25:["$","title",null,{"children":"Crypto Analysis log returns/kalman filter | Henrique Recidive | Observable"}] 49:T5ae,function resampleTradesData(tradesData) { const startTime = tradesData[0].timestamp; const endTime = tradesData[tradesData.length - 1].timestamp; const numIntervals = Math.ceil((endTime - startTime) / 1000); const resampledData = new Array(numIntervals); let intervalStartIndex = 0; let lastPrice = null; for (let i = 0; i < numIntervals; i++) { const intervalStartTime = startTime + i * 1000; const intervalEndTime = intervalStartTime + 1000; let sumPriceVolume = 0; let sumVolume = 0; let numTrades = 0; // Iterate over trades in the current interval and calculate volume-weighted average price while (intervalStartIndex < tradesData.length && tradesData[intervalStartIndex].timestamp < intervalEndTime) { const trade = tradesData[intervalStartIndex]; const tradeWeight = trade.volume * trade.price; sumPriceVolume += tradeWeight; sumVolume += trade.volume; numTrades++; lastPrice = trade.price; intervalStartIndex++; } if (sumVolume > 0) { const intervalPrice = sumPriceVolume / sumVolume; resampledData[i] = { timestamp: intervalStartTime, price: intervalPrice, volume: sumVolume }; } else { // No trades in this interval, fill in the last price resampledData[i] = { timestamp: intervalStartTime, price: lastPrice, volume: 0 }; } } return resampledData; } 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:Tc3c,// 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 = [ [dt, 0, 0], [0, dt, 0], [0, 0, dt] ] 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:T589,freq = { function calculateMcLeodPitch(audioData) { // Step 1: Compute the autocorrelation function var corr = new Float32Array(audioData.length); for (var i = 0; i < audioData.length; i++) { corr[i] = 0; for (var j = 0; j < audioData.length - i; j++) { corr[i] += audioData[j] * audioData[j + i]; } } // Step 2: Compute the McLeod Pitch Estimate var mcleod = new Float32Array(audioData.length); var maxVal = 0; var maxIdx = 0; for (var i = 1; i < audioData.length; i++) { var val = corr[i] - 2 * corr[i - 1] + corr[i - 2]; if (val > 0) { mcleod[i] = Math.sqrt(val); if (mcleod[i] > maxVal) { maxVal = mcleod[i]; maxIdx = i; } } else { mcleod[i] = 0; } } // Step 3: Interpolate the peak value to improve the estimate var y0 = mcleod[maxIdx - 1]; var y1 = mcleod[maxIdx]; var y2 = mcleod[maxIdx + 1]; var alpha = (y1 - y0) / (2 * (y1 + y2 - 2 * y0)); var pEst = maxIdx + alpha; // Step 4: Convert the McLeod Pitch Estimate to frequency var fEst = 1000 / pEst; return fEst; } // Usage: // Assume you have an array called `audioData` that contains the audio samples // You can call the function to get the frequency estimate as follows: return calculateMcLeodPitch(firHann.map(t => t.price)); }4d:T51f,class McLeodPitchMethod { constructor(sampleRate) { this.sampleRate = sampleRate; this.frameSize = 100; this.minFreq = 1; // in Hz this.maxFreq = 10000; // in Hz this.pitch = null; this.frameBuffer = new Array(this.frameSize).fill(0); } processFrame(frame) { // shift existing frame buffer to make room for new frame this.frameBuffer.splice(0, frame.length); this.frameBuffer.push(...frame); // compute autocorrelation const acf = new Array(this.frameSize).fill(0); for (let i = 0; i < this.frameSize; i++) { for (let j = 0; j < this.frameSize - i; j++) { acf[i] += this.frameBuffer[j] * this.frameBuffer[j + i]; } } // apply square root function for (let i = 0; i < this.frameSize; i++) { acf[i] = Math.sqrt(acf[i]); } // find index of maximum value within frequency range const minIdx = Math.floor(this.minFreq * this.frameSize / this.sampleRate); const maxIdx = Math.ceil(this.maxFreq * this.frameSize / this.sampleRate); const maxIdxInRange = acf.slice(minIdx, maxIdx + 1).reduce((iMax, x, i, arr) => x > arr[iMax] ? i : iMax, 0) + minIdx; // convert index to frequency in microhertz const freq = maxIdxInRange * this.sampleRate * 1e6 / this.frameSize; this.pitch = freq; } }4e:T51c,// pitchSimple = { // function pitchDetection(sampleRate, signal) { // // Compute