QuanTAlib/lib/averages/sma/Sma.Notebook.dib

#!meta

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#!markdown

# Simple Moving Average (SMA) Examples

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.

The **Simple Moving Average (SMA)** is the most basic form of moving average, calculating the arithmetic mean over a specified period. Unlike the EMA, the SMA assigns equal weight to all data points in the window, making it a good baseline for trend analysis.

**Key characteristics:**
- Equal weighting for all values in the period
- O(1) update complexity using running sum
- O(1) bar correction using scalar state
- Smooth output with good noise reduction
- More lag than EMA due to equal weighting

This notebook demonstrates:
1.  **Manual Data Processing**: Understanding Batch vs. Streaming modes.
2.  **Streaming with `isNew`**: Handling intra-bar updates.
3.  **Large Dataset Processing**: Using Geometric Brownian Motion (GBM) generated data.
4.  **Vectorized Operations**: Calculating multiple SMAs simultaneously.

#!csharp

// Reference the library
#r "..\..\bin\QuanTAlib.dll"

using System;
using System.Linq;
using QuanTAlib;

// Helper to print TSeries
void PrintSeries(TSeries series, int count = 5)
{
    Console.WriteLine($"Series Length: {series.Count}");
    foreach (var item in series.Take(count))
    {
        Console.WriteLine($"Time: {item.Time:HH:mm:ss}, Value: {item.Value:F2}");
    }
    if (series.Count > count) Console.WriteLine("...");
}

#!markdown

## 1. Manual Data: Batch vs. Streaming

We'll start with a small, manually created dataset to clearly see how Batch and Streaming operations work.

### Batch Processing
Batch processing calculates the SMA for the entire dataset at once. This is efficient for historical analysis.

#!csharp

// Create a small manual dataset
var manualData = new TSeries();
manualData.Add(DateTime.Now, 100.0);
manualData.Add(DateTime.Now.AddMinutes(1), 102.0);
manualData.Add(DateTime.Now.AddMinutes(2), 101.0);
manualData.Add(DateTime.Now.AddMinutes(3), 103.0);
manualData.Add(DateTime.Now.AddMinutes(4), 105.0);

Console.WriteLine("--- Input Data ---");
PrintSeries(manualData, 5);

// Batch Calculation
Console.WriteLine("\n--- Batch SMA (Period 3) ---");
var smaBatch = new Sma(3);
var resultBatch = smaBatch.Update(manualData);

PrintSeries(resultBatch, 5);

// Show the calculation for each step
Console.WriteLine("\nCalculation breakdown:");
Console.WriteLine("  SMA[0] = 100 / 1 = 100.00");
Console.WriteLine("  SMA[1] = (100 + 102) / 2 = 101.00");
Console.WriteLine("  SMA[2] = (100 + 102 + 101) / 3 = 101.00");
Console.WriteLine("  SMA[3] = (102 + 101 + 103) / 3 = 102.00");
Console.WriteLine("  SMA[4] = (101 + 103 + 105) / 3 = 103.00");

#!markdown

### Streaming Processing
Streaming processing updates the SMA one data point at a time. This is essential for real-time trading systems where data arrives sequentially.

#!csharp

Console.WriteLine("\n--- Streaming SMA (Period 3) ---");
var smaStream = new Sma(3);

foreach (var item in manualData)
{
    var result = smaStream.Update(item);
    Console.WriteLine($"Time: {item.Time:HH:mm:ss}, Input: {item.Value:F2}, SMA: {result.Value:F2}, IsHot: {smaStream.IsHot}");
}

// Verify that the last values match
var batchLast = resultBatch.Last().Value;
var streamLast = smaStream.Value.Value;
Console.WriteLine($"\nMatch: {Math.Abs(batchLast - streamLast) < 1e-10} (Batch: {batchLast:F2}, Stream: {streamLast:F2})");

// Show SMA properties
Console.WriteLine($"\nSMA Properties:");
Console.WriteLine($"  Name: {smaStream.Name}");
Console.WriteLine($"  WarmupPeriod: {smaStream.WarmupPeriod}");
Console.WriteLine($"  IsHot: {smaStream.IsHot}");

#!markdown

## 2. Streaming with `isNew` (Intra-bar Updates)

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.
*   `isNew = true`: The input is a new bar (advances time).
*   `isNew = false`: The input is an update to the current bar (recalculates without advancing).

