In stochastic processes, chaos theory and time series analysis, detrended fluctuation analysis (DFA) is a method for determining the statistical self-affinity of a signal. It is useful for analyzing time series that appear to be long-memory processes and noise. █ OVERVIEW We have introduced the concept of Hurst Exponent in our previous open indicator Hurst...

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Historical volatility is a statistical measure of the dispersion of returns for a given security or market index over a given period. This indicator provides different historical volatility model estimators with percentile gradient coloring and volatility stats panel. █ OVERVIEW There are multiple ways to estimate historical volatility. Other than the...

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In Finance, people usually assume the price follows a random walk or more precisely geometric Brownian motion. In 1988, Lo and MacKinlay came up with the variance ratio test to refute the random walk hypothesis and efficient market hypothesis. The variance ratio test is a simple test for market efficiency, autocorrelation, and whether price follows a random walk....

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Moments describe the shape features of a distribution. There are four essential Moments: Mean, Variance, Skewness, Kurtosis . The Moments of returns can provide a comprehensive view of the tendency, volatility , and risk of the market . It's important for traders to know these statistical properties of the instrument before trading them. █ OVERVIEW The...

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Reverse Indicator calculation: Oscillators value output are calculated based on the input price (open, high, low or close). This means certain input price can generate the according to the output value of the oscillator. They are both sides of an equation, the process is reversible. Once we know one side of the equation, we can get the value of the other side. We...

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The Omega Ratio is a risk-return performance measure of an investment asset, portfolio, or strategy. It is defined as the probability-weighted ratio, of gains versus losses for some threshold return target . The ratio is an alternative for the widely used Sharpe ratio and is based on information the Sharpe ratio discards. █ OVERVIEW As we have mentioned...

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The Hurst exponent is used as a measure of long-term memory of time series. It relates to the autocorrelations of the time series and the rate at which these decrease as the lag between pairs of values increases. The Hurst exponent is referred to as the "index of dependence" or "index of long-range dependence". It quantifies the relative tendency of a time series...

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In statistics, the Durbin–Watson statistic is a test statistic used to detect the presence of autocorrelation at lag 1 (AR(1) process) in the residuals (prediction errors) from a regression analysis. With the new array function tradingview implemented, we are able to do our calculations on the residuals. The residual is given by subtracting the actual value (in...

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Expected move is the amount that an asset is predicted to increase or decrease from its current price, based on the current levels of volatility. In this model, we assume asset price follows a log-normal distribution and the log return follows a normal distribution. Note: Normal distribution is just an assumption, it's not the real distribution of return...

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