the autocorrelation of the signal // let r = autocorrelation(signal); // // Find the peak of the autocorrelation function // let peakIndex = findPeak(r); // // Compute the pitch period in samples // let period = peakIndex; // // Compute the pitch frequency in Hz // let frequency = sampleRate / period; // return frequency; // } // function autocorrelation(signal) { // let len = signal.length; // let r = new Float32Array(len); // let mean = 0; // for (let i = 0; i < len; i++) { // mean += signal[i]; // } // mean /= len; // for (let lag = 0; lag < len; lag++) { // let sum = 0; // for (let i = 0; i < len - lag; i++) { // sum += (signal[i] - mean) * (signal[i + lag] - mean); // } // r[lag] = sum / (len - lag); // } // return r; // } // function findPeak(r) { // let len = r.length; // let maxVal = -1; // let maxIndex = -1; // for (let i = 0; i < len; i++) { // if (r[i] > maxVal) { // maxVal = r[i]; // maxIndex = i; // } // } // return maxIndex; // } // return pitchDetection(44100, filteredStates.map(t => t.velocity)) // }4f:T463,// pitchCycle = { // function mcleodPitchMethod(data) { // // Compute autocorrelation // const r = new Array(data.length).fill(0); // for (let tau = 0; tau < data.length; tau++) { // let sum = 0; // for (let i = 0; i < data.length - tau; i++) { // sum += data[i] * data[i + tau]; // } // r[tau] = sum; // } // // Find maximum peak in autocorrelation function // let maxVal = -Infinity; // let maxIndex = -1; // for (let i = 1; i < r.length; i++) { // if (r[i] > maxVal) { // maxVal = r[i]; // maxIndex = i; // } // } // // Compute frequency from index of maximum peak // const frequency = maxIndex / data.length; // // Convert frequency to Microhertz // const frequencyMicroHz = frequency * 1000000; // // Calculate sign of first difference // let sign = null; // if (data.length > 1) { // sign = Math.sign(data[1] - data[0]); // } // return { // frequencyMicroHz, // sign, // }; // } // return mcleodPitchMethod(firHann.map(t => t.firHann)); // }50:T865,class PitchIndicator { constructor(sampleRate) { this.sampleRate = sampleRate; this.pitch = -1; this.accuracy = 0; this.bufferSize = sampleRate * 0.1; // Use a buffer size of 100 ms this.inputBuffer = new Float32Array(this.bufferSize); this.corrBuffer = new Float32Array(this.bufferSize); this.cepsBuffer = new Float32Array(this.bufferSize); this.cepsLifter = new Float32Array(this.bufferSize); this.cepsPeak = 0; this.cepsMaxVal = -Infinity; this.cepsReady = false; } process(sample) { // Add new sample to the input buffer this.inputBuffer.set(this.inputBuffer.subarray(1)); this.inputBuffer[this.inputBuffer.length - 1] = sample; // Calculate autocorrelation this.corrBuffer.fill(0); for (let i = 0; i < this.bufferSize; i++) { for (let j = 0; j < this.bufferSize - i; j++) { this.corrBuffer[i] += this.inputBuffer[j] * this.inputBuffer[j + i]; } } // Calculate cepstrum this.cepsBuffer.fill(0); for (let i = 0; i < this.bufferSize; i++) { for (let j = 0; j < i; j++) { this.cepsBuffer[i] += this.corrBuffer[j] * this.cepsBuffer[i - j]; } this.cepsBuffer[i] = Math.log(Math.abs(this.cepsBuffer[i] + 1e-10)); } // Apply liftering this.cepsLifter.fill(0); let lifterSize = Math.round(this.sampleRate / 2000); // Use a lifter size of 5 ms for (let i = 0; i < lifterSize; i++) { this.cepsLifter[i] = 1; } for (let i = this.bufferSize - lifterSize; i < this.bufferSize; i++) { this.cepsLifter[i] = 1; } for (let i = 0; i < this.bufferSize; i++) { this.cepsBuffer[i] *= this.cepsLifter[i]; } // Find pitch estimate if (this.cepsReady) { for (let i = 0; i < this.bufferSize / 2; i++) { if (this.cepsBuffer[i] > this.cepsMaxVal) { this.cepsPeak = i; this.cepsMaxVal = this.cepsBuffer[i]; } } this.pitch = this.sampleRate / this.cepsPeak; this.accuracy = this.cepsMaxVal; } this.cepsReady = true; return { pitch: this.pitch, accuracy: this.accuracy, }; } }51:[] 29:{"id":"f7a6653bb390c3d6","slug":null,"title":"Crypto Analysis log returns/kalman 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'FISUSDT'","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":515,"value":"timeRange = ({\n start: new Date('2023-03-12T14:53:00Z'),\n end: new Date('2023-03-12T15:13:00Z'),\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":537,"value":"firstTrade = {\n const start = timeRange.start.getTime()\n return (\n // https://binance-docs.github.io/apidocs/spot/en/#compressed-aggregate-trades-list\n await fetch(`https://api.binance.com/api/v3/aggTrades?symbol=${symbol}&startTime=${start}&endTime=${start + 3600000}&limit=1`)\n ).json()\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"trades = {\n const start = timeRange.start.getTime()\n const end = timeRange.end.getTime()\n\n const firstTradeId = (await (\n // https://binance-docs.github.io/apidocs/spot/en/#compressed-aggregate-trades-list\n await fetch(`https://api.binance.com/api/v3/aggTrades?symbol=${symbol}&startTime=${start}&endTime=${start + 3600000}&limit=1`)\n ).json())[0].a\n\n let result = new Map()\n let lastTradeId = firstTradeId\n infinitLoop: while (true) {\n // https://binance-docs.github.io/apidocs/spot/en/#compressed-aggregate-trades-list\n const endpoint = `https://api.binance.com/api/v3/aggTrades?symbol=${symbol}&fromId=${lastTradeId}&limit=1000`\n const response = await fetch(endpoint)\n const tradesPage = await response.json()\n if (tradesPage.length === 0) break\n for (const trade of tradesPage) {\n if (trade.T > end) break infinitLoop\n result.set(trade.a, trade)\n }\n } \n return Array.from(result.values())\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":40,"value":"class CryptoPriceIndicator {\n constructor() {\n this.previousPrice = null;\n this.normalizedPrice = 100;\n }\n\n update(price) {\n let logReturn\n if (this.previousPrice !== null) {\n logReturn = Math.log(price / this.previousPrice);\n this.normalizedPrice *= Math.exp(logReturn);\n }\n\n this.previousPrice = price;\n return {\n normalizedPrice: Math.round(this.normalizedPrice * 10),\n logReturn: logReturn || 0,\n }\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"normalizedTrades = trades.sort((a, b) => a.T - b.T).map(t => ({\n timestamp: t.T,\n price: parseFloat(t.p),\n volume: parseFloat(t.q),\n}))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":4,"value":"$49","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":18,"value":"resampledTradesData = resampleTradesData(normalizedTrades).map(t => ({...t, timestamp: new Date(t.timestamp)}))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":51,"value":"resampledTrades = {\n const normalizer = new CryptoPriceIndicator();\n return resampledTradesData.map(t => {\n const normalizerResult = normalizer.update(t.price)\n return {\n ...t,\n ...normalizerResult,\n }\n })\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":345,"value":"secondsToPlot = 1100 // Five minutes","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":20,"value":"Plot.plot({\n marks: [\n Plot.lineY(resampledTrades.slice(-secondsToPlot), {x: 'timestamp', y: 'normalizedPrice'})\n ],\n grid: true,\n style: {\n width: 1024,\n }\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":502,"value":"class PriceElasticityIndicator {\n updateTick(tick) {\n if (!this.previousTick) {\n this.previousTick = tick\n return null\n }\n\n const priceChange = Math.log(tick.normalizedPrice / this.previousTick.normalizedPrice)\n const volumeChange = Math.log(tick.volume / this.previousTick.volume)\n\n if (priceChange === 0) {\n if (this.previousElasticity) {\n return this.previousElasticity\n }\n return null\n }\n\n const elasticity = volumeChange / priceChange\n\n this.previousTick = tick\n this.previousElasticity = elasticity\n return elasticity\n }\n}\n","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":504,"value":"elasticity = {\n const elasticityIndicator = new PriceElasticityIndicator();\n return resampledTrades.map(t => ({\n ...t,\n elasticity: elasticityIndicator.updateTick(t),\n }))\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":427,"value":"KalmanJS = require('https://bundle.run/kalmanjs@1.1.0')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":442,"value":"filtedTrades = {\n // Apply kalman filter\n const kalmanFilterPrice = new KalmanJS({R: 0.01, Q: 1/60, A: 1.1});\n const kalmanFilterLogReturns = new KalmanJS({R: 0.01, Q: 20, A: 1.1});\n return resampledTrades.map(t => ({\n ...t,\n filteredPrice: kalmanFilterPrice.filter(t.normalizedPrice),\n filteredLogReturn: kalmanFilterLogReturns.filter(t.logReturn),\n }))\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":464,"value":"Plot.plot({\n marks: [\n // Plot.lineY(filtedTrades.slice(-secondsToPlot), {x: 'timestamp', y: 'normalizedPrice'}),\n Plot.lineY(filtedTrades.slice(-secondsToPlot), {x: 'timestamp', y: 'filteredPrice', stroke: 'blue'})\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":"$undefined"},{"id":438,"value":"Plot.plot({\n marks: [\n Plot.lineY(filtedTrades.slice(-secondsToPlot), {x: 'timestamp', y: 'logReturn'}),\n Plot.lineY(filtedTrades.slice(-secondsToPlot), {x: 'timestamp', y: 'filteredLogReturn', stroke: 'blue'})\n ],\n grid: true,\n style: {\n width: 1024,\n }\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":26,"value":"class FIRHann {\n constructor(length) {\n this.length = length;\n this.derivativeValues = [];\n this.filterValue = 0;\n this.filterCoefficient = 0;\n }\n\n update(close, open) {\n const derivative = close - open;\n this.derivativeValues.unshift(derivative);\n if (this.derivativeValues.length > this.length) {\n this.derivativeValues.pop();\n }\n\n this.filterValue = 0;\n this.filterCoefficient = 0;\n for (let count = 1; count <= this.length; count++) {\n const filterCoefficient = 1 - Math.cos(2 * Math.PI * count / (this.length + 1));\n this.filterValue += filterCoefficient * this.derivativeValues[count - 1];\n this.filterCoefficient += filterCoefficient;\n }\n\n if (this.filterCoefficient !== 0) {\n this.filterValue /= this.filterCoefficient;\n } else {\n this.filterValue = 0;\n }\n\n return this.filterValue;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":28,"value":"firHann = {\n const indicator = new FIRHann(30);\n const result = []\n\n resampledTrades.forEach((trade, i) => {\n if (i === 0) return\n const firHann = indicator.update(trade.normalizedPrice, resampledTrades[i-1].normalizedPrice);\n result.push({\n timestamp: trade.timestamp,\n firHann,\n price: trade.price,\n })\n })\n\n return result\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":259,"value":"acceleration = {\n const data = firHann.map(t => ({...t, speed: t.firHann, timestamp: t.timestamp.getTime() / 1000}))\n \n // Step 2: Calculate change in speed\n const speedDeltas = data.map((item, index) => {\n if (index === 0) {\n return 0; // no previous speed, so delta is 0\n } else {\n return item.speed - data[index - 1].speed;\n }\n });\n \n // Step 3: Calculate time intervals\n const timeDeltas = data.map((item, index) => {\n if (index === 0) {\n return 0; // no previous timestamp, so delta is 0\n } else {\n return item.timestamp - data[index - 1].timestamp;\n }\n });\n \n // Step 4: Calculate acceleration\n const accelerations = speedDeltas.map((delta, index) => {\n let acceleration = 0\n if (index !== 0) {\n acceleration = delta / timeDeltas[index]\n }\n return {\n ...data[index],\n acceleration: delta / timeDeltas[index],\n timestamp: new Date(Math.round(data[index].timestamp * 1000))\n };\n });\n\n return accelerations\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":327,"value":"Plot.plot({\n marks: [\n Plot.lineY(acceleration.slice(-secondsToPlot), {x: 'timestamp', y: 'speed', stroke: 'green'}),\n Plot.lineY(acceleration.slice(-secondsToPlot), {x: 'timestamp', y: 'acceleration', stroke: 'red'}),\n ],\n grid: true,\n style: {\n width: 1024,\n }\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":471,"value":"class FIRRLS {\n constructor(length, forgettingFactor) {\n this.length = length;\n this.forgettingFactor = forgettingFactor;\n this.theta = Array(length).fill(0);\n this.P = Array.from({\n length: length\n }, (_, i) => {\n const initValue = 1 / (i + 1) / forgettingFactor;\n return Array.from({\n length: length\n }, (_, j) => i === j ? initValue : 0);\n });\n }\n\n