25:["$","title",null,{"children":"Crypto analysis | Henrique Recidive | Observable"}] 49:T6c9,logRenko = { // const startPrice = 100 // let actualStartPrice = null // const percentStep = 0.01 // const result = [] // normalizedCandles.forEach((candle, i) => { // let price = startPrice // let logReturns = 0 // if (i === 0) { // actualStartPrice = candle.close // } // else { // logReturns = Math.log(candle.close / actualStartPrice) // if (Math.abs(logReturns) >= percentStep) { // price = logReturns < 0 // ? startPrice - (startPrice * Math.abs(logReturns) / percentStep) // : startPrice + (startPrice * Math.abs(logReturns) / percentStep) // } // } // result.push({ // timestamp: candle.timestamp, // logReturns, // price, // }) // }) // return result let startPrice = null let lastPrice = null const percentStep = 0.01 const result = [] normalizedCandles.forEach((candle, i) => { let logReturns = 0 let price = 0 if (i === 0) { startPrice = candle.close } else { logReturns = Math.log(candle.close / startPrice) if (Math.abs(logReturns) >= percentStep) { // price = logReturns < 0 // ? startPrice - (startPrice * Math.abs(logReturns) / percentStep) // : startPrice + (startPrice * Math.abs(logReturns) / percentStep) // price = logReturns < 0 // ? - Math.round(Math.abs(logReturns) / percentStep) // : Math.round(Math.abs(logReturns) / percentStep) price = Math.round(logReturns / percentStep) lastPrice = price } else { price = lastPrice } } result.push({ timestamp: candle.timestamp, logReturns, price, }) }) return result }4a:T609,class MatrixUtils { // Compute the transpose of a matrix. static transpose(matrix) { const m = matrix.length const n = matrix[0].length const result = new Array(n) for (let j = 0; j < n; j++) { result[j] = new Array(m) for (let i = 0; i < m; i++) { result[j][i] = matrix[i][j] } } return result } // Compute the product of two matrices. static multiply(matrix1, matrix2) { const m = matrix1.length const n = matrix2[0].length const result = new Array(m) for (let i = 0; i < m; i++) { result[i] = new Array(n) for (let j = 0; j < n; j++) { let sum = 0 for (let k = 0; k < matrix1[0].length; k++) { sum += matrix1[i][k] * matrix2[k][j] } result[i][j] = sum } } return result } // Compute the sum of two matrices. static sum(matrix1, matrix2) { const m = matrix1.length const n = matrix1[0].length const result = new Array(m) for (let i = 0; i < m; i++) { result[i] = new Array(n) for (let j = 0; j < n; j++) { result[i][j] = matrix1[i][j] + matrix2[i][j] } } return result } // Compute the difference of two matrices. static subtract(matrix1, matrix2) { const m = matrix1.length const n = matrix1[0].length const result = new Array(m) for (let i = 0; i < m; i++) { result[i] = new Array(n) for (let j = 0; j < n; j++) { result[i][j] = matrix1[i][j] - matrix2[i][j] } } return result } }4b:Tc3f,// Define the Extended Kalman Filter class ExtendedKalmanFilter { constructor(state, covariance) { this.state = state this.covariance = covariance } // Predict the state and covariance given the elapsed time since the last prediction predict(dt) { // Calculate the state transition matrix and Jacobian const stateTransitionMatrix = this.jacobianF(this.state, dt) const jacobianMatrix = this.jacobianF(this.state, dt) // Predict the state using the state transition function this.state = this.stateTransition(this.state, dt) // Predict the covariance using the state transition matrix and Jacobian const covariance = this.covariance this.covariance = MatrixUtils.sum( MatrixUtils.multiply( stateTransitionMatrix, MatrixUtils.multiply( covariance, MatrixUtils.transpose(stateTransitionMatrix) ) ), MatrixUtils.multiply( jacobianMatrix, MatrixUtils.multiply(covariance, MatrixUtils.transpose(jacobianMatrix)) ) ) // Add process noise to the covariance const q = [ [0.1, 0, 0], [0, 0.1, 0], [0, 0, 0.1] ] this.covariance = MatrixUtils.sum(this.covariance, q) } // Update the state and covariance given a new observation update(observation, measurementNoise) { // Calculate the observation matrix and Jacobian const observationMatrix = this.jacobianH(this.state) // Calculate the innovation and innovation covariance const innovation = observation - this.state.price const innovationCovariance = MatrixUtils.sum( MatrixUtils.multiply( observationMatrix, MatrixUtils.multiply( this.covariance, MatrixUtils.transpose(observationMatrix) ) ), measurementNoise ) // Calculate the Kalman gain const kalmanGain = MatrixUtils.multiply( this.covariance, MatrixUtils.transpose(observationMatrix) ).map(row => row.map(value => value / innovationCovariance[0][0])) // Update the state and covariance using the Kalman gain and innovation const deltaState = MatrixUtils.multiply(kalmanGain, [[innovation]]) this.state.price += deltaState[0][0] this.state.velocity += deltaState[1][0] this.state.acceleration += deltaState[2][0] this.covariance = MatrixUtils.subtract( this.covariance, MatrixUtils.multiply( kalmanGain, MatrixUtils.multiply(observationMatrix, this.covariance) ) ) } // Define the state transition function f(x) stateTransition(state, dt) { const price = state.price + state.velocity * dt + 0.5 * state.acceleration * dt * dt const velocity = state.velocity + state.acceleration * dt const acceleration = state.acceleration return { price, velocity, acceleration } } // Define the Jacobian of the state transition function f(x) jacobianF(state, dt) { return [ [1, dt, 0.5 * dt * dt], [0, 1, dt], [0, 0, 1] ] } // Define the Jacobian of the observation function h(x) jacobianH(state) { return [[1, 0, 0]] } }4c:T558,{ const audio = new Float32Array(filteredStates.map(s => s.velocity)) const audioCtx = new AudioContext(); // Assuming you already have a Float32Array buffer with the original audio data const sourceBuffer = audioCtx.createBuffer(1, audio.length, audioCtx.sampleRate); const channelData = sourceBuffer.getChannelData(0); channelData.set(audio); // Calculate the new length and sample rate const newLength = sourceBuffer.length * 1000; // Double the length const newSampleRate = audioCtx.sampleRate; // Create a new OfflineAudioContext with the new length and sample rate const offlineCtx = new OfflineAudioContext(1, newLength, newSampleRate); // Create an AudioBufferSourceNode and connect it to the OfflineAudioContext const source = offlineCtx.createBufferSource(); source.buffer = sourceBuffer; source.connect(offlineCtx.destination); // Start playing the source source.start(0); // Render the OfflineAudioContext and get the resampled buffer offlineCtx.startRendering().then(renderedBuffer => { // Use the resampled buffer as the source for your AudioBufferSourceNode const resampledSource = audioCtx.createBufferSource(); resampledSource.buffer = renderedBuffer; resampledSource.connect(audioCtx.destination); // Start playing the resampled source resampledSource.start(0); }); }4d:T635,{ const audio = new Float32Array(filteredStates.map(s => s.velocity)) const audioCtx = new AudioContext(); // Assuming you already have a Float32Array buffer with the original audio data const sourceBuffer = audioCtx.createBuffer(1, audio.length, audioCtx.sampleRate); const channelData = sourceBuffer.getChannelData(0); channelData.set(audio); // Calculate the new sample rate const newSampleRate = 44100; // For example, resample to 44.1 kHz // Calculate the new length of the buffer const newLength = Math.round(channelData.length * (newSampleRate / audioCtx.sampleRate)); // Create a new buffer with the new length and the new sample rate const newBuffer = audioCtx.createBuffer(1, newLength, newSampleRate); // Fill the new buffer with the resampled data const newChannelData = newBuffer.getChannelData(0); for (let i = 0; i < newLength; i++) { const originalIndex = (i / newLength) * channelData.length; const floorIndex = Math.floor(originalIndex); const ceilIndex = Math.ceil(originalIndex); const fraction = originalIndex - floorIndex; const floorValue = channelData[floorIndex]; const ceilValue = channelData[ceilIndex]; const interpolatedValue = (1 - fraction) * floorValue + fraction * ceilValue; newChannelData[i] = interpolatedValue; } // Create an AudioBufferSourceNode and connect it to the AudioContext destination const source = audioCtx.createBufferSource(); source.buffer = newBuffer; source.connect(audioCtx.destination); // Start playing the source source.start(0); }4e:[] 29:{"id":"0029fcd82d05514d","slug":null,"title":"Crypto analysis","thumbnail":"5915e27826fd58e3806af38d200693185a8c1d5864a00bf623afc17084a9648e","access_level":"public","create_time":"$D2023-03-05T19:48:06.745Z","update_time":"$D2023-03-10T22:08:40.724Z","view_time":null,"first_public_time":"$D2023-03-05T19:48:06.745Z","has_unpublished_edits":null,"fork":{"id":"b30e09a00a845eb8","slug":null,"title":"Extended Kalman filter test","owner":{"id":"4f214c0cf299c92f","login":"recidive","name":"Henrique Recidive"}},"stars":0,"starred":false,"owner":{"type":"team","id":"4f214c0cf299c92f","login":"recidive","name":"Henrique 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analysis","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":5,"value":"symbol = 'UFTBUSD'","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":246,"value":"## One Year","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":16,"value":"timeframe = '15m'","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"endpoint = `https://api.binance.com/api/v3/klines?symbol=${symbol}&interval=${timeframe}&limit=1000`","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":21,"value":"candles = (await