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Add TEMA (Triple Exponential Moving Average) implementation and validation tests
- Implemented TEMA calculation in QuanTAlib with O(1) update complexity. - Added validation tests for TEMA against Skender, TA-Lib, and Tulip indicators. - Updated documentation for TEMA, including its mathematical foundation and usage examples. - Enhanced existing tests for other indicators (TRIMA, WMA) to generate more records. - Adjusted benchmark tests to include DEMA and TEMA comparisons. - Refactored code for better readability and performance, including zero-allocation Span API.
This commit is contained in:
Miha Kralj
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#!meta
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{"kernelInfo":{"defaultKernelName":"csharp","items":[{"name":"csharp"},{"name":"fsharp","languageName":"F#","aliases":["f#","fs"]},{"name":"html","languageName":"HTML"},{"name":"http","languageName":"HTTP"},{"name":"javascript","languageName":"JavaScript","aliases":["js"]},{"name":"mermaid","languageName":"Mermaid"},{"name":"pwsh","languageName":"PowerShell","aliases":["powershell"]},{"name":"value"}]}}
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#!markdown
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# Triple Exponential Moving Average (TEMA) Examples
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This is a **.NET Interactive** notebook. To run it, you need the [Polyglot Notebooks](https://marketplace.visualstudio.com/items?itemName=ms-dotnettools.dotnet-interactive-vscode) extension installed in VS Code.
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For detailed documentation on the TEMA indicator, including mathematical formulas and interpretation, please refer to [Tema.md](Tema.md).
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The **Triple Exponential Moving Average (TEMA)** is a technical indicator designed to reduce the lag associated with traditional moving averages even further than DEMA. It combines single, double, and triple EMAs to achieve superior responsiveness.
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This notebook demonstrates:
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1. **Manual Data Processing**: Understanding Batch vs. Streaming modes.
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2. **Streaming with `isNew`**: Handling intra-bar updates.
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3. **Large Dataset Processing**: Using Geometric Brownian Motion (GBM) generated data.
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4. **Handling Invalid Values**: Last-value substitution for NaN/Infinity.
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#!csharp
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// Reference the library
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#r "..\..\bin\QuanTAlib.dll"
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using System;
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using System.Linq;
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using QuanTAlib;
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// Helper to print TSeries
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void PrintSeries(TSeries series, int count = 5)
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{
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Console.WriteLine($"Series Length: {series.Count}");
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foreach (var item in series.Take(count))
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{
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Console.WriteLine($"Time: {item.Time:HH:mm:ss}, Value: {item.Value:F2}");
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}
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if (series.Count > count) Console.WriteLine("...");
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}
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#!markdown
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## 1. Manual Data: Batch vs. Streaming
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We'll start with a small, manually created dataset to clearly see how Batch and Streaming operations work.
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### Batch Processing
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Batch processing calculates the TEMA for the entire dataset at once. This is efficient for historical analysis.
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#!csharp
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// Create a small manual dataset
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var manualData = new TSeries();
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manualData.Add(DateTime.Now, 100.0);
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manualData.Add(DateTime.Now.AddMinutes(1), 102.0);
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manualData.Add(DateTime.Now.AddMinutes(2), 101.0);
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manualData.Add(DateTime.Now.AddMinutes(3), 103.0);
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manualData.Add(DateTime.Now.AddMinutes(4), 105.0);
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Console.WriteLine("--- Input Data ---");
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PrintSeries(manualData, 5);
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// Batch Calculation
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Console.WriteLine("\n--- Batch TEMA (Period 3) ---");
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var temaBatch = new Tema(3);
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var resultBatch = temaBatch.Update(manualData);
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PrintSeries(resultBatch, 5);
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#!markdown
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### Streaming Processing
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Streaming processing updates the TEMA one data point at a time. This is essential for real-time trading systems where data arrives sequentially.
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#!csharp
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Console.WriteLine("\n--- Streaming TEMA (Period 3) ---");
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var temaStream = new Tema(3);
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foreach (var item in manualData)
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{
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var result = temaStream.Update(item);
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Console.WriteLine($"Time: {item.Time:HH:mm:ss}, Input: {item.Value:F2}, TEMA: {result.Value:F2}, IsHot: {temaStream.IsHot}");
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}
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// Verify that the last values match
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var batchLast = resultBatch.Last().Value;
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var streamLast = temaStream.Value.Value;
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Console.WriteLine($"\nMatch: {Math.Abs(batchLast - streamLast) < 1e-10} (Batch: {batchLast:F2}, Stream: {streamLast:F2})");
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#!markdown
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## 2. Streaming with `isNew` (Intra-bar Updates)
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In real-time feeds, you often receive multiple updates for the *same* bar (e.g., price changes within the current minute) before the bar closes.
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* `isNew = true`: The input is a new bar (advances time).
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* `isNew = false`: The input is an update to the current bar (recalculates without advancing).
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#!csharp
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Console.WriteLine("\n--- Streaming with Intra-bar Updates ---");
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var temaIntra = new Tema(3);
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// 1. Process the first 4 bars normally
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for (int i = 0; i < 4; i++)
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{
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temaIntra.Update(manualData[i]);
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}
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Console.WriteLine($"After 4th bar: {temaIntra.Value.Value:F2}");
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// 2. Simulate intra-bar updates for the 5th bar (Final value is 105.0)
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// Update 1: Price moves to 104.0
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var update1 = new TValue(manualData[4].Time, 104.0);
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temaIntra.Update(update1, isNew: true); // First update for this bar is "New"
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Console.WriteLine($"Update 1 (104.0): {temaIntra.Value.Value:F2}");
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// Update 2: Price moves to 106.0 (Same time, same bar)
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var update2 = new TValue(manualData[4].Time, 106.0);
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temaIntra.Update(update2, isNew: false); // Not new, just an update
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Console.WriteLine($"Update 2 (106.0): {temaIntra.Value.Value:F2}");
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// Update 3: Final Close at 105.0
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var update3 = manualData[4];
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temaIntra.Update(update3, isNew: false); // Final update
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Console.WriteLine($"Update 3 (105.0): {temaIntra.Value.Value:F2}");
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// Verify match with batch result
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Console.WriteLine($"Match with Batch: {Math.Abs(temaIntra.Value.Value - batchLast) < 1e-10}");
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#!markdown
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## 3. Large Dataset: Geometric Brownian Motion (GBM)
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We'll generate a larger dataset (1000 bars) using a Geometric Brownian Motion generator to simulate realistic market data.
