I recently had a discussion with a respected colleague of mine. It got me thinking about the many differing points of view in finance. My colleague accepts that regime change is a correct phenomenon in financial time series, and you will find many published articles in respected journals proposing how to deal with this regime change. I might also add the many quants accept regime change.

And here we differ. I do not accept regime change. I know from past experience building time series forecasting models that regime change is model misspecification. Let me show you 3 graphs that support my point of view. Clearly Fig 1 is a linear trend.

**Figure 1: Time Series from Period 245 to Period 300**

**Figure 2: Time Series from Period 0 to Period 1000**

However, when we expand the range of the time series to between 0 and 1,000 (Fig 2) the linear trend of Fig 1 now becomes a regime change from a level around 0 prior to period 200 to a new level of about 7 after period 350. This must be proof of regime change. No? But wait.

**Figure 3: Another time series.**

Figure 3 is another example of regime change. Prior to period 150 the level is around 0, between periods 170 and 270 the level is about 110, and between periods 290 and 400 the level is about 230. This would be considered an example of two regime changes.

Because I generated both data sets I can inform you that Figure 3 was generated by Normally distributed random noise and nothing more. Figures 1 & 2 were also generated by Normally distributed noise and with a trend inserted between periods 250 and 300.

**First lesson**. A continuous function time series can present itself as a regime change when it is not, but in real life we cannot ‘rerun’ the time series to test if regime change will recur.

**Second lesson.** Statistical tests will affirm that regime change did occur when no regime change was present.

**Third lesson.** Figure 1 is a subset of Figure 2. Therefore, our interpretation of the data depends on our perspective.

**Fourth Lesson**. Therefore, my experience with time series would suggest that regime change is model misspecification.

**Fifth Lesson**. Even though economics & finance borrows heavily from the scientific method it is still an art.

Take care,

Ben

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Disclosure: I’m a capitalist too, and my musings & opinions on this blog are for informational/educational purposes and part of my efforts to learn from the mistakes of other people. Hope you do, too. These musings are not to be taken as financial advise, and are based on data that is assumed to be correct. Therefore, my opinions are subject to change without notice. This blog is not intended to either negate or advocate any persons, entity, product, services or political position.

Contact: Ben Solomon, Managing Principal, QuantumRisk

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## 4 Comments

Surely inserting a trend *IS* a regime change?

Correct you need a trend to get a ‘regime change’. My point was how long due you have to wait before a ‘regime change’ is a ‘regime change’ and not a changing trend. And even then it can be modeled with out presuming that ‘regime change’ is present.

Thanks,

Ben

I’ve done some work with what I call specialist models. I imagine it is similar to models for specific regimes. This example presented strikes me as illustrating a different problem. Developing a model from too short a period of time such that periods that differ in volatility or trend type are not present. That will lead to a model that fails to function under changed conditions.

David, yes it is true that specialist models would suggest regime changes but if you can build a general model (very difficult but can be done) that handles all the regime changes or specialist models then regime change is no longer a valid hypothesis.

Thanks,

Ben