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Markov

[SGM Markov Chain]Introduction A Markov chain is a mathematical model that describes a system evolving over time among a finite number of states. This model is based on the assumption that the future state of the system depends only on the current state and not on previous states, the so-called Markov property. In the context of financial markets, Markov chains can be used to model transitions between different market conditions, for example, the probability of a price going up after going up, or going down after going down. Script Description This script uses a Markov chain to calculate closing price transition probabilities across the entire accessible chart. It displays the probabilities of the following transitions: - Up after Up (HH): Probability that the price rises after going up. - Down after Down (BB): Probability that the price will go down after going down. - Up after Down (HB): Probability that the price goes up after going down. - Down after Up (BH): Probability that the price will go down after going up. Features - Color customization: Choose colors for each transition type. - Table Position: Select the position of the probability display table (top/left, top/right, bottom/left, bottom/right).
Pine Script™ indikatörü
Sigaud tarafından
MarkovAlgorithmLibrary "MarkovAlgorithm" Markov algorithm is a string rewriting system that uses grammar-like rules to operate on strings of symbols. Markov algorithms have been shown to be Turing-complete, which means that they are suitable as a general model of computation and can represent any mathematical expression from its simple notation. ~ wikipedia . reference: en.wikipedia.org rosettacode.org parse(rules, separator)   Parameters:      rules (string)      separator (string)   Returns: - `array _rules`: List of rules. --- Usage: - `parse("|0 -> 0|| 1 -> 0| 0 -> ")` apply(expression, rules)   Aplies rules to a expression.   Parameters:      expression (string) : `string`: Text expression to be formated by the rules.      rules (rule ) : `string`: Rules to apply to expression on a string format to be parsed.   Returns: - `string _result`: Formated expression. --- Usage: - `apply("101", parse("|0 -> 0|| 1 -> 0| 0 -> "))` apply(expression, rules)   Parameters:      expression (string)      rules (string)   Returns: - `string _result`: Formated expression. --- Usage: - `apply("101", parse("|0 -> 0|| 1 -> 0| 0 -> "))` rule   String pair that represents `pattern -> replace`, each rule may be ordinary or terminating.   Fields:      pattern (series string) : Pattern to replace.      replacement (series string) : Replacement patterns.      termination (series bool) : Termination rule.
Pine Script™ kitaplığı
RicardoSantos tarafından
3
MarkovChainLibrary "MarkovChain" Generic Markov Chain type functions. --- A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. --- reference: Understanding Markov Chains, Examples and Applications. Second Edition. Book by Nicolas Privault. en.wikipedia.org www.geeksforgeeks.org towardsdatascience.com github.com stats.stackexchange.com timeseriesreasoning.com www.ris-ai.com github.com gist.github.com github.com gist.github.com writings.stephenwolfram.com kevingal.com towardsdatascience.com spedygiorgio.github.io github.com www.projectrhea.org method to_string(this)   Translate a Markov Chain object to a string format.   Namespace types: MC   Parameters:      this (MC) : `MC` . Markov Chain object.   Returns: string method to_table(this, position, text_color, text_size)   Namespace types: MC   Parameters:      this (MC)      position (string)      text_color (color)      text_size (string) method create_transition_matrix(this)   Namespace types: MC   Parameters:      this (MC) method generate_transition_matrix(this)   Namespace types: MC   Parameters:      this (MC) new_chain(states, name)   Parameters:      states (state )      name (string) from_data(data, name)   Parameters:      data (string )      name (string) method probability_at_step(this, target_step)   Namespace types: MC   Parameters:      this (MC)      target_step (int) method state_at_step(this, start_state, target_state, target_step)   Namespace types: MC   Parameters:      this (MC)      start_state (int)      target_state (int)      target_step (int) method forward(this, obs)   Namespace types: HMC   Parameters:      this (HMC)      obs (int ) method backward(this, obs)   Namespace types: HMC   Parameters:      this (HMC)      obs (int ) method viterbi(this, observations)   Namespace types: HMC   Parameters:      this (HMC)      observations (int ) method baumwelch(this, observations)   Namespace types: HMC   Parameters:      this (HMC)      observations (int ) Node   Target node.   