The **List
Data** option in the Tradescape
Plot opens a report containing the numeric tradescape information:

Underlying Data

At three different lag fractions (0.7, 1, and 1.2), the underlying data are reported. The lag fraction assignments are arbitrary, the only purpose being to have at least one underlying point accessible in any tradescape scaling used. For each of these points, the EM length (EMLen() will be zero. This reflects the instance of no signaling, of a buy and hold. These are reported for both long-side and short-side tradescapes. For these underlying points, the robust trend (Trend) and its r² (Trendr²) are reported as well as the robust Sharpe, robust R³, and robust RRt reward to pain metrics. Also reported is the average retracement from the all-time high (AvgRt).

EM Tradescape Data

Most of the numeric data in the report will consist of the tradescape data arising from the EM signals. These contain the same information as the underlying for the signaled equity curve as well the average trade length (AvTLen), the number of complete trades or round trips (RndTrp), the win percentage of trades (WinPct), and the coincide error (CoincErr), the percent of bars where the signal is on the wrong side of the optimum zero-lag EM signal for that EM length.

Signal Data

For user-defined signals, there are two lines in the report. The first line with the extended information contains the results from the backtest of the user-defined signal. It includes the same information as that shown for the EM tradescape signals.

Additionally, there will be fields for the signal analysis. These include the signal number, the zero crossing counts for the slope of the EM signal (EMZC) and the change in sign count for the signal (SigZC). An optimization algorithm seeks to match these sign changes as closely as possible. Similarly, the average trade lengths are shown for the EM signal (EMAvTLen) and the user's signal (SigAvTLen). These should also be close to one another (the same count of entries and exits should produce approximately the same average trade length). If the algorithm achieves a successful math between the user's signal and an EM reference signal, it is possible to estimate the signal properties critical to performance.

First the lag at every bar, the correlation lag (CorrLag) is reported. This is general information, since it is the lag at the turns that matter for binary signaling. There are then six additional columns of information, the lag and its robust SD for both the maxima and minima in the time series, for just the maxima, and for just the minima. The last reported value is the coverage error (CovErr), the percent of signal transitions observed in the EM reference that fail to occur at some reasonable lag within the user signal.

The second line, immediately following the signal, contains the tradescape information for the exact EM length and lag fraction of the reference used for the signal analysis. The performance of the matching tradescape reference can thus be directly compared to the user signal, this reference being immediately below.

Report Items - Always Present

EM Len

This is the Expectation Model (EM) length in bars, the information content or time horizon used for the tradescape EM signals. If reported for a user-defined trading signal, this is the length of the EM signal that seeks to match the count of trades (the first derivative zero crossings or turns in the signals are matched). The EM length is a standardized information content, common to all procedures in the program.

LagFrac

This is the fraction of the lag relative to the EM length. For tradescape points, this is the amount of lag added to the EM signal. The lag fraction will be exact. For a user-defined signal entry, this will be the estimated lag fraction based on the estimated robust mean of the lag measured at the turns.

Lag

This is the actual lag value in bars used for the lag fraction in the plots. For the EM signals in the tradescape, this will be an integer, the amount of lag added to generate that point in the tradescape. For a user-defined signal entry, this will be the estimated robust mean of the lag measured at the turns.

AvTLen

This is the average trade length (entry to exit) in bars for all of the trades present in the backtest. If this is a tradescape point, this will be the average trade length that corresponds with this point in the tradescape's trading landscape. For a user-defined signal entry, this will be the average trade length from the actual signal backtest.

RndTrip

This is the count of round trip (entry-exit) trades present in the backtest. If this is a tradescape point, this will be the trade count that corresponds with this point in the tradescape's trading landscape. For a user-defined signal entry, this will be the trade count from the actual signal backtest.

WinPct

This is the win percentage for the trades present in the backtest. If this is a tradescape point, this will be the win rate that corresponds with this point in the tradescape's trading landscape. For a user-defined signal entry, this will be the win rate in the actual signal backtest.

Trend

This is the robust CAGR (cumulative annual growth rate) or 'trend' computed from fitting all of the equity curve points in a regression procedure. It is reported as an annual percentage. If this is a tradescape point, this will be the trend % that corresponds with this point in the tradescape's trading landscape. For a user-defined signal entry, this will be the annual trend % present in the signal's equity curve.