fetch(endpoint)).json()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":32,"value":"normalizedCandles = candles.map(c => ({timestamp: new Date(c[0]), close: Number(c[4]), volume: Number(c[5])}))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":24,"value":"Plot.plot({\n marks: [\n Plot.lineY(normalizedCandles.slice(-120), {x: 'timestamp', y: 'close'})\n ],\n grid: true,\n style: {\n width: 1024,\n }\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":252,"value":"$49","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":261,"value":"Plot.plot({\n marks: [\n Plot.lineY(logRenko.slice(-120), {x: 'timestamp', y: 'price'})\n ],\n grid: true,\n style: {\n width: 1024,\n }\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":130,"value":"$4a","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":42,"value":"$4b","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":105,"value":"filteredStates = {\n const dt = 1\n const state2 = { price: logRenko[0].price, velocity: 0.0, acceleration: 0.0 }\n const covariance = [\n [dt, 0.0, 0.0],\n [0.0, dt, 0.0],\n [0.0, 0.0, dt]\n ]\n \n const filter = new ExtendedKalmanFilter(state2, covariance)\n const states = []\n const predictedStates = []\n\n logRenko.forEach((observation, i) => {\n filter.update(observation.price, [[dt]])\n const state = {\n timestamp: observation.timestamp,\n ...filter.state\n }\n filter.predict(dt)\n \n const predictedState = {\n predictedPrice: filter.state.price,\n predictedVelocity: filter.state.velocity,\n predictedAcceleration: filter.state.acceleration,\n }\n predictedStates.push(predictedState)\n states.push({\n ...state,\n ...(predictedStates[i-1] ? predictedStates[i-1] : predictedState),\n truth: observation.price\n })\n })\n\n return states\n}\n","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":140,"value":"Plot.plot({\n marks: [\n Plot.lineY(filteredStates.slice(-60), {x: 'timestamp', y: 'truth'}),\n Plot.lineY(filteredStates.slice(-60), {x: 'timestamp', y: 'predictedPrice', stroke: 'grey'}),\n // Plot.lineY(filteredStates.slice(-100), {x: 'timestamp', y: 'price', stroke: 'lightgrey'}),\n // Plot.dot(filteredStates.slice(499).slice(-300), {x: 'timestamp', y: 'predictedPrice', stroke: 'grey'}),\n ],\n grid: true,\n style: {\n width: 1024,\n }\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":148,"value":"Plot.plot({\n marks: [\n // Plot.ruleY([0]),\n // Plot.dot(filteredStates.slice(500).slice(-100), {x: 'timestamp', y: 'predictedVelocity', stroke: 'green'}),\n // Plot.lineY(filteredStates.slice(500).slice(-100), {x: 'timestamp', y: 'predictedVelocity', stroke: 'lightgreen'}),\n Plot.lineY(filteredStates.slice(-60), {x: 'timestamp', y: 'velocity', stroke: 'green'}),\n // Plot.dot(filteredStates.slice(500).slice(-100), {x: 'timestamp', y: 'predictedAcceleration', stroke: 'red'}),\n // Plot.lineY(filteredStates.slice(500).slice(-100), {x: 'timestamp', y: 'predictedAcceleration', stroke: 'pink'}),\n Plot.lineY(filteredStates.slice(-60), {x: 'timestamp', y: 'acceleration', stroke: 'red'}),\n ],\n grid: true,\n style: {\n width: 1024,\n }\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":382,"value":"{\n const audio = new Float32Array(filteredStates.map(s => s.velocity))\n const audioCtx = new AudioContext();\n const buffer = audioCtx.createBuffer(1, audio.length, audioCtx.sampleRate);\n const channelData = buffer.getChannelData(0);\n channelData.set(audio);\n const source = audioCtx.createBufferSource();\n source.buffer = buffer;\n source.connect(audioCtx.destination);\n source.start();\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":385,"value":"$4c","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":389,"value":"$4d","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":402,"value":"{\n const audio = new Float32Array(filteredStates.map(s => s.acceleration))\n const audioCtx = new AudioContext();\n \n // Assuming you already have a Float32Array buffer with the original audio data\n \n const sourceBuffer = audioCtx.createBuffer(1, audio.length, audioCtx.sampleRate);\n const channelData = sourceBuffer.getChannelData(0);\n channelData.set(audio);\n \n // Calculate the playback rate\n const playbackRate = 0.005; // For example, play the sound at half speed\n \n // Create an AudioBufferSourceNode and connect it to the AudioContext destination\n const source = audioCtx.createBufferSource();\n source.buffer = sourceBuffer;\n source.playbackRate.value = playbackRate;\n source.connect(audioCtx.destination);\n \n // Start playing the source\n source.start(0);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":242,"value":"normalizedPrices = {\n const result = []\n const initialPrice = 1\n result.push(price)\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W4e","stdlib":"1"}} 24:null