USD/JPY Support/Resistance with Wavelets and Monte Carlo Simulation

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USD/JPY data as of 20 Aug 25 from FRED.

USD/JPY is one of the most interesting currency pairs to trade these days, with some opportunities  for short term gains. If we review the MAGA Man's Trade War and Tariff antics, we can see that of all the countries this school yard bully has bullied/cajoled/ran away from, Japan is most at his mercy. (In 2nd place is Europe). China doesn't give a hoot about Trump, India will keep buying Russian oil, the BRICS countries are making good progress in de-Dollarization, Russia will keep pummeling Ukraine. Japan, being the most dependent on the US market for its exports (steel, autos, semiconductors) has a high probability of tipping into a recession. (at least the South Korean economy is more diversified in its export markets)And with a debt/GDP ratio of 260, and rising inflation, there is not much room for fiscal or monetary stimulus. All this will be reflected in a new secular trend for USD/JPY.

In this post we will attempt to determine the rate of USD/JPY at the 5% quantile for the Support rate (S) and the 95% quantile for the Resistance rate (R). S= cut loss rate if crossed from above  and R=take profit rate if crossed from below. 

The chart above shows  the histogram of USD/JPY daily Close time series for 1 year. The slightly right-skewed histogram can be fitted with a Skewnorm Probability Distribution Function and we get S=142.4 and R=157.95. But the fitting of the data into a Skewnorm may be too crude.  So we will first de-noise the data with a Wavelet (Debauchies 4), and then do a Monte Carlo Simulation with the de-noised data, and dit the PDF to obtain S and R. 

Here is what the Wavelet has done to the data:

Why this wavelet: I used Daubechies 4 (db4) with soft-thresholding. db4 is a common choice for financial time series denoising due to good time-frequency localization and smoothness, preserving trend while attenuating high-frequency noise. *Wavelets are defintely more efficent at de-npising than moving averages. 

We then Run a 5000 trials Monte Carlo Simulation with the de-noised data and the PDF of the simulated data now assumes this shape:

This is a much better and less irregular shape so the S and R derived from this should be more predictable. S=139.83; R=152.85. 





 

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