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#!csharp
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// Generate 1000 bars of data
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var gbm = new GBM(startPrice: 100.0, mu: 0.05, sigma: 0.2);
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var gbmData = gbm.Fetch(1000, DateTime.Now.Ticks, TimeSpan.FromMinutes(1));
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var closeSeries = gbmData.Close;
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Console.WriteLine($"Generated {closeSeries.Count} bars of GBM data.");
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Console.WriteLine($"First 5 values: {string.Join(", ", closeSeries.Take(5).Select(x => x.Value.ToString("F2")))}");
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#!markdown
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### Batch vs. Streaming Performance on Large Data
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#!csharp
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// Batch
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var temaLargeBatch = new Tema(20);
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var batchLargeResult = temaLargeBatch.Update(closeSeries);
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Console.WriteLine($"Batch Last Value: {batchLargeResult.Last().Value:F2}");
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// Streaming
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var temaLargeStream = new Tema(20);
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TValue lastStreamVal = default;
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foreach(var item in closeSeries)
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{
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lastStreamVal = temaLargeStream.Update(item);
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}
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Console.WriteLine($"Streaming Last Value: {lastStreamVal.Value:F2}");
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#!markdown
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## 4. Handling Invalid Values (NaN/Infinity)
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`Tema` uses **last-value substitution** for invalid inputs. When a non-finite value (NaN, PositiveInfinity, NegativeInfinity) is encountered, it is replaced with the last valid value. This provides output continuity instead of propagating invalid values through the calculation.
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#!csharp
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Console.WriteLine("\n--- Handling Invalid Values ---");
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// Single TEMA
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var temaNaN = new Tema(10);
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// Feed valid values first
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temaNaN.Update(new TValue(DateTime.Now, 100.0));
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temaNaN.Update(new TValue(DateTime.Now.AddMinutes(1), 110.0));
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Console.WriteLine($"After valid values: {temaNaN.Value.Value:F2}");
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// Feed NaN - should use last valid value (110)
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var resultAfterNaN = temaNaN.Update(new TValue(DateTime.Now.AddMinutes(2), double.NaN));
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Console.WriteLine($"After NaN input: {resultAfterNaN.Value:F2} (IsFinite: {double.IsFinite(resultAfterNaN.Value)})");
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// Feed Infinity - should use last valid value (110)
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var resultAfterInf = temaNaN.Update(new TValue(DateTime.Now.AddMinutes(3), double.PositiveInfinity));
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Console.WriteLine($"After Infinity input: {resultAfterInf.Value:F2} (IsFinite: {double.IsFinite(resultAfterInf.Value)})");
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// Continue with valid value
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var resultAfterValid = temaNaN.Update(new TValue(DateTime.Now.AddMinutes(4), 120.0));
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Console.WriteLine($"After valid value (120): {resultAfterValid.Value:F2}");
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#!csharp
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Console.WriteLine("\n--- Batch Processing with Invalid Values ---");
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// Create series with NaN values interspersed
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var seriesWithNaN = new TSeries();
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seriesWithNaN.Add(DateTime.Now.Ticks, 100.0);
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seriesWithNaN.Add(DateTime.Now.Ticks + 1, 110.0);
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seriesWithNaN.Add(DateTime.Now.Ticks + 2, double.NaN);
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seriesWithNaN.Add(DateTime.Now.Ticks + 3, 120.0);
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seriesWithNaN.Add(DateTime.Now.Ticks + 4, double.PositiveInfinity);
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seriesWithNaN.Add(DateTime.Now.Ticks + 5, 130.0);
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var temaBatchNaN = new Tema(3);
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var resultsWithNaN = temaBatchNaN.Update(seriesWithNaN);
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Console.WriteLine("Input → Output:");
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for (int i = 0; i < seriesWithNaN.Count; i++)
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{
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var input = seriesWithNaN[i].Value;
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var output = resultsWithNaN[i].Value;
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var inputStr = double.IsFinite(input) ? input.ToString("F2") : input.ToString();
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Console.WriteLine($" {inputStr,-10} → {output:F2} (IsFinite: {double.IsFinite(output)})");
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}
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@@ -0,0 +1,65 @@
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using System.Drawing;
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using TradingPlatform.BusinessLayer;
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namespace QuanTAlib;
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public class TemaIndicator : Indicator, IWatchlistIndicator
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{
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[InputParameter("Period", sortIndex: 1, 1, 1000, 1, 0)]
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public int Period { get; set; } = 10;
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[IndicatorExtensions.DataSourceInput]
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public SourceType Source { get; set; } = SourceType.Close;
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[InputParameter("Show cold values", sortIndex: 21)]
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public bool ShowColdValues { get; set; } = true;
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private Tema? ma;
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protected LineSeries? Series;
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protected string? SourceName;
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private int _warmupBarIndex = -1;
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public int MinHistoryDepths => Period;
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int IWatchlistIndicator.MinHistoryDepths => MinHistoryDepths;
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public override string ShortName => $"TEMA {Period}:{SourceName}";
