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Explosive dynamics in exchange rates

Explosiveness in financial markets means that prices display exponential growth. In recent years statistical tests have been developed to locate mildly explosive bubble periods in real time. In conjunction with judgment on underlying fundamentals they help detecting price distortions. A new paper shows how tests for explosiveness can be applied to exchange rates. The tests suggest that developed market currencies have recurrently experienced episodes of explosive behaviour, reaching from a few days to up to three months. Currency level changes seem to reverse subsequently. Periods of explosiveness since 2000 have often been related to the U.S. dollar and financial market volatility.

Steenkamp, Daan (2017), “Explosiveness in G11 currencies”, Reserve Bank of New Zealand, Discussion Paper Series, DP2017/02, April 2017.
and some quotes from Phillips, Peter, Shu-Ping Shi and Jun Yu (2013), “Testing for Multiple Bubbles: Limit Theory of Real Time Detectors”, Cowles Foundation Discussion Paper no. 1951.

The post ties in with our lecture on price distortions.
The below are excerpts from the paper. Emphasis and cursive text have been added.

What is explosiveness?

“Explosiveness implies that there is an explosive root [i.e. elasticity of above 1 of price change tomorrow with respect to price change today] in…a time series, such that [an increase in today’s price leads to an even bigger increase in tomorrow’s price] for some subperiod of the sample.”

“One definition of a `bubble’ in an asset price is that the price exhibits explosive (i.e. exponential) dynamics… A large literature attempts to identify `rational’ bubbles in asset prices by looking for significant departures from their theoretically consistent fundamental value.”

How to recognize explosiveness?

“Recently developed tests by Phillips et al. (2015a) and Phillips et al. (2015b) provide an accurate way to gauge whether asset prices are experiencing explosive dynamics…[which means] for identifying periods when asset prices are experiencing exponential growth.”
Phillips, P., S.-P. Shi, and J. Yu (2015a). Testing for Multiple Bubbles: Historical Episodes of Exuberance and Collapse in the S&P 500. International Economic Review 56, 1043-1078.
Phillips, P. C., S.-P. Shi, and J. Yu (2015b). Testing for Multiple Bubbles:Limit Theory of Real Time Detectors. International Economic Review 56, 1079-1134.

“Bubbles are modeled using mildly explosive bubble episodes that are embedded within longer periods where the data evolves as a stochastic trend, thereby capturing normal market behavior as well as exuberance and collapse…estimates rely on recursive right tailed unit root tests (each with a different recursive algorithm) that may be used in real time to locate the origination and collapse dates of bubbles…Greenspan formulated…a question: ‘How do we know when irrational exuberance has unduly escalated asset values?’ It was this very question that the recursive test procedure…was designed to address.” [Philips, Shi and Yu]

“These tests are run recursively over a flexible sample window to detect breaks in the first-order autoregressive coefficient…Explosiveness is determined by comparing…[a] test statistic for each period to the simulated critical values… The start date of an explosive period is the earliest observation with a…statistic that exceeds the corresponding critical value under the distribution of [a stationary process], while the collapse date of the explosiveness is taken to be the first time that the…statistic declines to below the critical value…The dating algorithms are now being applied to a wide range of markets that include energy, real estate, and commodities, as well as financial assets…This methodology and its various applications have also attracted the attention of central bank economists, fiscal regulators, and the financial press.”

“There are two important advantages of these tests over standard unit root tests.

  • The first is that these tests have been shown to be good at correctly identifying such periods, especially when there are multiple periods of explosive dynamics over the full sample.
  • Secondly, unlike many of the earlier tests for bubbles, the validity of these tests for explosiveness is not dependent on the model used to determine the economic fundamentals that determine the value of the asset price under consideration.”

Have modern developed currencies shown explosive dynamics?

“This paper applies tests for explosiveness to eleven of the most commonly traded exchange rates at a daily frequency… The sample spans 3 January 2000 to 13 July 2016 (4177 observations) for all G11 currencies.”

“Unlike other asset prices, exchange rates do not typically exhibit explosive growth for extended periods. But they can experience explosive dynamics over short sub-samples…Periods of explosiveness tend to last for several days. Such episodes only involve small changes in actual currency levels, which usually reverse shortly after.”

For G11 currencies overall, explosive appreciations are more common than explosive depreciations. With the exception of the CAD, JPY, NOK and SEK, the other seven cross-rates have more explosive episodes in which the quote currency appreciates than explosive episodes where it depreciates. The USD:CHF currency pair experienced the highest proportion of explosive periods involving quote currency depreciation, while the USD:JPY experienced the highest proportion of appreciation episodes. Explosive periods lasted longer on average for crashes than for expansions. Such periods were longest overall on average in the USD:AUD cross-rate. This reflects two very long periods of explosiveness: 44 days beginning 6 May 2003 and 79 days beginning on 10 November 2003. The USD:NZD pair has the largest number of individual explosive episodes, although these have a shorter duration than some other cross-rates.”

“There is strong similarity between explosive periods in the broad value of the US dollar exchange rate and cross-rates, suggesting that there are relatively few instances where explosiveness in individual currencies reflected country-specific factors.”

“There is also evidence that explosive episodes have tended to coincide with periods of high market volatility.”


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