Fields:      index (series int) : . Key index of the node.      probability (series float) : . Probability rate of activation. state   State reference.   Fields:      name (series string) : . Name of the state.      index (series int) : . Key index of the state.      target_nodes (Node ) : . List of index references and probabilities to target states. MC   Markov Chain reference object.   Fields:      name (series string) : . Name of the chain.      states (state ) : . List of state nodes and its name, index, targets and transition probabilities.      size (series int) : . Number of unique states      transitions (matrix) : . Transition matrix HMC   Hidden Markov Chain reference object.   Fields:      name (series string) : . Name of thehidden chain.      states_hidden (state ) : . List of state nodes and its name, index, targets and transition probabilities.      states_obs (state ) : . List of state nodes and its name, index, targets and transition probabilities.      transitions (matrix) : . Transition matrix      emissions (matrix) : . Emission matrix      initial_distribution (float )
Pine Script™ kitaplığı
RicardoSantos tarafından
12
FunctionProbabilityViterbiLibrary "FunctionProbabilityViterbi" The Viterbi Algorithm calculates the most likely sequence of hidden states *(called Viterbi path)* that results in a sequence of observed events. viterbi(observations, transitions, emissions, initial_distribution)   Calculate most probable path in a Markov model.   Parameters:      observations (int ) : array . Observation states data.      transitions (matrix) : matrix . Transition probability table, (HxH, H:Hidden states).      emissions (matrix) : matrix . Emission probability table, (OxH, O:Observed states).      initial_distribution (float ) : array . Initial probability distribution for the hidden states.   Returns: array. Most probable path.
Pine Script™ kitaplığı
RicardoSantos tarafından
2
FunctionBaumWelchLibrary "FunctionBaumWelch" Baum-Welch Algorithm, also known as Forward-Backward Algorithm, uses the well known EM algorithm to find the maximum likelihood estimate of the parameters of a hidden Markov model given a set of observed feature vectors. --- ### Function List: > `forward (array pi, matrix a, matrix b, array obs)` > `forward (array pi, matrix a, matrix b, array obs, bool scaling)` > `backward (matrix a, matrix b, array obs)` > `backward (matrix a, matrix b, array obs, array c)` > `baumwelch (array observations, int nstates)` > `baumwelch (array observations, array pi, matrix a, matrix b)` --- ### Reference: > en.wikipedia.org > github.com > en.wikipedia.org > www.rdocumentation.org > www.rdocumentation.org forward(pi, a, b, obs)   Computes forward probabilities for state `X` up to observation at time `k`, is defined as the probability of observing sequence of observations `e_1 ... e_k` and that the state at time `k` is `X`.   Parameters:      pi (float ) : Initial probabilities.      a (matrix) : Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing states given a state matrix is size (M x M) where M is number of states.      b (matrix) : Emissions, matrix of observation probabilities b or beta = observation probabilities. Given state matrix is size (M x O) where M is number of states and O is number of different possible observations.      obs (int ) : List with actual state observation data.   Returns: - `matrix _alpha`: Forward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first dimension refers to the state and the second dimension to time. forward(pi, a, b, obs, scaling)   Computes forward probabilities for state `X` up to observation at time `k`, is defined as the probability of observing sequence of observations `e_1 ... e_k` and that the state at time `k` is `X`.   Parameters:      pi (float ) : Initial probabilities.      a (matrix) : Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing states given a state matrix is size (M x M) where M is number of states.      b (matrix) : Emissions, matrix of observation probabilities b or beta = observation probabilities. Given state matrix is size (M x O) where M is number of states and O is number of different possible observations.      obs (int ) : List with actual state observation data.      scaling (bool) : Normalize `alpha` scale.   Returns: - #### Tuple with: > - `matrix _alpha`: Forward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first dimension refers to the state and the second dimension to time. > - `array _c`: Array with normalization scale. backward(a, b, obs)   Computes backward probabilities for state `X` and observation at time `k`, is defined as the probability of observing the sequence of observations `e_k+1, ... , e_n` under the condition that the state at time `k` is `X`.   