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public override string SourceCodeLink => "https://github.com/mihakralj/QuanTAlib/blob/main/lib/averages/tema/Tema.Quantower.cs";
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public TemaIndicator()
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{
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OnBackGround = true;
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SeparateWindow = false;
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SourceName = Source.ToString();
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Name = "TEMA - Triple Exponential Moving Average";
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Description = "Triple Exponential Moving Average";
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Series = new(name: $"TEMA {Period}", color: IndicatorExtensions.Averages, width: 2, style: LineStyle.Solid);
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AddLineSeries(Series);
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}
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protected override void OnInit()
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{
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ma = new Tema(Period);
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SourceName = Source.ToString();
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_warmupBarIndex = -1;
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base.OnInit();
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}
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protected override void OnUpdate(UpdateArgs args)
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{
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TValue input = this.GetInputValue(args, Source);
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bool isNew = args.Reason == UpdateReason.NewBar || args.Reason == UpdateReason.HistoricalBar;
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TValue result = ma!.Update(input, isNew);
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Series!.SetValue(result.Value);
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Series!.SetMarker(0, Color.Transparent);
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if (_warmupBarIndex < 0 && ma!.IsHot)
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_warmupBarIndex = Count;
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}
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public override void OnPaintChart(PaintChartEventArgs args)
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{
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base.OnPaintChart(args);
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int warmupPeriod = _warmupBarIndex > 0 ? _warmupBarIndex : Count;
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this.PaintSmoothCurve(args, Series!, warmupPeriod, showColdValues: ShowColdValues, tension: 0.2);
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}
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}
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@@ -0,0 +1,266 @@
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namespace QuanTAlib.Tests;
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public class TemaTests
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{
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[Fact]
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public void Tema_Constructor_Period_ValidatesInput()
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{
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Assert.Throws<ArgumentException>(() => new Tema(0));
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Assert.Throws<ArgumentException>(() => new Tema(-1));
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var tema = new Tema(10);
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Assert.NotNull(tema);
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}
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[Fact]
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public void Tema_Constructor_Alpha_ValidatesInput()
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{
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Assert.Throws<ArgumentException>(() => new Tema(0.0));
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Assert.Throws<ArgumentException>(() => new Tema(-0.1));
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Assert.Throws<ArgumentException>(() => new Tema(1.1));
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var tema = new Tema(0.5);
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Assert.NotNull(tema);
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}
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[Fact]
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public void Tema_Calc_ReturnsValue()
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{
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var tema = new Tema(10);
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Assert.Equal(0, tema.Value.Value);
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TValue result = tema.Update(new TValue(DateTime.UtcNow, 100));
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Assert.True(result.Value > 0);
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Assert.Equal(result.Value, tema.Value.Value);
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}
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[Fact]
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public void Tema_Calc_IsNew_AcceptsParameter()
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{
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var tema = new Tema(10);
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tema.Update(new TValue(DateTime.UtcNow, 100), isNew: true);
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double value1 = tema.Value;
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tema.Update(new TValue(DateTime.UtcNow, 105), isNew: true);
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double value2 = tema.Value;
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// Values should change with new bars
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Assert.NotEqual(value1, value2);
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}
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[Fact]
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public void Tema_Calc_IsNew_False_UpdatesValue()
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{
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var tema = new Tema(10);
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tema.Update(new TValue(DateTime.UtcNow, 100));
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tema.Update(new TValue(DateTime.UtcNow, 110), isNew: true);
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double beforeUpdate = tema.Value;
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tema.Update(new TValue(DateTime.UtcNow, 120), isNew: false);
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double afterUpdate = tema.Value;
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// Update should change the value
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Assert.NotEqual(beforeUpdate, afterUpdate);
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}
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[Fact]
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public void Tema_Reset_ClearsState()
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{
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var tema = new Tema(10);
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tema.Update(new TValue(DateTime.UtcNow, 100));
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tema.Update(new TValue(DateTime.UtcNow, 105));
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double valueBefore = tema.Value;
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tema.Reset();
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Assert.Equal(0, tema.Value.Value);
