TRIMA

Overview of the Triangular Moving Average calculation.

The Triangular Moving Average (TRIMA) represents an average of prices but places weight on the middle prices of the time period. The calculations double-smooths the data using a window width that is one-half the length of the series.

The source code for the TRIMA function is available here.

/* TRIMA Description
 * =================
 * The triangular MA is a weighted moving average. Instead of the
 * TA_WMA who put more weigth on the latest price bar, the triangular
 * put more weigth on the data in the middle of the specified period.
 *
 * Examples:
 *   For TimeSerie={a,b,c,d,e,f...} ('a' is the older price)
 *
 *   1st value for TRIMA 4-Period is:  ((1*a)+(2*b)+(2*c)+(1*d)) / 6
 *   2nd value for TRIMA 4-Period is:  ((1*b)+(2*c)+(2*d)+(1*e)) / 6
 *
 *   1st value for TRIMA 5-Period is:  ((1*a)+(2*b)+(3*c)+(2*d)+(1*e)) / 9
 *   2nd value for TRIMA 5-Period is:  ((1*b)+(2*c)+(3*d)+(2*e)+(1*f)) / 9
 *
 * Generally Accepted Implementation
 * ==================================
 * Using algebra, it can be demonstrated that the TRIMA is equivalent to
 * doing a SMA of a SMA. The following explain the rules:
 *
 *  (1) When the period is even, TRIMA(x,period)=SMA(SMA(x,period/2),(period/2)+1)
 *  (2) When the period is odd,  TRIMA(x,period)=SMA(SMA(x,(period+1)/2),(period+1)/2)
 *
 * In other words:
 *  (1) A period of 4 becomes TRIMA(x,4) = SMA( SMA( x, 2), 3 )
 *  (2) A period of 5 becomes TRIMA(x,5) = SMA( SMA( x, 3), 3 )
 *
 * The SMA of a SMA is the algorithm generaly found in books.
 *
 * Tradestation Implementation
 * ===========================
 * Tradestation deviate from the generally accepted implementation by
 * making the TRIMA to be as follow:
 *    TRIMA(x,period) = SMA( SMA( x, (int)(period/2)+1), (int)(period/2)+1 );
 * This formula is done regardless if the period is even or odd.
 *
 * In other word:
 *  (1) A period of 4 becomes TRIMA(x,4) = SMA( SMA( x, 3), 3 )
 *  (2) A period of 5 becomes TRIMA(x,5) = SMA( SMA( x, 3), 3 )
 *  (3) A period of 6 becomes TRIMA(x,5) = SMA( SMA( x, 4), 4 )
 *  (4) A period of 7 becomes TRIMA(x,5) = SMA( SMA( x, 4), 4 )
 *
 * It is not clear to me if the Tradestation approach is a bug or a deliberate
 * decision to do things differently.
 *    
 * Metastock Implementation
 * ========================
 * Output is the same as the generally accepted implementation.
 *
 * TA-Lib Implementation
 * =====================
 * Output is also the same as the generally accepted implementation.
 *
 * For speed optimization and avoid memory allocation, TA-Lib use
 * a better algorithm than the usual SMA of a SMA.
 *
 * The calculation from one TRIMA value to the next is done by doing 4
 * little adjustment (the following show a TRIMA 4-period):
 *
 * TRIMA at time 'd': ((1*a)+(2*b)+(2*c)+(1*d)) / 6
 * TRIMA at time 'e': ((1*b)+(2*c)+(2*d)+(1*e)) / 6
 * 
 * To go from TRIMA 'd' to 'e', the following is done:
 *       1) 'a' and 'b' are substract from the numerator.
 *       2) 'd' is added to the numerator.
 *       3) 'e' is added to the numerator.
 *       4) Calculate TRIMA by doing numerator / 6
 *       5) Repeat sequence for next output
 *
 * These operations are the same steps done by TA-LIB:
 *       1) is done by numeratorSub
 *       2) is done by numeratorAdd.
 *       3) is obtain from the latest input
 *       4) Calculate and write TRIMA in the output
 *       5) Repeat for next output.
 *
 * Of course, numerotrAdd and numeratorSub needs to be
 * adjusted for each iteration.
 *
 * The update of numeratorSub needs values from the input at
 * the trailingIdx and middleIdx position.
 *
 * The update of numeratorAdd needs values from the input at
 * the middleIdx and todayIdx.
 */