Parameters:      a (matrix) : Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing states given a state matrix is size (M x M) where M is number of states      b (matrix) : Emissions, matrix of observation probabilities b or beta = observation probabilities. given state matrix is size (M x O) where M is number of states and O is number of different possible observations      obs (int ) : Array with actual state observation data.   Returns: - `matrix _beta`: Backward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first dimension refers to the state and the second dimension to time. backward(a, b, obs, c)   Computes backward probabilities for state `X` and observation at time `k`, is defined as the probability of observing the sequence of observations `e_k+1, ... , e_n` under the condition that the state at time `k` is `X`.   Parameters:      a (matrix) : Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing states given a state matrix is size (M x M) where M is number of states      b (matrix) : Emissions, matrix of observation probabilities b or beta = observation probabilities. given state matrix is size (M x O) where M is number of states and O is number of different possible observations      obs (int ) : Array with actual state observation data.      c (float ) : Array with Normalization scaling coefficients.   Returns: - `matrix _beta`: Backward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first dimension refers to the state and the second dimension to time. baumwelch(observations, nstates)   **(Random Initialization)** Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm to compute the statistics for the expectation step.   Parameters:      observations (int ) : List of observed states.      nstates (int)   Returns: - #### Tuple with: > - `array _pi`: Initial probability distribution. > - `matrix _a`: Transition probability matrix. > - `matrix _b`: Emission probability matrix. --- requires: `import RicardoSantos/WIPTensor/2 as Tensor` baumwelch(observations, pi, a, b)   Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm to compute the statistics for the expectation step.   Parameters:      observations (int ) : List of observed states.      pi (float ) : Initial probaility distribution.      a (matrix) : Transmissions, hidden transition matrix a or alpha = transition probability matrix of changing states given a state matrix is size (M x M) where M is number of states      b (matrix) : Emissions, matrix of observation probabilities b or beta = observation probabilities. given state matrix is size (M x O) where M is number of states and O is number of different possible observations   Returns: - #### Tuple with: > - `array _pi`: Initial probability distribution. > - `matrix _a`: Transition probability matrix. > - `matrix _b`: Emission probability matrix. --- requires: `import RicardoSantos/WIPTensor/2 as Tensor`
Pine Script™ kitaplığı
RicardoSantos tarafından
7
FunctionSMCMCLibrary "FunctionSMCMC" Methods to implement Markov Chain Monte Carlo Simulation (MCMC) markov_chain(weights, actions, target_path, position, last_value) a basic implementation of the markov chain algorithm   Parameters:      weights : float array, weights of the Markov Chain.      actions : float array, actions of the Markov Chain.      target_path : float array, target path array.      position : int, index of the path.      last_value : float, base value to increment.   Returns: void, updates target array mcmc(weights, actions, start_value, n_iterations) uses a monte carlo algorithm to simulate a markov chain at each step.   Parameters:      weights : float array, weights of the Markov Chain.      actions : float array, actions of the Markov Chain.      start_value : float, base value to start simulation.      n_iterations : integer, number of iterations to run.   Returns: float array with path.
Pine Script™ kitaplığı
RicardoSantos tarafından
2
SMA Stochastic ForecastThis tool uses a discrete-time non-Markovian Martingale stochastic process (Please do not confuse with the strategy of the same name) under the hood to forecast a future (up to 28 bars, customizable) behaviour of the Simple Moving Average. The longer the average period, the more accurate the forecast. The common cases are the next: You can apply two instances of this indicator to your chart to obtain a crossover forecast You can decrease an interval between forecasts to obtain a bunch of possible traectories Decreasing a forecast interval for two instances, you will get the Kraken This is the further improvement of my research work on forecasting Mr. @syrinxflunki was the only one who provided a clear and useful feedback after testing, so he get a free lifetime access. I respect a fair play. If you have any questions you can concat me via private messages. Good luck.
Pine Script™ indikatörü
everget tarafından
30