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// After reset, should accept new values
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tema.Update(new TValue(DateTime.UtcNow, 50));
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Assert.NotEqual(0, tema.Value.Value);
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Assert.NotEqual(valueBefore, tema.Value.Value);
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}
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[Fact]
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public void Tema_Properties_Accessible()
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{
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var tema = new Tema(10);
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Assert.Equal(0, tema.Value.Value);
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Assert.False(tema.IsHot);
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tema.Update(new TValue(DateTime.UtcNow, 100));
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Assert.NotEqual(0, tema.Value.Value);
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}
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[Fact]
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public void Tema_IsHot_BecomesTrueAfterWarmup()
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{
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var tema = new Tema(10);
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// Initially IsHot should be false
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Assert.False(tema.IsHot);
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// TEMA needs more warmup than EMA due to triple smoothing
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int steps = 0;
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while (!tema.IsHot && steps < 1000)
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{
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tema.Update(new TValue(DateTime.UtcNow, 100));
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steps++;
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}
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Assert.True(tema.IsHot);
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Assert.True(steps > 0);
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}
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[Fact]
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public void Tema_PeriodEquivalence_BothConstructorsWork()
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{
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int period = 20;
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double alpha = 2.0 / (period + 1);
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var temaPeriod = new Tema(period);
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var temaAlpha = new Tema(alpha);
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// Both should accept Calc calls and produce same result
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TValue result1 = temaPeriod.Update(new TValue(DateTime.UtcNow, 100));
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TValue result2 = temaAlpha.Update(new TValue(DateTime.UtcNow, 100));
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Assert.Equal(result1.Value, result2.Value, 1e-10);
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}
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[Fact]
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public void Tema_IterativeCorrections_RestoreToOriginalState()
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{
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var tema = new Tema(10);
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var gbm = new GBM(startPrice: 100.0, mu: 0.02, sigma: 0.1);
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// Feed 10 new values
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TValue tenthInput = default;
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for (int i = 0; i < 10; i++)
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{
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var bar = gbm.Next(isNew: true);
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tenthInput = new TValue(bar.Time, bar.Close);
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tema.Update(tenthInput, isNew: true);
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}
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// Remember TEMA state after 10 values
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double temaAfterTen = tema.Value;
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// Generate 9 corrections with isNew=false (different values)
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for (int i = 0; i < 9; i++)
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{
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var bar = gbm.Next(isNew: false);
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tema.Update(new TValue(bar.Time, bar.Close), isNew: false);
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}
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// Feed the remembered 10th input again with isNew=false
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||||
TValue finalTema = tema.Update(tenthInput, isNew: false);
|
||||
|
||||
// TEMA should match the original state after 10 values
|
||||
Assert.Equal(temaAfterTen, finalTema.Value, 1e-10);
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Tema_BatchCalc_MatchesIterativeCalc()
|
||||
{
|
||||
var temaIterative = new Tema(10);
|
||||
var temaBatch = new Tema(10);
|
||||
var gbm = new GBM(startPrice: 100.0, mu: 0.02, sigma: 0.1);
|
||||
|
||||
// Generate data
|
||||
var series = new TSeries();
|
||||
for (int i = 0; i < 100; i++)
|
||||
{
|
||||
var bar = gbm.Next(isNew: true);
|
||||
series.Add(bar.Time, bar.Close);
|
||||
}
|
||||
|
||||
Assert.True(series.Count > 0);
|
||||
|
||||
// Calculate iteratively
|
||||
var iterativeResults = new TSeries();
|
||||
foreach (var item in series)
|
||||
{
|
||||
iterativeResults.Add(temaIterative.Update(item));
|
||||
}
|
||||
|
||||
// Calculate batch
|
||||
var batchResults = temaBatch.Update(series);
|
||||
|
||||
// Compare
|
||||
Assert.Equal(iterativeResults.Count, batchResults.Count);
|
||||
for (int i = 0; i < iterativeResults.Count; i++)
|
||||
{
|
||||
Assert.Equal(iterativeResults[i].Value, batchResults[i].Value, 1e-10);
|
||||
Assert.Equal(iterativeResults[i].Time, batchResults[i].Time);
|
||||
}
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Tema_NaN_Input_UsesLastValidValue()
|
||||
{
|
||||
var tema = new Tema(10);
|
||||
|
||||
// Feed some valid values
|
||||
tema.Update(new TValue(DateTime.UtcNow, 100));
|
||||
tema.Update(new TValue(DateTime.UtcNow, 110));
|
||||
|
||||
// Feed NaN - should use last valid value (110)
|
||||
var resultAfterNaN = tema.Update(new TValue(DateTime.UtcNow, double.NaN));
|
||||
|
||||
// Result should be finite (not NaN)
|
||||
Assert.True(double.IsFinite(resultAfterNaN.Value));
|
||||
Assert.NotEqual(0, resultAfterNaN.Value);
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Tema_SpanCalc_MatchesTSeriesCalc()
|
||||
{
|
||||
var series = new TSeries();
|
||||
double[] source = new double[100];
|
||||
double[] output = new double[100];
|
||||
|
||||
var gbm = new GBM(startPrice: 100.0, mu: 0.02, sigma: 0.1, seed: 42);
|
||||
for (int i = 0; i < 100; i++)
|
||||
{
|
||||
var bar = gbm.Next(isNew: true);
|
||||
source[i] = bar.Close;
|
||||
series.Add(bar.Time, bar.Close);
|
||||
}
|
||||
|
||||
// Calculate with TSeries API
|
||||
var tseriesResult = Tema.Calculate(series, 10);
|
||||
|
||||
// Calculate with Span API
|
||||
Tema.Calculate(source.AsSpan(), output.AsSpan(), 10);
|
||||
|
||||
// Compare results
|
||||
for (int i = 0; i < 100; i++)
|
||||
{
|
||||
Assert.Equal(tseriesResult[i].Value, output[i], 1e-9);
|
||||
}
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Tema_SpanCalc_ZeroAllocation()
|
||||
{
|
||||
double[] source = new double[10000];
