Moving Average PropertiesThis indicator calculates and visualizes the Relative Smoothness (RS) and Relative Lag (RL) or call it accuracy of a selected moving average (MA) in comparison to the SMA of length 2 (the lowest possible length for a moving average and also the one closest to the price).
Median RS (Relative Smoothness):
Interpretation: The median RS represents the median value of the Relative Smoothness calculated for the selected moving average across a specified look-back period (max bar lookback is set at 3000).
Significance: A more negative (larger) median RS suggests that the chosen moving average has exhibited smoother price behavior compared to a simple moving average over the analyzed period. A less negative value indicates a relatively choppier price movement.
Median RL (Relative Lag):
Interpretation: The median RL represents the median value of the Relative Lag calculated for the selected moving average compared to a simple moving average of length 2.
Significance: A higher median RL indicates that the chosen moving average tends to lag more compared to a simple moving average. Conversely, lower values suggest less lag in the selected moving average.
Ratio of Median RS to Median RL:
Interpretation: This ratio is calculated by dividing the median RS by the median RL.
Significance: Traders might use this ratio to assess the balance between smoothness and lag in the chosen moving average. This a measure of for every % of lag what is the smoothness achieved. This can be used a benchmark to decide what length to choose for a MA to get an equivalent value between two stocks. For example a TESLA stock on a 15 minute time frame with a length of 12 has a value (ratio of RS/RL) of -150 , where as APPLE stock of length 35 on a 15 minute chart also has a value (ratio of RS/RL) of -150.
I imply that a MA of length 12 working on TESLA stock is equivalent to MA of length 35 on a APPLE stock. (THIS IS A EXAMPLE).
My assumption is that finding the right moving average length for a stock isn't a one-size-fits-all situation. It's not just about using a fixed length; it's about adapting to the unique characteristics of each stock. I believe that what works for one stock might not work for another because they have different levels of smoothness or lag in their price movements. So, instead of applying the same length to all stocks, I suggest adjusting the length of the moving average to match the values that we know work best for achieving the desired smoothness or lag or its ratio (RS/RL). This way, we're customizing the indicator for each stock, tailoring it to their individual behaviors rather than sticking to a one-size-fits-all approach.
Users can choose from various types of moving averages (EMA, SMA, WMA, VWMA, HMA) and customize the length of the moving average. RS measures the smoothness of the MA, while RL measures its lag compared to a simple moving average. The script plots the median RS and RL values, the selected MA, and the ratio of median RS to median RL on the price chart. Traders can use this information to assess the performance of different moving averages and potentially inform their trading decisions.
Smoothness
Filter Information Box - PineCoders FAQWhen designing filters it can be interesting to have information about their characteristics, which can be obtained from the set of filter coefficients (weights). The following script analyzes the impulse response of a filter in order to return the following information:
Lag
Smoothness via the Herfindahl index
Percentage Overshoot
Percentage Of Positive Weights
The script also attempts to determine the type of the analyzed filter, and will issue warnings when the filter shows signs of unwanted behavior.
DISPLAYED INFORMATION AND METHODS
The script displays one box on the chart containing two sections. The filter metrics section displays the following information:
- Lag : Measured in bars and calculated from the convolution between the filter's impulse response and a linearly increasing sequence of value 0,1,2,3... . This sequence resets when the impulse response crosses under/over 0.
- Herfindahl index : A measure of the filter's smoothness described by Valeriy Zakamulin. The Herfindahl index measures the concentration of the filter weights by summing the squared filter weights, with lower values suggesting a smoother filter. With normalized weights the minimum value of the Herfindahl index for low-pass filters is 1/N where N is the filter length.
- Percentage Overshoot : Defined as the maximum value of the filter step response, minus 1 multiplied by 100. Larger values suggest higher overshoots.
- Percentage Positive Weights : Percentage of filter weights greater than 0.