update(close, open) {\n const derivative = close - open;\n const x = [derivative, ...this.theta.slice(0, -1)];\n const y = x.reduce((sum, xi, i) => sum + xi * this.theta[i], 0);\n const e = derivative - y;\n const k = this.P.map(row => row.map(v => v * x.reduce((sum, xi, i) => sum + xi * row[i], 0)));\n const denominator = this.forgettingFactor + k.flat().reduce((sum, v) => sum + v, 0);\n this.P = this.P.map((row, i) => row.map((v, j) => v - k[i][j] / denominator));\n this.theta = this.theta.map((v, i) => v + k[i][0] * e / denominator);\n return this.theta[0];\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":474,"value":"firRLS = {\n const indicator = new FIRRLS(12, 0.0001);\n const result = []\n\n resampledTrades.forEach((trade, i) => {\n if (i === 0) return\n const rls = indicator.update(trade.normalizedPrice, resampledTrades[i-1].normalizedPrice);\n result.push({\n timestamp: trade.timestamp,\n rls,\n price: trade.price,\n })\n })\n\n return result\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":484,"value":"Plot.plot({\n marks: [\n Plot.lineY(firRLS.slice(-secondsToPlot), {x: 'timestamp', y: 'rls'})\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":"$undefined"},{"id":221,"value":"firHannTrend = {\n const indicator = new FIRHann(Math.round(240));\n const result = []\n\n resampledTrades.forEach((trade, i) => {\n if (i === 0) return\n const firHann = indicator.update(trade.normalizedPrice, resampledTrades[i-1].normalizedPrice);\n result.push({\n timestamp: trade.timestamp,\n firHann,\n price: trade.price,\n })\n })\n\n return result\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":225,"value":"Plot.plot({\n marks: [\n Plot.lineY(firHannTrend.slice(-secondsToPlot), {x: 'timestamp', y: 'firHann'})\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":"$undefined"},{"id":482,"value":"Plot.plot({\n marks: [\n Plot.lineY(firHannTrend.slice(-secondsToPlot), {x: 'timestamp', y: 'firHann'})\n ],\n grid: true,\n style: {\n width: 1024,\n }\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":199,"value":"class KalmanSmoother {\n constructor() {\n this.A = 1; // State transition matrix\n this.H = 1; // Observation matrix\n this.Q = 0.01; // Process noise covariance\n this.R = 1; // Observation noise covariance\n this.P = 1; // Estimate error covariance\n\n this.x = 0; // Initial state estimate\n this.K = 0; // Kalman Gain\n }\n\n smooth(data) {\n let smoothedData = [];\n let n = data.length;\n\n for (let i = 0; i < n; i++) {\n // Predicted state estimate\n let x_hat = this.A * this.x;\n // Predicted error covariance\n let P_hat = this.A * this.P * this.A + this.Q;\n // Kalman Gain\n this.K = P_hat * this.H / (P_hat * this.H * this.H + this.R);\n // Updated state estimate\n this.x = x_hat + this.K * (data[i] - this.H * x_hat);\n // Updated error covariance\n this.P = (1 - this.K * this.H) * P_hat;\n smoothedData.push(this.x);\n }\n\n return smoothedData;\n }\n} ","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":201,"value":"smoothedData = new KalmanSmoother().smooth(resampledTrades.map(t => t.normalizedPrice))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":203,"value":"Plot.plot({\n marks: [\n Plot.lineY(smoothedData.slice(-secondsToPlot)),\n // Plot.lineY(filteredStates.slice(-180), {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":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":81,"value":"$4a","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":83,"value":"$4b","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":85,"value":"filteredStates = {\n const data = resampledTrades.map((t, i) => ({...t, smoothed: smoothedData[i]}))\n \n const dt = 1/60\n const state2 = { price: data[0].smoothed, 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 data.forEach((observation, i) => {\n filter.update(observation.smoothed, [[1/60]])\n const state = {\n ...observation,\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}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":88,"value":"Plot.plot({\n marks: [\n Plot.lineY(filteredStates.slice(-secondsToPlot), {x: 