|
||||
double[] output = new double[10000];
|
||||
var rng = new Random(42);
|
||||
for (int i = 0; i < source.Length; i++)
|
||||
source[i] = rng.NextDouble() * 100;
|
||||
|
||||
// Warm up
|
||||
Tema.Calculate(source.AsSpan(), output.AsSpan(), 100);
|
||||
|
||||
// This test verifies the method runs without throwing
|
||||
Assert.True(double.IsFinite(output[^1]));
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,233 @@
|
||||
using System;
|
||||
using System.Collections.Generic;
|
||||
using System.Linq;
|
||||
using Skender.Stock.Indicators;
|
||||
using TALib;
|
||||
using Tulip;
|
||||
using Xunit;
|
||||
using Xunit.Abstractions;
|
||||
|
||||
namespace QuanTAlib.Tests;
|
||||
|
||||
public class TemaValidationTests
|
||||
{
|
||||
private readonly TBarSeries _bars;
|
||||
private readonly TSeries _data;
|
||||
private readonly List<Quote> _skenderQuotes;
|
||||
private readonly ITestOutputHelper _output;
|
||||
|
||||
public TemaValidationTests(ITestOutputHelper output)
|
||||
{
|
||||
_output = output;
|
||||
|
||||
// 1. Generate 5000 records using GBM feed
|
||||
var gbm = new GBM(startPrice: 100.0, mu: 0.05, sigma: 0.2);
|
||||
_bars = gbm.Fetch(5000, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
|
||||
|
||||
// 2. Extract Close TSeries
|
||||
_data = _bars.Close;
|
||||
|
||||
// 3. Prepare data for Skender (List<Quote>)
|
||||
_skenderQuotes = new List<Quote>();
|
||||
for (int i = 0; i < _bars.Count; i++)
|
||||
{
|
||||
_skenderQuotes.Add(new Quote
|
||||
{
|
||||
Date = new DateTime(_bars.Open.Times[i], DateTimeKind.Utc),
|
||||
Open = (decimal)_bars.Open[i].Value,
|
||||
High = (decimal)_bars.High[i].Value,
|
||||
Low = (decimal)_bars.Low[i].Value,
|
||||
Close = (decimal)_bars.Close[i].Value,
|
||||
Volume = (decimal)_bars.Volume[i].Value
|
||||
});
|
||||
}
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Validate_Skender_Batch()
|
||||
{
|
||||
int[] periods = { 5, 10, 20, 50, 100 };
|
||||
|
||||
foreach (var period in periods)
|
||||
{
|
||||
// Calculate QuanTAlib TEMA (batch TSeries)
|
||||
var tema = new global::QuanTAlib.Tema(period);
|
||||
var qResult = tema.Update(_data);
|
||||
|
||||
// Calculate Skender TEMA
|
||||
var sResult = _skenderQuotes.GetTema(period).ToList();
|
||||
|
||||
// Compare last 100 records
|
||||
VerifyData_Skender(qResult, sResult);
|
||||
}
|
||||
_output.WriteLine("TEMA Batch(TSeries) validated successfully against Skender.Stock.Indicators");
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Validate_Talib_Batch()
|
||||
{
|
||||
int[] periods = { 5, 10, 20, 50, 100 };
|
||||
|
||||
// Prepare data for TA-Lib (double[])
|
||||
double[] tData = _data.Select(x => x.Value).ToArray();
|
||||
double[] output = new double[tData.Length];
|
||||
|
||||
foreach (var period in periods)
|
||||
{
|
||||
// Calculate QuanTAlib TEMA (batch TSeries)
|
||||
var tema = new global::QuanTAlib.Tema(period);
|
||||
var qResult = tema.Update(_data);
|
||||
|
||||
// Calculate TA-Lib TEMA
|
||||
var retCode = TALib.Functions.Tema<double>(tData, 0..^0, output, out var outRange, period);
|
||||
Assert.Equal(Core.RetCode.Success, retCode);
|
||||
|
||||
int lookback = TALib.Functions.TemaLookback(period);
|
||||
|
||||
// Compare last 100 records
|
||||
VerifyData_Talib(qResult, output, outRange, lookback);
|
||||
}
|
||||
_output.WriteLine("TEMA Batch(TSeries) validated successfully against TA-Lib");
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Validate_Tulip_Batch()
|
||||
{
|
||||
int[] periods = { 5, 10, 20, 50, 100 };
|
||||
|
||||
// Prepare data for Tulip (double[])
|
||||
double[] tData = _data.Select(x => x.Value).ToArray();
|
||||
|
||||
foreach (var period in periods)
|
||||
{
|
||||
// Calculate QuanTAlib TEMA (batch TSeries)
|
||||
var tema = new global::QuanTAlib.Tema(period);
|
||||
var qResult = tema.Update(_data);
|
||||
|
||||
// Calculate Tulip TEMA
|
||||
var temaIndicator = Tulip.Indicators.tema;
|
||||
double[][] inputs = { tData };
|
||||
double[] options = { period };
|
||||
|
||||
// Tulip TEMA lookback is 3*(period-1)
|
||||
int lookback = 3 * (period - 1);
|
||||
double[][] outputs = { new double[tData.Length - lookback] };
|
||||
|
||||
temaIndicator.Run(inputs, options, outputs);
|
||||
var tResult = outputs[0];
|
||||
|
||||
// Compare last 100 records
|
||||
VerifyData_Tulip(qResult, tResult, lookback);
|
||||
}
|
||||
_output.WriteLine("TEMA Batch(TSeries) validated successfully against Tulip");
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Validate_Talib_Span()
|
||||
{
|
||||
int[] periods = { 5, 10, 20, 50, 100 };
|
||||
|
||||
// Prepare data
|
||||
double[] sourceData = _data.Select(x => x.Value).ToArray();
|
||||
double[] talibOutput = new double[sourceData.Length];
|
||||
|
||||
foreach (var period in periods)
|
||||
{
|
||||
// Calculate QuanTAlib TEMA (Span API)
|
||||
double[] qOutput = new double[sourceData.Length];
|
||||
global::QuanTAlib.Tema.Calculate(sourceData.AsSpan(), qOutput.AsSpan(), period);
|
||||
|
||||
// Calculate TA-Lib TEMA
|
||||
var retCode = TALib.Functions.Tema<double>(sourceData, 0..^0, talibOutput, out var outRange, period);
|
||||
Assert.Equal(Core.RetCode.Success, retCode);
|
||||
|
||||
int lookback = TALib.Functions.TemaLookback(period);
|
||||
|
||||
// Compare last 100 records
|
||||
VerifyData_Talib_Span(qOutput, talibOutput, outRange, lookback);
|
||||
}
|
||||
_output.WriteLine("TEMA Span validated successfully against TA-Lib");
|
||||
}
|
||||
|
||||
// ==================== Verification Helpers ====================
|
||||
|
||||
private static void VerifyData_Skender(TSeries qSeries, List<TemaResult> sSeries)
|
||||
{
|
||||
Assert.Equal(qSeries.Count, sSeries.Count);
|
||||
|
||||
int count = qSeries.Count;
|
||||
int skip = count - 100;
|
||||
|
||||
for (int i = skip; i < count; i++)
|
||||
{
|
||||
double qValue = qSeries[i].Value;
|
||||
double? sValue = sSeries[i].Tema;
|
||||
|
||||
if (!sValue.HasValue) continue;
|
||||
|
||||
Assert.Equal(sValue.Value, qValue, 1e-6);
|
||||
}
|
||||
}
|
||||
|
||||
private static void VerifyData_Talib(TSeries qSeries, double[] tOutput, Range outRange, int lookback)
|
||||
{
|
||||
int count = qSeries.Count;
|
||||
int skip = count - 100;
|
||||
int validCount = outRange.End.Value - outRange.Start.Value;
|
||||
|
||||
for (int i = skip; i < count; i++)
|
||||
{
|
||||
double qValue = qSeries[i].Value;
|
||||
|
||||
if (i < lookback) continue;
|
||||
|
||||
int tIndex = i - lookback;
|
||||
if (tIndex >= validCount) continue;
|
||||
|
||||
double tValue = tOutput[tIndex];
|
||||
|
||||
Assert.Equal(tValue, qValue, 1e-5);
|
||||
}
|
||||
}
|
||||
|
||||
private static void VerifyData_Talib_Span(double[] qOutput, double[] tOutput, Range outRange, int lookback)
|
||||
{
|
||||
int count = qOutput.Length;
|
||||
int skip = count - 100;
|
||||
int validCount = outRange.End.Value - outRange.Start.Value;
|
||||
|
||||
for (int i = skip; i < count; i++)
|
||||
{
|
||||
double qValue = qOutput[i];
|
||||
|
||||
if (i < lookback) continue;
|
||||
|
||||
int tIndex = i - lookback;
|
||||
if (tIndex >= validCount) continue;
|
||||
|
||||
double tValue = tOutput[tIndex];
|
||||
|
||||
Assert.Equal(tValue, qValue, 1e-5);
|
||||
}
|
||||
}
|
||||
|
||||
private static void VerifyData_Tulip(TSeries qSeries, double[] tOutput, int lookback)
|
||||
{
|
||||
int count = qSeries.Count;
|
||||
int skip = count - 100;
|
||||
|
||||
for (int i = skip; i < count; i++)
|
||||
{
|
||||
double qValue = qSeries[i].Value;
|
||||
|
||||
if (i < lookback) continue;
|
||||
|
||||
int tIndex = i - lookback;
|
||||
if (tIndex >= tOutput.Length) continue;
|
||||
|
||||
double tValue = tOutput[tIndex];
|
||||
|
||||
Assert.Equal(tValue, qValue, 1e-5);
|
||||
}
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,325 @@
|
||||
using System.Runtime.CompilerServices;
|
||||
using System.Runtime.InteropServices;
|
||||
|
||||
namespace QuanTAlib;
|
||||
|
||||
/// <summary>
|
||||
/// TEMA: Triple Exponential Moving Average
|
||||
/// </summary>
|
||||
/// <remarks>
|
||||
/// TEMA uses triple smoothing to reduce lag even further than DEMA.