Each of these calculations is based on the filter's impulse response, with the impulse position controlled by the Impulse Position setting (its default is 1000). Make sure the number of inputs the filter uses is smaller than Impulse Position and that the number of bars on the chart is also greater than Impulse Position . In order for these metrics to be as accurate as possible, make sure the filter weights add up to 1 for low-pass and band-stop filters, and 0 for high-pass and band-pass filters.
The comments section displays information related to the type of filter analyzed. The detection algorithm is based on the metrics described above. The script can detect the following type of filters:
All-Pass
Low-Pass
High-Pass
Band-Pass
Band-Stop
It is assumed that the user is analyzing one of these types of filters. The comments box also displays various warnings. For example, a warning will be displayed when a low-pass/band-stop filter has a non-unity pass-band, and another is displayed if the filter overshoot is considered too important.
HOW TO SET THE SCRIPT UP
In order to use this script, the user must first enter the filter settings in the section provided for this purpose in the top section of the script. The filter to be analyzed must then be entered into the:
f(input)
function, where `input` is the filter's input source. By default, this function is a simple moving average of period length . Be sure to remove it.
If, for example, we wanted to analyze a Blackman filter, we would enter the following:
f(input)=>
pi = 3.14159,sum = 0.,sumw = 0.
for i = 0 to length-1
k = i/length
w = 0.42 - 0.5 * cos(2 * pi * k) + 0.08 * cos(4 * pi * k)
sumw := sumw + w
sum := sum + w*input
sum/sumw
EXAMPLES
In this section we will look at the information given by the script using various filters. The first filter we will showcase is the linearly weighted moving average (WMA) of period 9.
As we can see, its lag is 2.6667, which is indeed correct as the closed form of the lag of the WMA is equal to (period-1)/3 , which for period 9 gives (9-1)/3 which is approximately equal to 2.6667. The WMA does not have overshoots, this is shown by the the percentage overshoot value being equal to 0%. Finally, the percentage of positive weights is 100%, as the WMA does not possess negative weights.
Lets now analyze the Hull moving average of period 9. This moving average aims to provide a low-lag response.
Here we can see how the lag is way lower than that of the WMA. We can also see that the Herfindahl index is higher which indicates the WMA is smoother than the HMA. In order to reduce lag the HMA use negative weights, here 55% (as there are 45% of positive ones). The use of negative weights creates overshoots, we can see with the percentage overshoot being 26.6667%.
The WMA and HMA are both low-pass filters. In both cases the script correctly detected this information. Let's now analyze a simple high-pass filter, calculated as follows:
input - sma(input,length)
Most weights of a high-pass filters are negative, which is why the lag value is negative. This would suggest the indicator is able to predict future input values, which of course is not possible. In the case of high-pass filters, the Herfindahl index is greater than 0.5 and converges toward 1, with higher values of length . The comment box correctly detected the type of filter we were using.
Let's now test the script using the simple center of gravity bandpass filter calculated as follows:
wma(input,length) - sma(input,length)
The script correctly detected the type of filter we are using. Another type of filter that the script can detect is band-stop filters. A simple band-stop filter can be made as follows:
input - (wma(input,length) - sma(input,length))
The script correctly detect the type of filter. Like high-pass filters the Herfindahl index is greater than 0.5 and converges toward 1, with greater values of length . Finally the script can detect all-pass filters, which are filters that do not change the frequency content of the input.
WARNING COMMENTS
The script can give warning when certain filter characteristics are detected. One of them is non-unity pass-band for low-pass filters. This warning comment is displayed when the weights of the filter do not add up to 1. As an example, let's use the following function as a filter:
sum(input,length)
Here the filter pass-band has non unity, and the sum of the weights is equal to length . Therefore the script would display the following comments:
We can also see how the metrics go wild (note that no filter type is detected, as the detected filter could be of the wrong type). The comment mentioning the detection of high overshoot appears when the percentage overshoot is greater than 50%. For example if we use the following filter:
5*wma(input,length) - 4*sma(input,length)
The script would display the following comment:
We can indeed see high overshoots from the filter:
@alexgrover for PineCoders
Look first. Then leap.
