Structural Breaks, Changepoints, and Regime-Switching Models
Summary
The document compares structural breaks, changepoints, and regimes in time series. A structural break is framed as a change in a population regression relationship, which may occur abruptly or evolve gradually. Changepoint methods instead seek whether and when statistical properties shift, potentially dividing observations into segments with distinct parameters. The text notes that breaks can be treated as a particular form of changepoint.
Regimes are described as persistent market conditions, while regime-switching models allow model parameters to vary across a set of states. This creates a close connection: both changepoint analysis and regime models represent changing data behavior, but the excerpt leaves their distinction as an open question. It does not give specific detection algorithms, transition models, or empirical comparisons. In practice, fixed break dates and state-switching dynamics imply different assumptions about when changes happen and how long a state lasts; model choice depends on the structure being represented and the intended use.
Key ideas
- Structural breaks refer to changes in a population relationship, including abrupt or gradual coefficient changes.
- Changepoint detection tests for changes in a time series’ statistical properties and may estimate their locations.
- A set of changepoints partitions observations into segments that can have different parameters.
- Regime-switching models describe a process whose parameters vary across persistent states.
- The document establishes conceptual overlap but does not provide algorithms or empirical evidence to choose between approaches.
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Full text
# Structural Breaks/Changepoints vs Regimes
# Structural Breaks/Changepoints vs Regimes
Structural break is defined as(taken from Introduction to Econometrics by Stock & Watson):
> When the population regression function changes over the course of the sample"
> Breaks can arise either from a discrete change in the population regression coefficients at a distinct date or from a gradual evolution of the coefficients over longer period of time.
Change points and changepoint detection is defined as:(source:)
> A particular change point test seeks to identify the specific period of time that relates to a change in the probability distribution of a stochastic process or time series. In general, the problem concerns both detecting whether or not a change has occurred, or whether several changes might have occurred, and identifying the times of any such changes. To establish a relatively general framework for the detection of a change point, we can assume that we have an ordered sequence of data, $y_t=\{y_1, \ldots, y_T\}$. A change point is then said to arise within this dataset when there exists a time, $\tau \in\{1, \ldots, T-1\}$, such that the statistical properties of $\{y_1, \ldots, y_\tau\}$ and $\{y_{\tau+1}, \ldots, y_T\}$ are different in some way. Extending this idea for a single change point to multiple changes, we can allow for $m$ change points, that are associated with positions, $\tau_{1: m}=\{\tau_1, \ldots, \tau_m\}$. Each change point position is then ordered so that $\tau_i<\tau_j$ if, and only if, $i<j$. Consequently the $m$ change points will split the data into $m+1$ segments, where the $i$ th segment may be summarised by a set of parameters. The parameters associated with the $i$ th segment will be denoted $\{\theta_i, \phi_i\}$, where $\phi_i$ is a possible set of nuisance parameters and $\theta_i$ is the set of parameters that may describe the change. In this case, we typically want to test how many segments are needed to provide the best representation of the data generating process.
They discuss tests for finding changes in mean and/or variance, and that structural breaks are a specific case of changepoints.
Here are a few definitions I found for regimes ,regimes shifts/switch, and regime switching models:
- regimes are " periods of fairly persistent market conditions." (from Two Sigma)
> Regime shifts are large, abrupt, persistent changes in the structure and function of ecosystems, the climate, financial systems or other complex systems. A regime is a characteristic behaviour of a system which is maintained by mutually reinforced processes or feedbacks. Regimes are considered persistent relative to the time period over which the shift occurs. The change of regimes, or the shift, usually occurs when a smooth change in an internal process (feedback) or a single disturbance (external shocks) triggers a completely different system behavior. (from Wikipedia)
> Regime Shift Model acknowledges that a time series can exist in different "states," each characterized by its unique set of statistical properties. These states represent distinct periods in which the behavior of the data undergoes significant changes. The transition from one state to another is governed by specific processes or variables, reflecting shifts triggered by fundamental changes in macroeconomic variables, policies, or regulations.(from Wright Research)
> Regime‐switching models are time-series models in which parameters are allowed to take on different values in each of some fixed number of “regimes.”(taken from here)
I am wondering what the connection is between structural breaks/changepoints and regime/regime switching/regime switching models? And whether changepoint detection can be used for regime switching? When I see that last definition for regime switching model say "parameters are allowed to take on different values", that does seem similar to structural breaks being a change in regression coefficients?Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.