The Z-score The Z-score, also known as the standard score, is a statistical measurement that describes a value's relationship to the mean of a group of values. It's measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score. Z-scores may be positive or negative, with a positive value indicating the score is above the mean and a negative score indicating it is below the mean.
The concept of Z-score was introduced by statistician Carl Friedrich Gauss as part of his "method of the least squares," which was an important step in the development of the normal distribution and Z-score tables. It's a key concept in statistics and is used in various statistical tests.
In financial analysis, Z-scores are used to determine whether a data point is usual or unusual. You can think of it as a measure of how many standard deviations an element is from the mean. For instance, a Z-score of 1.0 would denote a value that is one standard deviation from the mean. Z-scores are also used to predict probabilities, with Z-scores having a distribution that is expected to be normal.
In trading, a Z-score is used to determine how often a trading system may produce a string of winners or losers. It can help a trader to understand whether the losses or profits they see are something that the system would most likely produce, or if it's a once in a blue moon situation. This helps traders make decisions about when to start or stop a system.
I just wanted to play a bit with the Z-score I guess.
Feel free to share your findings if you discover additional applications for this strategy or identify timeframes where it appears to perform more optimally.
How it works:
This strategy is based on a statistical concept called Z-score, which measures the number of standard deviations a data point is from the mean. In other words, it helps determine how unusual or usual a data point is.
In the context of this strategy, Z-score is applied to a 10-period EMA (Exponential Moving Average) of Heikin-Ashi candlestick close prices. The Z-score is calculated over a look-back period of 25 bars.
The EMA of the Z-score is then calculated over a 20-bar period, and the upper and lower thresholds (bounds for buy and sell signals) are defined using the 90th and 10th percentiles of this EMA score.
Long positions are taken when the Z-score crosses above the lower threshold or crosses above the mid-line (50th percentile). An additional long entry is made when the Z-score crosses above the highest value the EMA has been in the past 100 periods.
Short positions are initiated when the EMA crosses below the upper threshold, lower threshold or the highest value the EMA has been in the past 100 periods.
Positions are closed when opposing entry conditions are met, for example, a long position is closed when the short entry condition is true, and vice versa.
Set your desired start date for the strategy. This can be modified in the timestamp("YYYY MM DD") function at the top of the script.
Calculus
Mathematical Derivatives of PriceThis indicator is meant to show the Velocity (1st order derivative), Acceleration (2nd order derivative), Jerk (3rd order derivative), Snap (4th order derivative), Crackle (5th order derivative), & Pop (6th order derivative) of price. The values at the top of the indicator window are in this order from left to right. I don't particularly know how this would be used in a trading strategy, but if you're ever curious about how quickly price is moving and how much it is accelerating, then you could use this tool.
*If you only care about velocity and acceleration, and don't like how squished the window is because of the long decimal numbers then edit the "precision" value in the first line of the script to a smaller number of your choosing.*
Indicator IntegratorHere is a light piece of code, The Indicator Integrator. It sums up a function (like an integral for you calculus folks). Unlike the 'cum' function that does a million bars of look back you can change the look back period, like limits of integration.
Built in is a difference of the close from an SMA. And there is an ROC. By changing what is summed up in the loop you can sum up the differences from the SMA or sum up the ROC. Pick your SMA length/ROC length. Then pick your look back period of how much to add up (bars to add up). There is a built in SMA smoother of three bars on the final summation.
Comments welcomed