Trendr²

This is the r² or coefficient of determination from the regression used to compute the Trend. This varies from 0 to 1. An equity curve with little retracement will have an r² close to 1.

Sharpe

This is a modified Sharpe ratio that consists of the robust Trend divided by the annualized volatility computed from the SD of closing prices. The risk-free rate is assumed to be zero. This is probably the most commonly used reward-to-risk metric.

R³

This is a reward-to-pain ratio based on Curtis Faith's published work which uses a count of the worst drawdowns, both magnitude and duration, to estimate a more practical pain estimate for trading. It also uses the robust trend for the reward. The R³ is detailed in this white paper.

RRt

This is a simple and robust reward-to-pain ratio that uses the robust trend as the reward and the average retracement as the pain. The RRt is detailed in this white paper.

AvgRt

This is the average retracement in the equity curve as as percentage. This is the pain in the RRt computation.

CoinErr

This is the percentage of the time the signal is on the wrong side of the ideal (zero-lag) EM reference. For a tradescape point, this measures the extent to which trades are shifted to the "wrong side" by the introduced lag. For a user-defined trading signal, this compares the trading signal with the zero-lag version of the EM signal with matching trade count and reports the percentage the trading signal fails to coincide with the ideal lag-free EM reference.

Report Items - Trading Signals Only

Sys

This is the reference number of the trading signal.

EMZC

This is the zero-crossing count of the first derivative of the EM reference that seeks to match the trade count of the real-world signal. The EMZC and SigZC should match closely. Note that with real-world data, it is not always possible to realize the same trade count. Also, this is a minimization problem with local minima sometimes resulting in a less than optimal match. If the algorithm fails to match the zero-crossing count, you should assume a higher measure of error in the lag and coverage error estimates.

SigZC

This is the count of sign changes in the user-defined trading signal. The EMZC and SigZC should match closely. Again, if the algorithm fails to match the zero-crossing count, you should assume a higher measure of error in the lag and coverage error estimates.

EMAvTLen

This is the average trade length of the EM signal taken mathematically from the zero-crossing data. Because of how trades are opened and closed in the backtest engine and the use of all available data in this computation, these values will not match the backtest values. The purpose is to give a more familiar item than the zero crossing count for comparing the effectiveness of the matching. Even if the trade counts (the ZC counts) perfectly match, there may be differences in the average trade lengths. The EMAvTLen and SigAvTLen should be reasonably close.

SigAvTLen

This is the average trade length of the user's trading signal taken mathematically from its sign changes. Again, the EMAvTLen and SigAvTLen should be reasonably close.

CorrLag

This is the lag estimate most users are familiar with. It accounts all points in two different time series and determines an estimate for the extent to which one is shifted in time from the other. A lag measurement caution is here for those instances where the similarity between the reference and trading signal is too poor for a valid analysis.

Lag

This is the lag estimate of all turning points in the signal. It is a robust mean of the lag measured at the extrema (both minima and maxima). The user signal is mapped point by point to the reference (EM) signal. For each turn in the EM signal, an algorithm searches within a given lag tolerance (based on the correlation lag) for a corresponding turn in the user-defined trading signal. If one is found, it is stored in a table of upside, downside, and all turns with the lag measured in each. Only those turns that coincide are accounted. These are robust averages that use the interior 68 percentile of the lags accumulated.

LagSD

This is the robust SD of the lag values for all of the turns in the signal. It is the width of the interior 68 percentile bounds.

MaxLag

This is the lag estimate of the maxima turning points in the signal.

MaxLagSD

This is the robust SD of the lag values for the maxima turning points in the signal.

MinLag

This is the lag estimate of the minima turning points in the signal.

MinLagSD

This is the robust SD of the lag values for the minima turning points in the signal.

CovgErr

This is the coverage error of all turning points in the signal. It is reported as a percentage. When the user signal is mapped point by point to the reference (EM) signal, for each turn in the EM signal, an algorithm searches within a given lag tolerance (based on the correlation lag) for a corresponding turn in the user-defined trading signal. If one is found, the turn is deemed to be covered. There is no ability in the coverage or lag estimates to estimate trading signals that appear before the zero lag EM reference. If a trading signal can actually anticipate a turn before it is registered in the ideal zero-lag EM reference, that turn is not accounted in the coverage.