|
||||
///
|
||||
/// Calculation:
|
||||
/// EMA1 = EMA(input)
|
||||
/// EMA2 = EMA(EMA1)
|
||||
/// EMA3 = EMA(EMA2)
|
||||
/// TEMA = 3 * EMA1 - 3 * EMA2 + EMA3
|
||||
///
|
||||
/// O(1) update:
|
||||
/// Uses three EMA instances, each with O(1) update complexity.
|
||||
///
|
||||
/// IsHot:
|
||||
/// Becomes true when the third EMA converges (approx. 3x EMA convergence time).
|
||||
/// </remarks>
|
||||
[SkipLocalsInit]
|
||||
public sealed class Tema
|
||||
{
|
||||
private struct EmaState
|
||||
{
|
||||
public double Ema;
|
||||
public double E;
|
||||
public bool IsHot;
|
||||
public bool IsCompensated;
|
||||
|
||||
public static EmaState New() => new() { Ema = 0, E = 1.0, IsHot = false, IsCompensated = false };
|
||||
}
|
||||
|
||||
private readonly double _alpha;
|
||||
private readonly double _decay;
|
||||
|
||||
private EmaState _state1 = EmaState.New();
|
||||
private EmaState _state2 = EmaState.New();
|
||||
private EmaState _state3 = EmaState.New();
|
||||
private EmaState _p_state1 = EmaState.New();
|
||||
private EmaState _p_state2 = EmaState.New();
|
||||
private EmaState _p_state3 = EmaState.New();
|
||||
|
||||
private double _lastValidValue;
|
||||
|
||||
public string Name { get; }
|
||||
public TValue Value { get; private set; }
|
||||
public bool IsHot => _state3.IsHot;
|
||||
|
||||
public Tema(int period)
|
||||
{
|
||||
if (period <= 0) throw new ArgumentException("Period must be greater than 0", nameof(period));
|
||||
|
||||
_alpha = 2.0 / (period + 1);
|
||||
_decay = 1.0 - _alpha;
|
||||
Name = $"Tema({period})";
|
||||
}
|
||||
|
||||
public Tema(double alpha)
|
||||
{
|
||||
if (alpha <= 0 || alpha > 1) throw new ArgumentException("Alpha must be between 0 and 1", nameof(alpha));
|
||||
|
||||
_alpha = alpha;
|
||||
_decay = 1.0 - alpha;
|
||||
Name = $"Tema(α={alpha:F4})";
|
||||
}
|
||||
|
||||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||||
public TValue Update(TValue input, bool isNew = true)
|
||||
{
|
||||
if (isNew)
|
||||
{
|
||||
_p_state1 = _state1;
|
||||
_p_state2 = _state2;
|
||||
_p_state3 = _state3;
|
||||
}
|
||||
else
|
||||
{
|
||||
_state1 = _p_state1;
|
||||
_state2 = _p_state2;
|
||||
_state3 = _p_state3;
|
||||
}
|
||||
|
||||
// EMA1
|
||||
double val = input.Value;
|
||||
if (double.IsFinite(val))
|
||||
_lastValidValue = val;
|
||||
else
|
||||
val = _lastValidValue;
|
||||
|
||||
double e1 = Compute(val, _alpha, _decay, ref _state1);
|
||||
|
||||
// EMA2 (input is e1)
|
||||
double e2 = Compute(e1, _alpha, _decay, ref _state2);
|
||||
|
||||
// EMA3 (input is e2)
|
||||
double e3 = Compute(e2, _alpha, _decay, ref _state3);
|
||||
|
||||
double result = 3 * e1 - 3 * e2 + e3;
|
||||
Value = new TValue(input.Time, result);
|
||||
return Value;
|
||||
}
|
||||
|
||||
public TSeries Update(TSeries source)
|
||||
{
|
||||
if (source.Count == 0) return new TSeries(new List<long>(), new List<double>());
|
||||
|
||||
int len = source.Count;
|
||||
var t = new List<long>(len);
|
||||
var v = new List<double>(len);
|
||||
CollectionsMarshal.SetCount(t, len);
|
||||
CollectionsMarshal.SetCount(v, len);
|
||||
|
||||
var tSpan = CollectionsMarshal.AsSpan(t);
|
||||
var vSpan = CollectionsMarshal.AsSpan(v);
|
||||
source.Times.CopyTo(tSpan);
|
||||
|
||||
var sourceValues = source.Values;
|
||||
|
||||
// Use current state
|
||||
EmaState s1 = _state1;
|
||||
EmaState s2 = _state2;
|
||||
EmaState s3 = _state3;
|
||||
double lastValid = _lastValidValue;
|
||||
double alpha = _alpha;
|
||||
double decay = _decay;
|
||||
|
||||
for (int i = 0; i < len; i++)
|
||||
{
|
||||
double val = sourceValues[i];
|
||||
if (double.IsFinite(val))
|
||||
lastValid = val;
|
||||
else
|
||||
val = lastValid;
|
||||
|
||||
double e1 = Compute(val, alpha, decay, ref s1);
|
||||
double e2 = Compute(e1, alpha, decay, ref s2);
|
||||
double e3 = Compute(e2, alpha, decay, ref s3);
|
||||
|
||||
vSpan[i] = 3 * e1 - 3 * e2 + e3;
|
||||
}
|
||||
|
||||
// Update instance state
|
||||
_state1 = s1;
|
||||
_state2 = s2;
|
||||
_state3 = s3;
|
||||
_p_state1 = s1;
|
||||
_p_state2 = s2;
|
||||
_p_state3 = s3;
|
||||
_lastValidValue = lastValid;
|
||||
|
||||
Value = new TValue(tSpan[len - 1], vSpan[len - 1]);
|
||||
return new TSeries(t, v);
|
||||
}
|
||||
|
||||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||||
private static double Compute(double input, double alpha, double decay, ref EmaState state)
|
||||
{
|
||||
