NZD/USD 2005-2008: Predictability Overview

The correlation patterns we see in one of the world’s most volatile exchange rates, the New Zealand Dollar/US Dollar exchange rate, are very similar to those seen in AUD/JPY.

The interest rate differential has been in favor of the New Zealand Dollar.

The basic autocorrelation

NZD/USD autocorrelation 1 hour time-lag bin

Fig.1: Autocorrelation of hourly logarithmic returns in NZD/USD. The time lag is in “business time” (periods without update ticks are excluded). The red band shows the level of noise as iferred from martingale simulations (see text).

As before we employ autocorrelation as a straightforward, inter-disciplinary, non-proprietary technique to test market efficiency in the NZD/USD market. In Fig.1 we look for features on the time scale of up to two days such as to suite the time scale of day trading or swing trading. The hatched red band shows the range of statistical noise (namely its expectation plus minus its RMS deviation). Statistical noise was obtained by simulating 20 independent time series of the length corresponding to that of the NZD/USD series, each one constructed to reproduce the measured distribution of returns for the time period under study (including the fat tails!), but completely devoid of correlations (martingale time series). From these, the expectation and RMS of the autocorrelation amplitude in each time lag bin were calculated. The one-hour time lag “contrarian” feature (a significant anticorrelation) we saw in this type of plot for other currency pairs involving USD ( AUD/USD ) is quite strong in the NZD/USD autocorrelation. It is noteworthy that the negative feature around 0 is more than one bin wide, it involves the -3 hour bin as well. The autocorrelation being an average of a product of hourly returns taken with a lag, this negativity means that we are way too frequently (more frequently than in the corresponding martingale time series) taking a product of opposite sign returns — or that the product of the opposite sign returns by far outweighs that of the same sign returns. Because trend reversals on the time scale of one to three hours happen either too often or are too lucrative, NZD/USD, like GBP/JPY, AUD/USD and AUD/JPY analyzed before, may well be the market where winning strategy requires being a contrarian on a short time scale.

A group of time lag bins 12-24 hours away from show a significantly positive correlaiton. In other words, the currency pair has a tendency to repeat its moves 12-24 hours after they happened — a feature worth a closer look as a forecasting mechanism.

Bull/bear asymmetry in NZD/USD

NZD/USD bullish and bearish autocorrelation

Fig.3: NZD/USD bullish and bearish autocorrelations. Yellow: correlating only positive hourly returns. Blue: correlating only negative hourly returns.

In Fig.3 we construct autocorrelations of the subsamples of the full time series (the “bullish” and “bearish” ones) selected by taking only positive and negative returns respectively. The 24 hour cycle of bullish and bearish action, clearly seen in most other currency pairs, is not well pronounced here for some reason. In this regard, NZD/USD is similar to AUD/JPY.

Typically, the “bearish” correlation has a higher amplitude whenever the base currency has a higher interest rate. This has been seen with AUD/USD , AUD/JPY , USD/JPY , GBP/JPY , USD/CAD , (although the interest rate differential has not been that high, it is in favor of USD), CHF/JPY , EUR/JPY, EUR/CHF. Conversely, the “bullish” correlation has a higher amplitude whenever the quote currency has a higher interest rate, as seen with EUR/AUD and EUR/GBP. While in the case of classic carry-trade currency pairs such as AUD/JPY I associated this feature with the unwinding of the carry-trade, the underlying mechanism is likely to be similar for other currency pairs. It seems, you can “jump on the bandwagon” of selling a high yield currency with more confidence than doing the opposite, as the higher amplitude and a bump in the NZD-bearish plot demonstrate.

The fact that one can read the sign of interest rate differential off the public forex quotes via basic correlation analysis indeed goes against the efficient market dogma and indicates that despite large liquidity such interest rate differentials are not completely discounted by the markets and there remain profit opportunities for algorithmic trading .


The NZD/USD currency pair has been showing a “contrarian” trend reversal tendency which is likely to be part of a stable wave-like pattern. Therefore, NZD/USD is not completely “efficient” from the point of view of basic two-point correlation analysis. Long term prospects of NZD/USD are the subject of fundamental analysis and are outside the scope of this article. Cross-correlations with other markets are to be discussed in the up-coming articles. In this report we use data for the period from 00:00 2005-08-16 to 00:00 2008-02-01 (New York time).