STD-Filtered, Ultra Low Lag Moving Average [Loxx]

STD-Filtered, Ultra Low Lag Moving Average is a FIR filter that smooths price using a low-pass filtering with weights derived from a normalized cardinal since function. This indicator attempts to reduce lag to an extreme degree. Try this on various time frames with various Type inputs, 0 is the default, so see where the sweet spot is for your trading style.

What is a Finite Impulse Response Filter?
In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR) filters, which may have internal feedback and may continue to respond indefinitely (usually decaying).

The impulse response (that is, the output in response to a Kronecker delta input) of an Nth-order discrete-time FIR filter lasts exactly {\displaystyle N+1}N+1 samples (from first nonzero element through last nonzero element) before it then settles to zero.

FIR filters can be discrete-time or continuous-time, and digital or analog.

A FIR filter is (similar to, or) just a weighted moving average filter, where (unlike a typical equally weighted moving average filter) the weights of each delay tap are not constrained to be identical or even of the same sign. By changing various values in the array of weights (the impulse response, or time shifted and sampled version of the same), the frequency response of a FIR filter can be completely changed.

An FIR filter simply CONVOLVES the input time series (price data) with its IMPULSE RESPONSE. The impulse response is just a set of weights (or "coefficients") that multiply each data point. Then you just add up all the products and divide by the sum of the weights and that is it; e.g., for a 10-bar SMA you just add up 10 bars of price data (each multiplied by 1) and divide by 10. For a weighted-MA you add up the product of the price data with triangular-number weights and divide by the total weight.

Ultra Low Lag Moving Average's weights are designed to have MAXIMUM possible smoothing and MINIMUM possible lag compatible with as-flat-as-possible phase response.

What is Normalized Cardinal Sine?
The sinc function sinc(x), also called the "sampling function," is a function that arises frequently in signal processing and the theory of Fourier transforms.

In mathematics, the historical unnormalized sinc function is defined for x ≠ 0 by

sinc x = sinx / x

In digital signal processing and information theory, the normalized sinc function is commonly defined for x ≠ 0 by

sinc x = sin(pi * x) / (pi * x)

How this works, (easy mode)
1. Use a HA or HAB source type
2. The lower the Type value the smoother the moving average
3. Standard deviation stepping is added to further reduce noise

Included

• Bar coloring
  
• Signals
  
• Alerts
  
• Loxx's Expanded Source Types
  

Versionshinweise:

Removed an unused windowing loop. I was going to restrict this for forecasting purposes in the future, but for now, it's removed so this is much much faster.