I did little work on regime switch model. A matlab code is available by a researcher. You can google for regime switch model in matlab.

EXCHANGE RATE & UNDERLYING REGIME

Exchange rate under a given regime would display very stable pattern. If the patterns change and that change is significant, it may be due to either (i) regime change, or (ii) economic shock. Regime change will cause the exchange rate to change as the market would adjust and readjust to the new regime. This new adjustment would become stabilized (see y(t) below). However, if it is a shock, the change would readjust itself to the old pattern because there is no institutional or fundamental change that would affect the exchange rate.

EXISTING REGIME

In order to detect regime change, one must have adequate data series over a period of time to allow the data to show its characteristic. The time series data would produce a characteristic pattern that confirms to the linear structure of:

(1) Y’ = a1 + bX + e

… where a1 = Y-intercept, b = independent factor, and e = forecast error. This model is a normal run of the existing regime.

In subsequent periods, b may vary, but the pattern of Y’ would still obey the same characteristic pattern. Assume then that there is a change:

(2) Y’’ = a2 + bX + e

And that a1 > a2 or a1 < a2. the Y-intercept of the two periods are not equal. This signifies that there has been a change that could be explained by the law of probability. It also follows the change of a1 to a2 was not also predictable. For this reason, it is necessary to construct a new model to accommodate a2.

REGIME SWITCHING

Generally, the abrupt change of the Y-intercept described above is not deterministic, i.e. could not have been reasonably predicted. Regime switching occurs in such a manner. While Y’ obeys a predictable patter with a fixed Y-intercept, the subsequent change produces a Y-intercept that is due to institutional change. Thus, Y’’ may be rewritten as:

(3) Y(regime) = C + bX + e

… where the Y-intercept C results from a two-state Markov chain: a period of a prior regime and a period under a new regime. The difference between (a1 – C) > 0 or (a1 – C) < 0; that is the difference is real and significant. The challenge is to locate the period when the switching occur.

DETECTION INDICATOR

The indicator used for regime switching is the Y-intercept in the equation Y = a + bX + c. Assume then that several samples had been taken, say several time periods, i.e. t1, t2, … tn, and that regression analysis is run for each period; the result shows that a1, a2, …, a^n are not equal. Does it mean that there is a regime switching? No. In order to constitute regime switching we need to use only two periods: one prior to regime switching and one after the regime switching. The challenge is to find this pair of Y-intercept at various time period.

One way to find the pair is to undertake series of data set over several time periods and list all their Y-intercepts for each period. A period that shows a peak or a trough from the mean is a suspected pair. The second step is to select the pair and verify whether there is a regime change. The verification may be accomplished by the Anderson-Darling test.

The Anderson-Darling test requires n > 5 or minimum sample size of 6. Here, the sample is the individual a1, a2, …, a^n or Y-intercepts for each period, i.e. 3 before and 3 after the suspected change. The critical value for the Anderson-Darling test A^2 at 0.95 confidence interval is 0.787; the decision rule follows: if A^2(observed) > 0.787, there has been a regime change, otherwise accept the null hypothesis (no regime change).

In order to prove that no Type I or Type II error had been committed, several segments of the data length of 6 to 7 elements (periods) may be retested. Prior periods where there is no regime change, the A^2 value would be less than 0.787. There will be a data segment that would break this pattern showing A^2 > 0.787.

NUMBER OF REGIMES

For purposes of constructing a predicting model, this issue may be moot. A system does not switch regime so often so as to necessitate the accounting for number of regimes used---unless one runs a data series that covers a span of many years or decades. For practical purposes, i.e. a specified segment of time series data, to proof the regime switching the number of regime is not relevant to the extent that it does not play a role in determining the current exchange rate. However, if the time series data prove that there had been several regimes switching in the period, then the switching frequency may be observed. However, this data (regime switching frequency) cannot be used to forecast potential switching in the new future---it only shows a past count.

GOODNESS-OF-FIT

After the evidence of regime has been verified then a model may be constructed. Use any conventional methods to test the goodness-of-fit and readjust the model accordingly. At this point, basic statistical tests combined with econometrics would be helpful.

You can also find out with RAT software, there are many examples of Markov Switching models. Nonetheless, you should have an underllying therory justifying regime switching for exchange rate. you need to find out whether it is the level that react differently according to specific regimes (boom or recession) or it is the volatility. for volatiltiy, MS GARCH or ARCH can then be used. So you need to provide a sound theoretical motivation for the use of regime switching.