**SMA achieves O(1) bar correction** by saving scalar state after each `isNew=true` update.

#!csharp

Console.WriteLine("\n--- Streaming with Intra-bar Updates ---");
var smaIntra = new Sma(3);

// 1. Process the first 4 bars normally
for (int i = 0; i < 4; i++)
{
    smaIntra.Update(manualData[i]);
}
Console.WriteLine($"After 4th bar: {smaIntra.Value.Value:F2}");

// 2. Simulate intra-bar updates for the 5th bar (Final value is 105.0)
// Update 1: Price moves to 104.0
var update1 = new TValue(manualData[4].Time, 104.0);
smaIntra.Update(update1, isNew: true); // First update for this bar is "New"
Console.WriteLine($"Update 1 (104.0): {smaIntra.Value.Value:F2}");

// Update 2: Price moves to 106.0 (Same time, same bar)
var update2 = new TValue(manualData[4].Time, 106.0);
smaIntra.Update(update2, isNew: false); // Not new, just an update
Console.WriteLine($"Update 2 (106.0): {smaIntra.Value.Value:F2}");

// Update 3: Final Close at 105.0
var update3 = manualData[4];
smaIntra.Update(update3, isNew: false); // Final update
Console.WriteLine($"Update 3 (105.0): {smaIntra.Value.Value:F2}");

// Verify match with batch result
Console.WriteLine($"Match with Batch: {Math.Abs(smaIntra.Value.Value - batchLast) < 1e-10}");

#!markdown

## 3. Large Dataset: Geometric Brownian Motion (GBM)

We'll generate a larger dataset (1000 bars) using a Geometric Brownian Motion generator to simulate realistic market data.

#!csharp

// Generate 1000 bars of data
var gbm = new GBM(startPrice: 100.0, mu: 0.05, sigma: 0.2);
var gbmData = gbm.Fetch(1000, DateTime.Now.Ticks, TimeSpan.FromMinutes(1));
var closeSeries = gbmData.Close;

Console.WriteLine($"Generated {closeSeries.Count} bars of GBM data.");
Console.WriteLine($"First 5 values: {string.Join(", ", closeSeries.Take(5).Select(x => x.Value.ToString("F2")))}");

#!markdown

### Batch vs. Streaming Performance on Large Data

#!csharp

// Batch
var smaLargeBatch = new Sma(20);
var batchLargeResult = smaLargeBatch.Update(closeSeries);
Console.WriteLine($"Batch Last Value: {batchLargeResult.Last().Value:F2}");

// Streaming
var smaLargeStream = new Sma(20);
TValue lastStreamVal = default;
foreach(var item in closeSeries)
{
    lastStreamVal = smaLargeStream.Update(item);
}
Console.WriteLine($"Streaming Last Value: {lastStreamVal.Value:F2}");

// Verify match
Console.WriteLine($"Match: {Math.Abs(batchLargeResult.Last().Value - lastStreamVal.Value) < 1e-10}");

#!markdown

## 4. Vectorized SMA (Multiple Periods)

`SmaVector` allows calculating multiple SMAs (e.g., 5, 10, 20) simultaneously. This is useful for comparing different timeframes.

### Vectorized Batch

#!csharp

int[] periods = { 5, 10, 20 };
Console.WriteLine($"\n--- Vectorized Batch SMA (Periods: {string.Join(", ", periods)}) ---");

var smaVectorBatch = new SmaVector(periods);
var vectorBatchResults = smaVectorBatch.Calculate(closeSeries);

for (int i = 0; i < periods.Length; i++)
{
    Console.WriteLine($"SMA({periods[i]}) Last Value: {vectorBatchResults[i].Last().Value:F2}");
}

#!markdown

### Vectorized Streaming

#!csharp

Console.WriteLine($"\n--- Vectorized Streaming SMA (Periods: {string.Join(", ", periods)}) ---");

var smaVectorStream = new SmaVector(periods);
TValue[] lastVectorVal = null;

foreach(var item in closeSeries)
{
    lastVectorVal = smaVectorStream.Update(item);
}

for (int i = 0; i < periods.Length; i++)
{
    Console.WriteLine($"SMA({periods[i]}) Last Value: {lastVectorVal[i].Value:F2}");
}

// Verification
bool allMatch = true;
for (int i = 0; i < periods.Length; i++)
{
    if (Math.Abs(vectorBatchResults[i].Last().Value - lastVectorVal[i].Value) > 1e-10)
    {
        allMatch = false;
        break;
    }
}
Console.WriteLine($"\nAll Vectorized Stream/Batch values match: {allMatch}");

#!markdown

## 5. Handling Invalid Values (NaN/Infinity)

Both `Sma` and `SmaVector` use **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.