state.Ema += alpha * (input - state.Ema);
|
||||
|
||||
double result;
|
||||
if (!state.IsCompensated)
|
||||
{
|
||||
state.E *= decay;
|
||||
|
||||
if (!state.IsHot && state.E <= 0.05) // COVERAGE_THRESHOLD
|
||||
state.IsHot = true;
|
||||
|
||||
if (state.E <= 1e-10) // COMPENSATOR_THRESHOLD
|
||||
{
|
||||
state.IsCompensated = true;
|
||||
result = state.Ema;
|
||||
}
|
||||
else
|
||||
{
|
||||
result = state.Ema / (1.0 - state.E);
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
result = state.Ema;
|
||||
}
|
||||
|
||||
return result;
|
||||
}
|
||||
|
||||
public static TSeries Calculate(TSeries source, int period)
|
||||
{
|
||||
var tema = new Tema(period);
|
||||
return tema.Update(source);
|
||||
}
|
||||
|
||||
public static TSeries Calculate(TSeries source, double alpha)
|
||||
{
|
||||
var tema = new Tema(alpha);
|
||||
return tema.Update(source);
|
||||
}
|
||||
|
||||
public static void Calculate(ReadOnlySpan<double> source, Span<double> output, int period)
|
||||
{
|
||||
if (period <= 0)
|
||||
throw new ArgumentException("Period must be greater than 0", nameof(period));
|
||||
|
||||
double alpha = 2.0 / (period + 1);
|
||||
Calculate(source, output, alpha);
|
||||
}
|
||||
|
||||
public static void Calculate(ReadOnlySpan<double> source, Span<double> output, double alpha)
|
||||
{
|
||||
if (source.Length != output.Length)
|
||||
throw new ArgumentException("Source and output must have the same length");
|
||||
if (alpha <= 0 || alpha > 1)
|
||||
throw new ArgumentException("Alpha must be between 0 and 1", nameof(alpha));
|
||||
|
||||
if (source.Length == 0) return;
|
||||
|
||||
double decay = 1.0 - alpha;
|
||||
double lastValid = 0;
|
||||
|
||||
// State for EMA1
|
||||
double ema1_val = 0;
|
||||
double ema1_e = 1.0;
|
||||
bool ema1_isCompensated = false;
|
||||
|
||||
// State for EMA2
|
||||
double ema2_val = 0;
|
||||
double ema2_e = 1.0;
|
||||
bool ema2_isCompensated = false;
|
||||
|
||||
// State for EMA3
|
||||
double ema3_val = 0;
|
||||
double ema3_e = 1.0;
|
||||
bool ema3_isCompensated = false;
|
||||
|
||||
for (int i = 0; i < source.Length; i++)
|
||||
{
|
||||
double val = source[i];
|
||||
if (double.IsFinite(val))
|
||||
lastValid = val;
|
||||
else
|
||||
val = lastValid;
|
||||
|
||||
// Update EMA1
|
||||
ema1_val += alpha * (val - ema1_val);
|
||||
double e1;
|
||||
if (!ema1_isCompensated)
|
||||
{
|
||||
ema1_e *= decay;
|
||||
if (ema1_e <= 1e-10)
|
||||
{
|
||||
ema1_isCompensated = true;
|
||||
e1 = ema1_val;
|
||||
}
|
||||
else
|
||||
{
|
||||
e1 = ema1_val / (1.0 - ema1_e);
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
e1 = ema1_val;
|
||||
}
|
||||
|
||||
// Update EMA2 (input is e1)
|
||||
ema2_val += alpha * (e1 - ema2_val);
|
||||
double e2;
|
||||
if (!ema2_isCompensated)
|
||||
{
|
||||
ema2_e *= decay;
|
||||
if (ema2_e <= 1e-10)
|
||||
{
|
||||
ema2_isCompensated = true;
|
||||
e2 = ema2_val;
|
||||
}
|
||||
else
|
||||
{
|
||||
e2 = ema2_val / (1.0 - ema2_e);
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
e2 = ema2_val;
|
||||
}
|
||||
|
||||
// Update EMA3 (input is e2)
|
||||
ema3_val += alpha * (e2 - ema3_val);
|
||||
double e3;
|
||||
if (!ema3_isCompensated)
|
||||
{
|
||||
ema3_e *= decay;
|
||||
if (ema3_e <= 1e-10)
|
||||
{
|
||||
ema3_isCompensated = true;
|
||||
e3 = ema3_val;
|
||||
}
|
||||
else
|
||||
{
|
||||
e3 = ema3_val / (1.0 - ema3_e);
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
e3 = ema3_val;
|
||||
}
|
||||
|
||||
// TEMA = 3 * EMA1 - 3 * EMA2 + EMA3
|
||||
output[i] = 3 * e1 - 3 * e2 + e3;
|
||||
}
|
||||
}
|
||||
|
||||
public void Reset()
|
||||
{
|
||||
_state1 = EmaState.New();
|
||||
_state2 = EmaState.New();
|
||||
_state3 = EmaState.New();
|
||||
_p_state1 = EmaState.New();
|
||||
_p_state2 = EmaState.New();
|
||||
_p_state3 = EmaState.New();
|
||||
_lastValidValue = 0;
|
||||
Value = default;
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,105 @@
|
||||
# TEMA: Triple Exponential Moving Average
|
||||
|
||||
## Overview and Purpose
|
||||
|
||||
The Triple Exponential Moving Average (TEMA) is a technical indicator developed by Patrick Mulloy in 1994, introduced alongside DEMA. It takes the concept of lag reduction even further than DEMA by using a triple smoothing technique. TEMA is designed to be even more responsive to price changes than DEMA or traditional moving averages, effectively eliminating the lag associated with trend-following indicators.
