Regime Changes in Financial Markets (Ang-Timmermann Review)
What breaks in a trading test when market relationships change between regimes?
A shift can alter the conditional distribution of returns and the persistence of its state. Parameters estimated in one regime may describe that period well while producing poor forecasts after the transition.
Evidence map
| Aspect | Finding |
|---|---|
| What it is | A survey of what regime-switching models have established about asset returns and where they fail. |
| Key result / formula | The workhorse is Hamilton's Markov switching model: a latent state s_t follows a Markov chain with transition matrix P, and conditional on the state the return is drawn from a state-specific distribution, r_t | s_t ~ N(μ_s, σ_s²) in the simplest case; the filter delivers the probability of each state given data up to t, the smoother the probability given the full sample. |
| Why it matters for backtesting | The regime node in Stochastly is where the review bites, and the failure mode is precise: a strategy switched on in the calm state and off in the turbulent state looks superb when the states are assigned with smoothed probabilities, because the assignment uses bars that had not yet occurred. |
What it is
The claim is that financial series change behaviour abruptly and then persist in the new behaviour, that means, volatilities, autocorrelations and cross-covariances differ across regimes, and that a small number of persistent states reproduces fat tails, volatility clustering, skewness and time-varying correlations without assuming them.
Key result / formula
The recurring empirical picture for equity indices is two regimes, one calm with positive mean and one turbulent with low or negative mean and high volatility, the turbulent state shorter but persistent; the review documents the same structure in interest rates, exchange rates and in the correlation between stocks and bonds, and notes that correlations across assets rise in the high-volatility state, which is when diversification is needed. The authors are explicit about the limits. The number of regimes is hard to test because the usual likelihood-ratio statistic is non-standard when a regime's parameters are unidentified under the null; smoothed probabilities are sharp because they use the future, while the filtered probabilities available in real time lag the true switch; and the economic value of regime-based allocation rests on forecasting transitions, which the data support weakly. Regime models describe the past well and forecast the state slightly better than persistence.
Why it matters for backtesting
The test on the user's bars is to run the regime filter causally, parameters estimated on an expanding or rolling window and only filtered probabilities used to gate the strategy, and to compare with the smoothed version: the difference between the two is the hindsight in the edge. A second test is the transition question itself: does the filtered probability at t predict the state at t + 1 better than "same as today"? If not, the regime filter is a volatility filter with extra steps, and [Volatility Targeting] does the same job with fewer parameters. This note complements [Regime-Switching Models (Markov Switching, HMM)], which covers estimation; what neither can test on bars is whether a regime absent from the sample, the one the user fears, resembles any that appeared.
Source
Ang & Timmermann, "Regime Changes and Financial Markets", Annual Review of Financial Economics 4, 2012, 313-337. Primary source