// ENDPOINT MOVING AVERAGE
/// <include file='./info.xml' path='indicators/type[@name="Main"]/*' />
///
public static IEnumerable <EpmaResult> GetEpma <TQuote>(
IEnumerable <TQuote> history,
int lookbackPeriod)
where TQuote : IQuote
{
// check parameter arguments
ValidateEpma(history, lookbackPeriod);
// initialize
List <SlopeResult> slopeResults = GetSlope(history, lookbackPeriod)
.ToList();
int size = slopeResults.Count;
List <EpmaResult> results = new(size);
// roll through history
for (int i = 0; i < size; i++)
{
SlopeResult s = slopeResults[i];
EpmaResult r = new()
{
Date = s.Date,
Epma = s.Slope * (i + 1) + s.Intercept
};
results.Add(r);
}
return(results);
}
// STANDARD DEVIATION CHANNELS
/// <include file='./info.xml' path='indicator/*' />
///
public static IEnumerable <StdDevChannelsResult> GetStdDevChannels <TQuote>(
this IEnumerable <TQuote> history,
int?lookbackPeriod = 20,
decimal standardDeviations = 2)
where TQuote : IQuote
{
// assume whole history when lookback is null
if (lookbackPeriod is null)
{
lookbackPeriod = history.Count();
}
// check parameter arguments
ValidateStdDevChannels(history, lookbackPeriod, standardDeviations);
// initialize
List <SlopeResult> slopeResults = GetSlope(history, (int)lookbackPeriod).ToList();
int size = slopeResults.Count;
List <StdDevChannelsResult> results = slopeResults
.Select(x => new StdDevChannelsResult {
Date = x.Date
})
.ToList();
// roll through history in reverse
for (int w = size - 1; w >= lookbackPeriod - 1; w -= (int)lookbackPeriod)
{
SlopeResult s = slopeResults[w];
// add regression line (y = mx + b) and channels
for (int p = w - (int)lookbackPeriod + 1; p <= w; p++)
{
if (p >= 0)
{
StdDevChannelsResult d = results[p];
d.Centerline = s.Slope * (p + 1) + s.Intercept;
decimal width = standardDeviations * (decimal)s.StdDev;
d.UpperChannel = d.Centerline + width;
d.LowerChannel = d.Centerline - width;
d.BreakPoint = (p == w - lookbackPeriod + 1);
}
}
}
return(results);
}
// SLOPE AND LINEAR REGRESSION
/// <include file='./info.xml' path='indicator/*' />
///
public static IEnumerable <SlopeResult> GetSlope <TQuote>(
this IEnumerable <TQuote> history,
int lookbackPeriod)
where TQuote : IQuote
{
// sort history
List <TQuote> historyList = history.Sort();
// check parameter arguments
ValidateSlope(history, lookbackPeriod);
// initialize
int size = historyList.Count;
List <SlopeResult> results = new(size);
// roll through history
for (int i = 0; i < size; i++)
{
TQuote h = historyList[i];
int index = i + 1;
SlopeResult r = new()
{
Date = h.Date
};
results.Add(r);
// skip initialization period
if (index < lookbackPeriod)
{
continue;
}
// get averages for period
decimal sumX = 0m;
decimal sumY = 0m;
for (int p = index - lookbackPeriod; p < index; p++)
{
TQuote d = historyList[p];
sumX += p + 1m;
sumY += d.Close;
}
decimal avgX = sumX / lookbackPeriod;
decimal avgY = sumY / lookbackPeriod;
// least squares method
decimal sumSqX = 0m;
decimal sumSqY = 0m;
decimal sumSqXY = 0m;
for (int p = index - lookbackPeriod; p < index; p++)
{
TQuote d = historyList[p];
decimal devX = (p + 1m - avgX);
decimal devY = (d.Close - avgY);
sumSqX += devX * devX;
sumSqY += devY * devY;
sumSqXY += devX * devY;
}
r.Slope = sumSqXY / sumSqX;
r.Intercept = avgY - r.Slope * avgX;
// calculate Standard Deviation and R-Squared
double stdDevX = Math.Sqrt((double)sumSqX / lookbackPeriod);
double stdDevY = Math.Sqrt((double)sumSqY / lookbackPeriod);
r.StdDev = stdDevY;
if (stdDevX * stdDevY != 0)
{
double R = ((double)sumSqXY / (stdDevX * stdDevY)) / lookbackPeriod;
r.RSquared = R * R;
}
}
// add last Line (y = mx + b)
SlopeResult last = results.LastOrDefault();
for (int p = size - lookbackPeriod; p < size; p++)
{
SlopeResult d = results[p];
d.Line = last.Slope * (p + 1) + last.Intercept;
}
return(results);
}
// SLOPE AND LINEAR REGRESSION
public static IEnumerable <SlopeResult> GetSlope(IEnumerable <Quote> history, int lookbackPeriod)
{
// clean quotes
List <Quote> historyList = Cleaners.PrepareHistory(history).ToList();
// validate parameters
ValidateSlope(history, lookbackPeriod);
// initialize
List <SlopeResult> results = new List <SlopeResult>();
// roll through history for interim data
for (int i = 0; i < historyList.Count; i++)
{
Quote h = historyList[i];
SlopeResult r = new SlopeResult
{
Index = (int)h.Index,
Date = h.Date
};
results.Add(r);
// skip initialization period
if (h.Index < lookbackPeriod)
{
continue;
}
// get averages for period
decimal sumX = 0m;
decimal sumY = 0m;
for (int p = r.Index - lookbackPeriod; p < r.Index; p++)
{
Quote d = historyList[p];
sumX += (decimal)d.Index;
sumY += d.Close;
}
decimal avgX = sumX / lookbackPeriod;
decimal avgY = sumY / lookbackPeriod;
// least squares method
decimal sumSqX = 0m;
decimal sumSqY = 0m;
decimal sumSqXY = 0m;
for (int p = r.Index - lookbackPeriod; p < r.Index; p++)
{
Quote d = historyList[p];
decimal devX = ((decimal)d.Index - avgX);
decimal devY = (d.Close - avgY);
sumSqX += devX * devX;
sumSqY += devY * devY;
sumSqXY += devX * devY;
}
r.Slope = sumSqXY / sumSqX;
r.Intercept = avgY - r.Slope * avgX;
// calculate Standard Deviation and R-Squared
double stdDevX = Math.Sqrt((double)sumSqX / lookbackPeriod);
double stdDevY = Math.Sqrt((double)sumSqY / lookbackPeriod);
r.StdDev = stdDevY;
if (stdDevX * stdDevY != 0)
{
double R = ((double)sumSqXY / (stdDevX * stdDevY)) / lookbackPeriod;
r.RSquared = R * R;
}
}
// add last Line (y = mx + b)
SlopeResult last = results[historyList.Count - 1];
for (int p = last.Index - lookbackPeriod; p < last.Index; p++)
{
SlopeResult d = results[p];
d.Line = last.Slope * d.Index + last.Intercept;
}
return(results);
}
