a different mean. Regimes are mutually exclusive, meaning that they occur one at a time. When measuring a process over time, we may observe multiple regimes, with the system switching between them sequentially.
Gideon wants to see how negative affect evolves over time in a patient diagnosed with bipolar disorder. The patient switches between depressive and manic states while Gideon tracks their negative affect. By looking at the trajectory of negative affect, Gideon can roughly distinguish periods with a high average of negative affect and low average of negative affect.
2 Regime switching
When your process exhibits multiple regimes over time, it switches between regimes over time. Regime switches are sudden: from one moment to the next, the process of interest is completely taken over by a different regime. Detecting such transitions can be a main topic of research (Hartelman et al., 1998). Important considerations for this are when and how regime switches take place. In the following, we discuss the timing and possible mechanisms of regime switching.
2.1 Timing of regime switches
Regime switching may only be understood if regime switching takes place during the measurement period. Therefore, it is important to think about the timescale of the regime switching process. For example, if regime switching occurs more frequently than the frequency of the measurements, regime switches may be missed. Additionally, when the time frame of your measurements refers to an interval in time (e.g., “in the past hour”), the process of interest may have exhibited multiple regimes during this interval which may bias the observation.
Flora tracks daily social anxiety in a single participant. At the end of each day in the study, the participant reports how socially anxious they felt that day on average. Flora finds that the participant’s social anxiety is very stable over time. However, the participant feels very distinct states of anxiety or no anxiety during the day depending on whether or not they are in a social situation. As the participant encounters a roughly similar amount of social situations each day, this change in anxiety during the day is not captured in the daily average.
One may also be interested in only capturing a single regime. For example, when we are interested in studying individuals who suffer from depression, we do not want our sample to include participants who recover during the measurement period. Therefore, when interested in a single regime, it is also important to think about when the process of interest is in this regime.
2.2 Regime switching mechanisms
When a process switches between regimes, we may be interested in understanding the mechanism of this regime switching. We may distinguish three mechanisms that cause a process to switch between regimes: (1) a process may excite itself to switch between regimes; (2) an observed, or manifest, variable causes regime switching in a process; or (3) or an unobserved latent variable causes regime switching in a process. We explain these three mechanisms in more detail below.
2.2.1 Self-excited regime switching
A process may switch between regimes due to a change in its own properties, referred to as [self-exciting regime switching]. These autonomous properties are required to vary over time, otherwise a process would always stay in the same regime. To capture a self-excited regime switch in a process, you need to observe the relevant changes in properties.
Marissa studies individuals that suffer from binge drinking. When the participants start a binge drinking episode, they report the amount of alcoholic beverages consumed in the past hour. When participants consumed at least one alcoholic beverage they were more likely to consume more alcoholic beverages in the near future. However, when they reached a certain total amount of alcoholic beverages during the binge drinking episode, their alcohol consumption decreased.
2.2.2 Manifest regime switching
There may be an observed variable that controls the regime switches of a process, referred to as manifest regime switching. This manifest variable needs to vary over time as otherwise it cannot control switches in regimes of a process. To capture a regime switch controlled by a change in a manifest variable, you need to observe this change.
Akash works for a big company and investigates the effect of workload experienced by his colleagues on burnout symptoms. He measures perceived workload and severeness of several burnout symptoms on a weekly basis. He finds that while a higher workload is associated with worse burnout symptoms the following week, overall burnout symptoms bounce back quickly and tend to fluctuate around a healthy average. However, when a colleague persistently perceives a high workload for at least 6 weeks, the burnout symptoms start fluctuating around a non-healthy average.
2.2.3 Latent regime switching
Regime switching in a process may also be caused by an unobserved latent construct, known as latent regime switching. To capture a latent regime switching process, one needs to be able to estimate this latent construct in some way. Regime switching may also take place based on probabilities (e.g., a process may have a 90% probability to stay in the current regime and a 10% probability to switch to another regime) and this probabilistic process is seen as latent. A modeling approach that incorporates this probabilistic regime switching is hidden Markov modeling (HMM) (Rabiner, 1989).
Ilja studies how the interplay of several depression symptoms cause individuals to switch between depressive and healthy states. He measures the severeness of depression symptoms in participants multiple times per day over several days. On each occasion, he estimates the correlation between the variables and finds overall that when all the correlations are high, an individual is more likely to be in a depressive state at the next moment.
3 Not accounting for multiple regimes
It is important to think about whether the process of interest exhibits multiple regimes to be able to capture all relevant aspects of the process. When a process switches between regimes during our measurement period and you do not account for this, you may miss important inferences. For example, you may assume a process only has one regime with one average, but in reality the process switches between two regimes characterized by different averages. If you only look at the overall average you may come to a different conclusion than when you would have looked at the regime-specific averages.
Kayra tracks the happiness of a participant to determine whether this person is happy. The participants reports their happiness every day for a month on a scale from -5 (unhappy) to 5 (happy). After data collection, Kayra computes an average happiness of 2 and concludes that the participant is overall moderately happy. However, after reporting this finding to the participant, they indicated that they felt really unhappy at certain periods. Kayra looks at the trajectory of the reported happiness, and sees that there are periods of low happiness and periods of high happiness. Kayra decides to compute the means for these periods separately, and finds an average of -2 in the unhappy period and an average of 4 in the happy period.
4 Think more about
Theoretical considerations can help narrow down how many regimes you want to capture and what characteristics within regimes you want to observe.
- There may not always be strong theories to determine the amount of regimes in a process. Exploratory analyses may be necessary, where the process needs to be monitored long enough to establish the existence of multiple regimes.
- If you want to estimate specific statistical properties within regimes, be aware that some statistical properties may require a larger sample size than others (e.g., a mean needs fewer observations than an autoregressive parameter).
5 Takeaway
When a process switches between regimes, you need to consider whether you want to capture these regime switches or focus on a single regime. In both cases, understanding the regime switching mechanism will help determine how to set up your sampling design.
6 Further reading
We have collected various topics for you to read more about below.
- Ergodicity
- Stationariy
- [Time-varying processes]
Acknowledgments
This work was supported by the European Research Council (ERC) Consolidator Grant awarded to E. L. Hamaker (ERC-2019-COG-865468).
References
Citation
@article{berkhout2025,
author = {Berkhout, Sophie W. and de Jong, Daan},
title = {Regime Switching Processes},
journal = {MATILDA},
number = {2025-05-23},
date = {2025-05-23},
url = {https://matilda.fss.uu.nl/articles/regime-switching-processes.html},
langid = {en}
}