'timestamp', y: 'price'}),\n Plot.lineY(filteredStates.slice(-secondsToPlot), {x: 'timestamp', y: 'predictedPrice', stroke: 'grey'}),\n // Plot.lineY(filteredStates.slice(-100), {x: 'timestamp', y: 'price', stroke: 'lightgrey'}),\n // Plot.dot(filteredStates.slice(499).slice(-300), {x: 'timestamp', y: 'predictedPrice', stroke: 'grey'}),\n ],\n grid: true,\n style: {\n width: 1024,\n }\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":96,"value":"Plot.plot({\n marks: [\n Plot.lineY(filteredStates.slice(-secondsToPlot), {x: 'timestamp', y: 'velocity', stroke: 'green'}),\n Plot.lineY(filteredStates.slice(60, 240), {x: 'timestamp', y: 'acceleration', stroke: 'red'}),\n // Plot.lineY(filteredStates.slice(60, 240), {x: 'timestamp', y: 'predictedVelocity', stroke: 'lightgreen'}),\n // Plot.lineY(filteredStates.slice(60, 240), {x: 'timestamp', y: 'predictedAcceleration', stroke: 'pink'}),\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":"$undefined"},{"id":334,"value":"kineticEnergy = {\n function calculateKineticEnergy(mass, velocity) {\n // Calculate kinetic energy using the formula KE = 0.5 * m * v^2\n const kineticEnergy = 0.5 * mass * velocity ** 2;\n \n return kineticEnergy;\n }\n\n return filteredStates.map(t => ({\n ...t,\n kineticEnergy: calculateKineticEnergy(t.volume, t.velocity)\n }))\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":341,"value":"Plot.plot({\n marks: [\n Plot.lineY(kineticEnergy.slice(-secondsToPlot), {x: 'timestamp', y: 'velocity', stroke: 'green'}),\n Plot.lineY(kineticEnergy.slice(-secondsToPlot), {x: 'timestamp', y: 'kineticEnergy', stroke: 'blue'}),\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":"$undefined"},{"id":408,"value":"firHannSmoothed = {\n const indicator = new FIRHann(30);\n const result = []\n\n smoothedData.forEach((x, i) => {\n if (i === 0) return\n const firHann = indicator.update(x, smoothedData[i-1]);\n result.push(firHann)\n })\n\n return result\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":412,"value":"Plot.plot({\n marks: [\n Plot.lineY(firHannSmoothed.slice(-secondsToPlot)),\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":177,"value":"$4c","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":165,"value":"$4d","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":167,"value":"mcleod = {\n const indicator = new McLeodPitchMethod(1);\n return indicator.processFrame(firHann.slice(-300));\n // const result = []\n\n // firHann.forEach((trade, i) => {\n // if (i === 0) return\n // const mcleod = indicator.processFrame([trade.firHann]);\n // result.push({\n // timestamp: trade.timestamp,\n // mcleod,\n // price: trade.price,\n // })\n // })\n\n // return result\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":152,"value":"$4e","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":156,"value":"$4f","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":117,"value":"$50","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":119,"value":"// pitch = {\n// let pitchIndicator = new PitchIndicator(44100);\n// const result = []\n\n// filteredStates.slice(100).forEach((trade, i) => {\n// if (i === 0) return\n// let pitch = pitchIndicator.process(trade.velociity);\n// result.push({\n// timestamp: trade.timestamp,\n// pitch: pitch.pitch,\n// pitchAccuracy: pitch.accuracy,\n// price: trade.price,\n// })\n// })\n\n// return result\n// }","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":127,"value":"// Plot.plot({\n// marks: [\n// Plot.lineY(pitch, {x: 'timestamp', y: 'pitch', stroke: 'blue'}),\n// // Plot.lineY(filteredStates.slice(-300), {x: 'timestamp', y: 'acceleration', stroke: 'red'}),\n// ],\n// grid: true,\n// style: {\n// width: 1024,\n// }\n// })","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":132,"value":"Plot.plot({\n marks: [\n Plot.lineY(pitch.slice(-300), {x: 'timestamp', y: 'pitchAccuracy', stroke: 'blue'}),\n // Plot.lineY(filteredStates.slice(-300), {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":"$undefined"}],"files":"$W51","stdlib":"1"}} 24:null