Linear — Göstergeler ve Stratejiler

Trend Library "Trend" calculateSlopeTrend(source, length, thresholdMultiplier) Parameters: source (float) length (int) thresholdMultiplier (float) Purpose: The primary goal of this function is to determine the short-term trend direction of a given data series (like closing prices). It does this by calculating the slope of the data over a specified period and then comparing that slope against a dynamic threshold based on the data's recent volatility. It classifies the trend into one of three states: Upward, Downward, or Flat. Parameters: `source` (Type: `series float`): This is the input data series you want to analyze. It expects a series of floating-point numbers, typically price data like `close`, `open`, `hl2` (high+low)/2, etc. `length` (Type: `int`): This integer defines the lookback period. The function will analyze the `source` data over the last `length` bars to calculate the slope and standard deviation. `thresholdMultiplier` (Type: `float`, Default: `0.1`): This is a sensitivity factor. It's multiplied by the standard deviation to determine how steep the slope needs to be before it's considered a true upward or downward trend. A smaller value makes it more sensitive (detects trends earlier, potentially more false signals), while a larger value makes it less sensitive (requires a stronger move to confirm a trend). Calculation Steps: Linear Regression: It first calculates the value of a linear regression line fitted to the `source` data over the specified `length` (`ta.linreg(source, length, 0)`). Linear regression finds the "best fit" straight line through the data points. Slope Calculation: It then determines the slope of this linear regression line. Since `ta.linreg` gives the *value* of the line on the current bar, the slope is calculated as the difference between the current bar's linear regression value (`linRegValue`) and the previous bar's value (`linRegValue `). A positive difference means an upward slope, negative means downward. Volatility Measurement: It calculates the standard deviation (`ta.stdev(source, length)`) of the `source` data over the same `length`. Standard deviation is a measure of how spread out the data is, essentially quantifying its recent volatility. Adaptive Threshold: An adaptive threshold (`threshold`) is calculated by multiplying the standard deviation (`stdDev`) by the `thresholdMultiplier`. This is crucial because it means the definition of a "flat" trend adapts to the market's volatility. In volatile times, the threshold will be wider, requiring a larger slope to signal a trend. In quiet times, the threshold will be narrower. Trend Determination: Finally, it compares the calculated `slope` to the adaptive `threshold`: If the `slope` is greater than the positive `threshold`, the trend is considered **Upward**, and the function returns `1`. If the `slope` is less than the negative `threshold` (`-threshold`), the trend is considered **Downward**, and the function returns `-1`. If the `slope` falls between `-threshold` and `+threshold` (inclusive of 0), the trend is considered **Flat**, and the function returns `0`. Return Value: The function returns an integer representing the determined trend direction: `1`: Upward trend `-1`: Downward trend `0`: Flat trend In essence, this library function provides a way to gauge trend direction using linear regression, but with a smart filter (the adaptive threshold) to avoid classifying minor noise or low-volatility periods as significant trends.

regressions Library "regressions" This library computes least square regression models for polynomials of any form for a given data set of x and y values. fit(X, y, reg_type, degrees) Takes a list of X and y values and the degrees of the polynomial and returns a least square regression for the given polynomial on the dataset. Parameters: X (array) : (float ) X inputs for regression fit. y (array) : (float ) y outputs for regression fit. reg_type (string) : (string) The type of regression. If passing value for degrees use reg.type_custom degrees (array) : (int ) The degrees of the polynomial which will be fit to the data. ex: passing array.from(0, 3) would be a polynomial of form c1x^0 + c2x^3 where c2 and c1 will be coefficients of the best fitting polynomial. Returns: (regression) returns a regression with the best fitting coefficients for the selecected polynomial regress(reg, x) Regress one x input. Parameters: reg (regression) : (regression) The fitted regression which the y_pred will be calulated with. x (float) : (float) The input value cooresponding to the y_pred. Returns: (float) The best fit y value for the given x input and regression. predict(reg, X) Predict a new set of X values with a fitted regression. -1 is one bar ahead of the realtime Parameters: reg (regression) : (regression) The fitted regression which the y_pred will be calulated with. X (array) Returns: (float ) The best fit y values for the given x input and regression. generate_points(reg, x, y, left_index, right_index) Takes a regression object and creates chart points which can be used for plotting visuals like lines and labels. Parameters: reg (regression) : (regression) Regression which has been fitted to a data set. x (array) : (float ) x values which coorispond to passed y values y (array) : (float ) y values which coorispond to passed x values left_index (int) : (int) The offset of the bar farthest to the realtime bar should be larger than left_index value. right_index (int) : (int) The offset of the bar closest to the realtime bar should be less than right_index value. Returns: (chart.point ) Returns an array of chart points plot_reg(reg, x, y, left_index, right_index, curved, close, line_color, line_width) Simple plotting function for regression for more custom plotting use generate_points() to create points then create your own plotting function. Parameters: reg (regression) : (regression) Regression which has been fitted to a data set. x (array) y (array) left_index (int) : (int) The offset of the bar farthest to the realtime bar should be larger than left_index value. right_index (int) : (int) The offset of the bar closest to the realtime bar should be less than right_index value. curved (bool) : (bool) If the polyline is curved or not. close (bool) : (bool) If true the polyline will be closed. line_color (color) : (color) The color of the line. line_width (int) : (int) The width of the line. Returns: (polyline) The polyline for the regression. series_to_list(src, left_index, right_index) Convert a series to a list. Creates a list of all the cooresponding source values from left_index to right_index. This should be called at the highest scope for consistency. Parameters: src (float) : (float ) The source the list will be comprised of. left_index (int) : (float ) The left most bar (farthest back historical bar) which the cooresponding source value will be taken for. right_index (int) : (float ) The right most bar closest to the realtime bar which the cooresponding source value will be taken for. Returns: (float ) An array of size left_index-right_index range_list(start, stop, step) Creates an from the start value to the stop value. Parameters: start (int) : (float ) The true y values. stop (int) : (float ) The predicted y values. step (int) : (int) Positive integer. The spacing between the values. ex: start=1, stop=6, step=2: Returns: (float ) An array of size stop-start regression Fields: coeffs (array__float) degrees (array__float) type_linear (series__string) type_quadratic (series__string) type_cubic (series__string) type_custom (series__string) _squared_error (series__float) X (array__float)

