Because all markets have different degrees of
weak-form efficiency, prior and current market action have varying utility in
forecasting future action. When this utility is high, it makes sense to feed a trading system indicators that summarize
aspects of past market activity. To not do so would be tantamount to pouring vital information down the drain.
For example, suppose your SP500 forecast/trading system requires knowledge
spanning the last 200 price-bars of each of five markets: S&P, Bonds, Yen, CRB, and DM. If this system were given
only today's prices and no historical data, performance would be seriously impaired.
A problem arises when attempting to feed your system all 200 historical price
samples from each market. Each forecast would require 1000 (5x200) input values. Professional traders realize this is
too many and one must be very selective when choosing historical data for a model. So which samples do you use?
Uniformly spaced sampling of historical prices, such as selecting every tenth day, is seductively appealing in its
simplicity, yet very wasteful and can miss important price action.
It is shocking that most traders have no idea which historical samples to use:
should the trading system include yesterday's ADX value and of the day before, the week before, every other day, week,
THE KEY ISSUE
Markets oscillate from being overbought and oversold. It's due, in part, to a kind
of psychological momentum that tends to persist despite changes in market conditions. Each market has its own
time-varying momentum (TVM), each with different cycle lengths. These TVM influence each other. Their cumulative effect
contributes to the market's complex price waveform. (See chart below)
So for a trading system to work properly, it must receive the historical samples
required for detecting all possible TVMs affecting the market you wish to trade. Although slow TVMs may be sampled
slowly (once per month), fast TVMs must be sampled quickly (once per bar). So the big question is: what is the best
spread of samples in a financial time series when you do not have a clue which TVMs are driving the market?
BREAKTHROUGH: WAVELET-LIKE SAMPLING
The breakthrough is this: optimal sampling requires getting just enough samples to
detect the presence of slow moving TVMs, just enough for detecting the medium-slow TVMs, and so on. Our product, WAV,
achieves this so efficiently that WAV uses only 17 samples to effectively capture information from 200 historical bars
of a financial time-series! Imagine how much time you will save developing trading systems that require only 17 instead
of 200 input variables!
The astute reader may argue that you cannot just sample individual prices spaced
far apart in time, because you will be ignoring all the price activity occurring between those samples. WAV handles
this. It considers all price action by applying a scientific method of detrending, wavelet-like sampling and signal
filtering. The result: information from hundreds of price points compressed into just a handful of numbers for your
WAV is a unique hybrid of my own design between Wavelet filtering and Nyquist
filtered sub-sampling. Its a great way to achieve time compression. That is, WAV gives you the ability to represent a
lot of historical information about any time series with a small set of feature variables.
WAV compresses time by representing a large amount of historal price action with a
significantly smaller number of values. For example, when using daily price data, you can input to a forecasting model
information about the last 139 days using only 15 numbers from WAV. That's a compression ratio of more than 9:1.
Here's a brief description of how the user views WAV ...
As with all technical indicators, WAV stops at every bar and updates its
calculations. Data is gathered by examining the most recent N bars of a time series. The user specifies both the
lookback value N and the time series to be processed.
Unlike other technical indicators, when WAV stops at each bar, it produces not
one but several output values. These few values efficiently represent the activity of the time series over the past N
bars. What makes WAV so valuable is that the typical number of values produced by WAV is very small relative to
The user typically feeds WAV's output values to a forecasting model or other
kind of leading indicator. In Microsoft Excel, WAV arranges each set of values row-by-row. In TradeStation, a user
function can ask WAV to produce all the values in the set.