Wavelets are filters decomposing in a specific number of frequencies a signal across time, they are unique in that they can analyze non-stationary signals (most time series are). They decompose the signal in scaling and detail coefficients (high frequency and low frequency parts). You can attempt to find the true price, meaning the signal, having extracted all the existing noise types, however is very hard. In volatile instruments knowing the noise component is important as most of the price at any given time is provided by the noise component. However, my guess is that for highly illiquid securities the price will be that of the true signal without noise. Also the more illiquid a security is the more data you need to be able to run statistically significant results.
Having said that, it is very difficult to find and correctly identify the true signal when there is a large component of noise embedded in the signal and the frequencies of noise are not known. So statistical probabilistic methods for determining where the signal resides in the frequency structure are important when the component of noise is not known before hand. Having determined statistically where the signal/s reside then you can extract and classify the different noise components that go along with the signal and model them using stochastic methods for white noise. (White noise is completely unpredictable but what is predictable is the volatility of white noise) so you model the volatility of white noise. For different noise types you have different functions describing them. Rising, falling, logarithmic and power slopes across the frequency spectrum.
Using both discrete and continuous wavelets the following considerations are important:
- One signal maybe spread across different frequencies.
- Sometimes there are many signals at once acting at different frequencies with different energy levels.
- Signals raise and decay in energy across time (equivalent of volatility for a given signal increasing or falling).
I hope this helps