AIS Lehmer Moving Average

The Lehmer mean can be considered as a window function, the weight coefficients of which depend on the values ​​of the variables used in the calculation. This average is non-linear because exponentiation is used in its calculation.
The characteristics of the indicator depend on two parameters:
  • iPeriod - indicator period, valid value is greater than or equal to 2;
  • iPower - exponent, which is used when calculating indicator values. Valid range is -32768 to 32767

With iPower = 0 we get the harmonic mean,
with iPower = 1 - arithmetic mean,
and for iPower = 2, the counterharmonic mean.
With a large exponent, the Lehmer mean highlights the maximum boundary of the time series. And with negative exponents, the minima are emphasized. Due to this property, the Lehmer mean can be used both for smoothing the time series and for constructing channels.

The first picture shows a channel calculated using Close prices with exponents of +500 and -500.
The second picture shows the same channel with iPower = +1000 and -1000.
In the third and fourth figures, Lehmer's mean is applied to the High and Low prices at +/- 1000 and +/- 5000.
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The script allows selecting the required 'Filter level' value of the AIS-MTF MT5 indicator. Run the script on the required chart and selected timeframe. Once its operation is complete, the HPS.csv file will be created in the Files folder. Open the file. You will see three columns. The 'Filter lvl' column represents the value of the 'Filter level' for the AIS-MTF indicator. Am. dev. - degree and direction of the indicator's deviation from the price level (sorted in ascending order). Negative valu
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This script allows selecting the TakeProfit and StopLoss levels. It analyzes the history data, and then calculates the probability of reaching a given price level. How the script works Suppose you have a trading strategy and you want to select the TakeProfit and StopLoss levels. Run the script and set the parameter: Number of Bars - the average position holding time in bars. Once the script operation is complete, the AIS-PPL.csv file will be created in the Files folder in the terminal data cata
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AIS Correct Averages indicator allows you to determine the beginning of the trend movement in the market. Another important quality of the indicator is a clear signal of the end of the trend. The indicator is not redrawn or recalculated. Displayed values h_AE - the upper limit of the AE channel l_AE - the lower boundary of the AE channel h_EC - High value projected for the current bar l_EC - Low predicted value for the current bar Signals for the indicator The main channel signal is the inters
The AIS Weighted Moving Average indicator calculates weighted moving average, allowing to determine the beginning of market trend. Weights are calculated taking into account the specific characteristics of each bar. This allows filtering random market movements. The main signal, confirming the beginning of a trend, is change in the direction of indicator line movement and the intersection of the indicator lines with the indicator price. WH (blue line) - the weighted average High price. WL (red l
The AIS Advanced Grade Feasibility indicator is designed for forecasting levels that a price can reach in future. Its operation is based on the analysis of the last three bars and creating the forecast. The indicator can be used on any timeframe and any currency pair. Using settings, you can achieve the desired quality of the forecast. Depth of forecast - sets the desired depth of forecast in bars. The recommended values for these parameters are 18-31. You can try beyond this range. But in this
The indicator is designed to measure the price volatility. This allows determining the moments for opening or closing trade positions more accurately. High intensity of the market indicates the instability of its movement, but allows for better results. And, conversely, low intensity of the market indicates the stability of its movement. Parameters Bars to process - the number of bars to measure the price movements. A low value of this parameter allows determining the moments of rapid price mov
This indicator uses the Fibonacci p-numbers to smooth a price series. This allows combining the advantages of the simple and exponential moving averages. The smoothing coefficients depend on the level of the p-number, which is set in the indicator parameters. The higher the level, the greater the influence of the simple moving average and the less significant the exponential moving average. Parameters Fibonacci Numbers Order - order of the Fibonacci p-number, specified by trader. Valid values a
The indicator is based on the analysis of interaction of two filters. The first filter is the popular Moving Average. It helps to identify linear price movements and to smooth minor price fluctuations. The second filter is the Sliding Median. It is a non-linear filter. It allows to filter out noise and single spikes in the price movement. A predictive filter implemented in this indicator is based on the difference between these filters. The indicator is trained during operation and is therefore
This indicator studies the price action as a combination of micro-trends. All micro-trends are analyzed and averaged. Price movement is filtered based on this averaging. IP_High and IP_Low (blue and red dashed lines) show the instantaneous price movement. They display the forecast only for the current price values, taking into account only the number of bars defined by the 'Filter level' parameter. SP_High and SP_Low (blue and red solid lines) smooth the price movements with respect to history.
The script allows selecting the required 'Filter level' value of the AIS-MTF indicator. Run the script on the required chart and selected timeframe. Once its operation is complete, the HPS.csv file will be created in the Files folder. Open the file. You will see three columns. The 'Filter lvl' column represents the value of the 'Filter level' for the AIS-MTF indicator. Am. dev. - degree and direction of the indicator's deviation from the price level (sorted in ascending order). Negative values i