LTI_Filters Linear Time-Invariant (LTI) filters are fundamental tools in signal processing that operate with consistent behavior over time and linearly respond to input signals. They are crucial for analyzing and manipulating signals in various applications, ensuring the output signal's integrity is maintained regardless of when an input is applied or its magnitude. The Windowed Sinc filter is a specific type of LTI filter designed for digital signal processing. It employs a Sinc function, ideal for low-pass filtering, truncated and shaped within a finite window to make it practically implementable. This process involves multiplying the Sinc function by a window function, which tapers off towards the ends, making the filter finite and suitable for digital applications. Windowed Sinc filters are particularly effective for tasks like data smoothing and removing unwanted frequency components, balancing between sharp cutoff characteristics and minimal distortion. The efficiency of Windowed Sinc filters in digital signal processing lies in their adept use of linear algebra, particularly in the convolution process, which combines input data with filter coefficients to produce the desired output. This mathematical foundation allows for precise control over the filtering process, optimizing the balance between filtering performance and computational efficiency. By leveraging linear algebra techniques such as matrix multiplication and Toeplitz matrices, these filters can efficiently handle large datasets and complex filtering tasks, making them invaluable in applications requiring high precision and speed, such as audio processing, financial signal analysis, and image restoration. Library "LTI_Filters" offset(length, enable) Calculates the time offset required for aligning the output of a filter with its input, based on the filter's length. This is useful for centered filters where the output is naturally shifted due to the filter's operation. Parameters: length (simple int) : The length of the filter. enable (simple bool) : A boolean flag to enable or dissable the offset calculation. Returns: The calculated offset if enabled; otherwise, returns 0. lti_filter(filter_type, source, length, prefilter, centered, fc, window_type) General-purpose Linear Time-Invariant (LTI) filter function that can apply various filter types to a data series. Can be used to apply a variety of LTI filters with different characteristics to financial data series or other time series data. Parameters: filter_type (simple string) : Specifies the type of filter. ("Sinc", "SMA", "WMA") source (float) : The input data series to filter. length (simple int) : The length of the filter. prefilter (simple bool) : Boolean indicating whether to prefilter the input data. centered (simple bool) : Determines whether the filter coefficients are centered. fc (simple float) : Filter cutoff. Expressed like a length. window_type (simple string) : Type of window function to apply. ("Hann", "Hamming", "Blackman", "Triangular", "Lanczos", "None") Returns: The filtered data series. lti_sma(source, length, prefilter) Applies a Simple Moving Average (SMA) filter to the data series. Useful for smoothing data series to identify trends or for use as a component in more complex indicators. Parameters: source (float) : The input data series to filter. length (simple int) : The length of the SMA filter. prefilter (simple bool) : Boolean indicating whether to prefilter the input data. Returns: The SMA-filtered data series. lti_wma(source, length, prefilter, centered) Applies a Weighted Moving Average (WMA) filter to a data series. Ideal for smoothing data with emphasis on more recent values, allowing for dynamic adjustments to the weighting scheme. Parameters: source (float) : The input data series to filter. length (simple int) : The length of the WMA filter. prefilter (simple bool) : Boolean indicating whether to prefilter the input data. centered (simple bool) : Determines whether the filter coefficients are centered. Returns: The WMA-filtered data series. lti_sinc(source, length, prefilter, centered, fc, window_type) Applies a Sinc filter to a data series, optionally using a window function. Particularly useful for signal processing tasks within financial analysis, such as smoothing or trend identification, with the ability to fine-tune filter characteristics. Parameters: source (float) : The input data series to filter. length (simple int) : The length of the Sinc filter. prefilter (simple bool) : Boolean indicating whether to prefilter the input data. centered (simple bool) : Determines whether the filter coefficients are centered. fc (simple float) : Filter cutoff. Expressed like a length. window_type (simple string) : Type of window function to apply. ("Hann", "Hamming", "Blackman", "Triangular", "Lanczos", "None") Returns: The Sinc-filtered data series.

regress Library "regress" produces the slope (beta), y-intercept (alpha) and coefficient of determination for a linear regression regress(x, y, len) regress: computes alpha, beta, and r^2 for a linear regression of y on x Parameters: x : the explaining (independent) variable y : the dependent variable len : use the most recent "len" values of x and y Returns: : alpha is the x-intercept, beta is the slope, an r2 is the coefficient of determination Note: the chart does not show anything, use the return values to compute model values in your own application, if you wish.