I've come across the term regime switch in volatilities when reading about the modelling of interest rates but could not find a definition for a regime switch and what a regime is.
Can somebody give an intuitive definition of a regime and a regime switch and provide examples?
The idea of regime switching in volatility is rooted in the observation that volatility is usually fairly consistent and "mild", and occasionally very high, say during a market crash. The concept goes further, though. Not only does the volatility level differ markedly in different regimes, but the behavior of volatility does as well (degree of mean reversion, shape of smile, term structure skew, etc). Many models use different regimes to allow the tuning of parameters under different regimes, then switching between regimes, to more accurately model observed behavior.
For an exploration for how market behavior can vary under different regimes: http://www.emanuelderman.com/writing/entry/regimes-of-volatility-risk-april-1999
Regime switching is another way to describe structural changes in a data series. For example, an inflation timeseries may change states from ARMA to linear as the economy moves from a period of cyclical growth to prolonged recession. A stock price may, say, be determined by and correlated to the main equity index when it has a large market capitalisation and then by a sub-index when it's relative size shrinks - consider Apple. Regime switching enables a very powerful dynamic regression analysis of time series by incorporating both of these periods.
The "zero bound" at low interest rates would lead to a significantly decreased volatility regime whereas the period of high central bank policy rates arising from high inflation in 1970/80s was characterised by greater volatility - a regime change.
A general application of regime switching is via state space modelling with use of a Dynamic Linear Model (http://helios.fmi.fi/~lainema/dlm/dlmtut.html).
A great text to discover more is Nelson & Kim, State Space Models in Regime Switching, or Hamilton's Time Series Analysis.
Intuition :
Lets observe the U.S. ex post real interest rates from 1961 to 1986 :
At first look it is not easy to identify different states of the economy.
Now lets apply an econometric model that will try to identify those different states and observe the result:
The econometric model identifies 3 different states of the economy, this is what we call three regimes.
Basically the model firstly needs to determine the number of regime switch ( when the "state of the world" changes) : 2 regimes switch in this example.
Secondly once a regime switch has been identified, one or several parameters of the model will change.
In the above figures, two very basics switching models are employed.
One is a single intercept + some random errors. Another is the same but with the variance of the errors that change at each new regime.
Regime-switching models that are employed are obviously much advanced, they have lot of parameters but the intuition is the same, models needs to detect structural changes in the series then some parameters of the models will be impacted by those changes.
So the intuition behind these models is to get a model with some coefficients that are regime dependent.
Ps: Illustrations are taken from the official documentation of PcGive (econometric software).
One of the most famous definition of Regimes and Regime Switching in Financial Markets comes from Wyckoff Cycle
Wyckoff believed that prices judged by supply and demand, go through periods of advance, accumulation, decline an distribution based on the movement of smart money.
In the quantitative world one can use state space models to model such regime shifts. Here, in this paper https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3144169 I try to model regimes as Wyckoff cycles using econometric methods and analyzes the market behavior around these regimes.
For example if you think the volatility of short term rates is 0.1 during economic exapansions and 0.15 during recessions, then that would be a very simple regime switch model. The parameters of the model (in this case just the vol) change from time to time. Specifically it 'switches' at certain times from one value to another. (And that is different from a model where vol is constantly changing, which would be called a 'stochastic vol' model).
There are techniques in statistics, based on Markov Chains, that can be used to estimate Regime Switch models. [Kuan: Lecture on regime Switching Model, 40 page PDF http://homepage.ntu.edu.tw/~ckuan/pdf/Lec-Markov_note_spring%202010.pdf ].