#!csharp

Console.WriteLine("\n--- Handling Invalid Values ---");

// Single SMA
var smaNaN = new Sma(10);

// Feed valid values first
smaNaN.Update(new TValue(DateTime.Now, 100.0));
smaNaN.Update(new TValue(DateTime.Now.AddMinutes(1), 110.0));
Console.WriteLine($"After valid values: {smaNaN.Value.Value:F2}");

// Feed NaN - should use last valid value (110)
var resultAfterNaN = smaNaN.Update(new TValue(DateTime.Now.AddMinutes(2), double.NaN));
Console.WriteLine($"After NaN input: {resultAfterNaN.Value:F2} (IsFinite: {double.IsFinite(resultAfterNaN.Value)})");

// Feed Infinity - should use last valid value (110)
var resultAfterInf = smaNaN.Update(new TValue(DateTime.Now.AddMinutes(3), double.PositiveInfinity));
Console.WriteLine($"After Infinity input: {resultAfterInf.Value:F2} (IsFinite: {double.IsFinite(resultAfterInf.Value)})");

// Continue with valid value
var resultAfterValid = smaNaN.Update(new TValue(DateTime.Now.AddMinutes(4), 120.0));
Console.WriteLine($"After valid value (120): {resultAfterValid.Value:F2}");

#!csharp

Console.WriteLine("\n--- Batch Processing with Invalid Values ---");

// Create series with NaN values interspersed
var seriesWithNaN = new TSeries();
seriesWithNaN.Add(DateTime.Now.Ticks, 100.0);
seriesWithNaN.Add(DateTime.Now.Ticks + 1, 110.0);
seriesWithNaN.Add(DateTime.Now.Ticks + 2, double.NaN);
seriesWithNaN.Add(DateTime.Now.Ticks + 3, 120.0);
seriesWithNaN.Add(DateTime.Now.Ticks + 4, double.PositiveInfinity);
seriesWithNaN.Add(DateTime.Now.Ticks + 5, 130.0);

var smaBatchNaN = new Sma(3);
var resultsWithNaN = smaBatchNaN.Update(seriesWithNaN);

Console.WriteLine("Input → Output:");
for (int i = 0; i < seriesWithNaN.Count; i++)
{
    var input = seriesWithNaN[i].Value;
    var output = resultsWithNaN[i].Value;
    var inputStr = double.IsFinite(input) ? input.ToString("F2") : input.ToString();
    Console.WriteLine($"  {inputStr,-10} → {output:F2} (IsFinite: {double.IsFinite(output)})");
}

#!csharp

Console.WriteLine("\n--- Vectorized SMA with Invalid Values ---");

int[] periodsNaN = { 5, 10 };
var smaVectorNaN = new SmaVector(periodsNaN);

// Feed values including invalid ones
var inputsNaN = new double[] { 100, 110, double.NaN, 120, double.PositiveInfinity, 130 };
var time = DateTime.Now;

foreach (var val in inputsNaN)
{
    var results = smaVectorNaN.Update(new TValue(time, val));
    var inputStr = double.IsFinite(val) ? val.ToString("F2") : val.ToString();
    Console.WriteLine($"Input: {inputStr,-10} → SMA(5): {results[0].Value:F2}, SMA(10): {results[1].Value:F2}");
    time = time.AddMinutes(1);
}

Console.WriteLine("\nAll outputs are finite - invalid inputs were substituted with last valid values.");

#!markdown

## 6. SMA vs EMA Comparison

The SMA and EMA are both trend-following indicators, but they weight data differently:

- **SMA**: Equal weight to all values in the window
- **EMA**: More weight to recent values (exponentially decreasing)

#!csharp

Console.WriteLine("\n--- SMA vs EMA Comparison (Period 10) ---");

var compareData = new TSeries();
var baseTime = DateTime.Now;
for (int i = 0; i < 20; i++)
{
    // Create data with a sudden spike at position 10
    double value = (i == 10) ? 150.0 : 100.0;
    compareData.Add(baseTime.AddMinutes(i), value);
}

var smaCompare = new Sma(10);
var emaCompare = new Ema(10);

Console.WriteLine("Position | Input  |   SMA   |   EMA   | Difference");
Console.WriteLine("---------+--------+---------+---------+-----------");

for (int i = 0; i < compareData.Count; i++)
{
    var smaVal = smaCompare.Update(compareData[i]);
    var emaVal = emaCompare.Update(compareData[i]);
    var input = compareData[i].Value;
    var diff = smaVal.Value - emaVal.Value;
    
    Console.WriteLine($"   {i,2}    | {input,6:F0} | {smaVal.Value,7:F2} | {emaVal.Value,7:F2} | {diff,+9:F2}");
}

Console.WriteLine("\nNote: After the spike (position 10), EMA reacts faster due to higher weight on recent values.");
Console.WriteLine("SMA takes longer to reflect changes as all values have equal weight.");