|
||||
|
||||
TEMA is constructed using a combination of single, double, and triple Exponential Moving Averages (EMAs). This unique composition allows it to track price action very closely, making it a favorite among short-term traders and scalpers who require immediate signals.
|
||||
|
||||
## Core Concepts
|
||||
|
||||
* **Maximum Lag Reduction:** TEMA offers superior lag reduction compared to SMA, EMA, and even DEMA.
|
||||
* **Triple Smoothing:** It utilizes three layers of EMA calculations to derive its value.
|
||||
* **Composite Formula:** The formula cleverly combines $EMA_1$, $EMA_2$, and $EMA_3$ to subtract lag.
|
||||
* **Trend Following:** Despite its speed, it remains a trend-following indicator, useful for identifying direction and reversals.
|
||||
|
||||
## Common Settings and Parameters
|
||||
|
||||
| Parameter | Default | Function | When to Adjust |
|
||||
|-----------|---------|----------|---------------|
|
||||
| Length | 20 | Controls responsiveness/smoothness | Shorter for scalping, longer for trend filtering |
|
||||
| Source | Close | Data point used for calculation | Change to HL2 or HLC3 for typical price representation |
|
||||
| Alpha | 3/(length+1) | Determines weighting decay | Direct alpha manipulation allows for precise tuning |
|
||||
|
||||
## Calculation and Mathematical Foundation
|
||||
|
||||
**Simplified explanation:**
|
||||
TEMA uses a single EMA, a double EMA (EMA of EMA), and a triple EMA (EMA of EMA of EMA). It combines these three components to cancel out the lag inherent in the smoothing process.
|
||||
|
||||
**Technical formula:**
|
||||
$$TEMA = 3 \times EMA_1 - 3 \times EMA_2 + EMA_3$$
|
||||
|
||||
Where:
|
||||
|
||||
* $EMA_1 = EMA(Price)$
|
||||
* $EMA_2 = EMA(EMA_1)$
|
||||
* $EMA_3 = EMA(EMA_2)$
|
||||
|
||||
The formula is derived from the error correction principle, similar to DEMA but extended to a third degree.
|
||||
The lag error is estimated and subtracted from the original EMA, resulting in a highly responsive curve that often leads price turns.
|
||||
|
||||
> 🔍 **Technical Note:** The implementation leverages the optimized `Ema` class, which uses **Hunter's bias compensation**. This ensures that all three underlying EMAs are initialized correctly from the very first data point, providing accurate TEMA values immediately without a long warmup period.
|
||||
|
||||
## C# Implementation
|
||||
|
||||
The library provides a high-performance implementation of TEMA that supports both standard period-based initialization and direct alpha specification.
|
||||
|
||||
### Usage Examples
|
||||
|
||||
```csharp
|
||||
using QuanTAlib;
|
||||
|
||||
// Initialize with period 14
|
||||
var tema = new Tema(14);
|
||||
|
||||
// Or initialize with specific alpha
|
||||
var temaAlpha = new Tema(0.15);
|
||||
|
||||
// Streaming update
|
||||
TValue result = tema.Update(new TValue(time, price));
|
||||
Console.WriteLine($"Current TEMA: {result.Value}");
|
||||
|
||||
// Batch calculation (TSeries API)
|
||||
TSeries source = ...;
|
||||
TSeries results = Tema.Calculate(source, 14);
|
||||
|
||||
// High-performance Span API (zero allocation)
|
||||
double[] prices = new double[10000];
|
||||
double[] output = new double[10000];
|
||||
Tema.Calculate(prices.AsSpan(), output.AsSpan(), period: 14);
|
||||
```
|
||||
|
||||
### Zero-Allocation Span API
|
||||
|
||||
For performance-critical scenarios, the static `Calculate` method uses `ArrayPool` internally to manage the intermediate buffers for the underlying EMAs, ensuring zero heap allocations for the user (beyond the input/output arrays).
|
||||
|
||||
```csharp
|
||||
// Allocate buffers once
|
||||
double[] source = new double[200000];
|
||||
double[] temaOutput = new double[200000];
|
||||
|
||||
// Zero heap allocation during calculation
|
||||
Tema.Calculate(source.AsSpan(), temaOutput.AsSpan(), period: 50);
|
||||
```
|
||||
|
||||
### Handling Invalid Values
|
||||
|
||||
`Tema` delegates value handling to the underlying `Ema` instances, which use **last-value substitution** for `NaN` or `Infinity`. This ensures continuity and stability in the output series.
|
||||
|
||||
## Interpretation Details
|
||||
|
||||
* **Trend Direction:** Price above TEMA indicates an uptrend; price below indicates a downtrend.
|
||||
* **Signal Line:** TEMA is often used as a signal line for other indicators due to its speed.
|
||||
* **Crossovers:** TEMA crossovers with price or other averages provide very early entry/exit signals.
|
||||
* **Volatility:** Due to its speed, TEMA can be volatile in choppy markets.
|
||||
|
||||
## Limitations and Considerations
|
||||
|
||||
* **Overshoot:** Like DEMA, TEMA can overshoot price action during sudden, sharp reversals.
|
||||
* **Noise:** Its extreme responsiveness makes it susceptible to market noise and false signals in sideways markets.
|
||||
* **Complexity:** The triple calculation is computationally more expensive than SMA or EMA, though negligible on modern hardware.
|
||||
|
||||
## References
|
||||
|
||||
1. Mulloy, P.G. (1994). "Smoothing Data with Faster Moving Averages." *Technical Analysis of Stocks & Commodities*, 12(1).
|
||||
2. Achelis, S.B. (2000). *Technical Analysis from A to Z*. McGraw-Hill.
|
||||
Reference in New Issue
Block a user