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This indicator implements the process of simple linear smoothing. One of the disadvantages of exponential smoothing is the rapid attenuation of the signal. This does not allow for a full-fledged monitoring of long-term tendency of a price series. Linear smoothing allows fine-tuning the signal filtering. The indicator is configured by selecting the parameters: LP - period of smoothing. The higher the value, the more long-term tendencies are displayed by the indicator. Valid values are from 0 to 2
Этот индикатор представляет гибридный фильтр основанный на совместном использовании медианы и скользящей средней. Использование медианы позволяет отфильтровывать аномальные выбросы и случайные импульсы в значениях ценового ряда. При этом на трендовую составляющую медианный фильтр не действует, оставляя ее без изменений. Так как медианный фильтр является нелинейным, то для сглаживания его значений используется скользящая средняя. Такой подход позволяет более точно выделять не только тренд, но и п
This indicator is a combination of two modified Lanczos filters. The first filter serves to extrapolate the price. Based on past values, he predicts a possible price movement within the current bar. That is, it shows what the price would be if the past trends remained unchanged. The second filter for smoothing and averaging prices within the window, determined by the level of the filter. Thanks to the selection of weights, this filter is most actively responding to the periodic component that is
This script is designed so that the trader can determine the average duration of trade transactions, at which the ratio of possible profits and losses will be optimal. First, let's look at the general approach to determining the optimal duration of trade transactions. We introduce the following variables: R   - the result of the transaction; T   - the time during which the transaction was open; W - the time between the closing of the previous transaction and the opening of the next one. Every tr
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Let's look at the nature of price changes in the Forex market, not paying attention to the reasons why these changes occur. This approach will allow us to identify the main factors affecting the price movement. For example, let's take the opening prices of bars on the EUR-USD currency pair and the H1 timeframe. For these prices, we construct the Lameray diagram (Figure 1). In this diagram, it can be seen that the price movement basically occurs according to a linear equation. To determine the pa
This indicator is more informative. His work is based on the assumption that the price movement in the market can be represented as noise of a particular color, which depends on the parameters of the distribution of price values. Thanks to this, it is possible to analyze the price change from different angles, and considering the price movement as noise of a particular color, one can get information about the current state of affairs in the market and make a forecast about the price behavior. W
Despite some drawbacks of the “ AIS Color Noise Filter ” indicator, the idea to use it to smooth the price series and forecast prices looks quite attractive. This is due to several reasons: first, taking into account several noise components allows building a forecast on factors independent of each other, which can improve the quality of forecasting; secondly, the noise characteristics of the price series behave quite stably throughout the entire history, which makes it possible to obtain stabl
Very often, in the study of financial series apply their smoothing. Using smoothing, you can remove high-frequency components - it is believed that they are caused by random factors and therefore irrelevant. Smoothing always includes some way of averaging the data, in which random changes in the time series mutually absorb each other. Most often, for this purpose, simple or weighted moving average methods are used, as well as exponential smoothing. Each of these methods has its advantages and d
In order to isolate long-term and non-random components, it is necessary to know not only how much the price has changed, but also how these changes occurred. In other words - we are interested not only in the values ​​of price levels, but also in the order in which these levels replace each other. Through this approach, one can find long-term and stable factors that influence (or may influence) the price change at a given point in time. And knowledge of these factors allows you to make a more
One of the powerful methods of analysis is the modeling of financial series using Levy processes. The main advantage of these processes is that they can be used to model a huge number of phenomena - from the simplest to the most complex. Suffice it to say that the idea of ​​the fractal price movement in the market is only a special case of Levy processes. On the other hand, with proper selection of parameters, any Levy process can be represented as a simple moving average. Figure 1 shows an exa
Very often, the trader is faced with the task of determining the extent to which the price may change in the near future. For this purpose, you can use the Johnson distribution type SB. The main advantage of this distribution is that it can be used even with a small amount of accumulated data. The empirical approach used in determining the parameters of this distribution, allows you to accurately determine the maximum and minimum levels of the price channel. These values ​​can be used in differ
This indicator allows you to determine the likelihood that the price will reach one or another level. Its algorithm is quite simple and is based on the use of statistical data on the price levels of a particular currency pair. Thanks to the collected historical data, it is possible to determine the extent to which the price will change during the current bar. Despite its simplicity, this indicator can provide invaluable assistance in trading. So, with its help it is possible to determine TakePr
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