MACD Function Returning Incorrect Values

Question

I am trying to use PHPs trader functions (available as a PECL extension) to calculate the moving average convergence/divergence (MACD) of various securities. However, the values returned do not seem to match my calculations.

Consider the following array of close prices for a stock:

$close = array (
  0 => 459.99,
  1 => 448.85,
  2 => 446.06,
  3 => 450.81,
  4 => 442.8,
  5 => 448.97,
  6 => 444.57,
  7 => 441.4,
  8 => 430.47,
  9 => 420.05,
  10 => 431.14,
  11 => 425.66,
  12 => 430.58,
  13 => 431.72,
  14 => 437.87,
  15 => 428.43,
  16 => 428.35,
  17 => 432.5,
  18 => 443.66,
  19 => 455.72,
  20 => 454.49,
  21 => 452.08,
  22 => 452.73,
  23 => 461.91,
  24 => 463.58,
  25 => 461.14,
  26 => 452.08,
  27 => 442.66,
  28 => 428.91,
  29 => 429.79,
  30 => 431.99,
  31 => 427.72,
  32 => 423.2,
  33 => 426.21,
  34 => 426.98,
  35 => 435.69,
  36 => 434.33,
  37 => 429.8,
  38 => 419.85,
  39 => 426.24,
  40 => 402.8,
  41 => 392.05,
  42 => 390.53,
  43 => 398.67,
  44 => 406.13,
  45 => 405.46,
  46 => 408.38,
  47 => 417.2,
  48 => 430.12,
  49 => 442.78,
  50 => 439.29,
  51 => 445.52,
  52 => 449.98,
  53 => 460.71,
  54 => 458.66,
  55 => 463.84,
  56 => 456.77,
  57 => 452.97,
  58 => 454.74,
  59 => 443.86,
  60 => 428.85,
  61 => 434.58,
  62 => 433.26,
  63 => 442.93,
  64 => 439.66,
  65 => 441.35,
);

Based on these numbers, the MACD, signal line, and MACD histogram should come out to:

// MACD
Array
(
    [0] => 8.275269504
    [1] => 7.703378381
    [2] => 6.416074757
    [3] => 4.237519783
    [4] => 2.552583325
    [5] => 1.37888572
    [6] => 0.102981491
    [7] => -1.258401953
    [8] => -2.07055819
    [9] => -2.621842328
    [10] => -2.32906674
    [11] => -2.181632115
    [12] => -2.402626273
    [13] => -3.342121681
    [14] => -3.530363136
    [15] => -5.507471249
    [16] => -7.851274229
    [17] => -9.719367455
    [18] => -10.42286651
    [19] => -10.26016216
    [20] => -10.06920961
    [21] => -9.571919612
    [22] => -8.369633492
    [23] => -6.301635724
    [24] => -3.599681509
    [25] => -1.720148361
    [26] => 0.269003232
    [27] => 2.180173247
    [28] => 4.508637809
    [29] => 6.118020154
    [30] => 7.722430594
    [31] => 8.327453809
    [32] => 8.403441185
    [33] => 8.508406323
    [34] => 7.625761844
    [35] => 5.649949083
    [36] => 4.494654765
    [37] => 3.432989362
    [38] => 3.333473854
    [39] => 2.956662856
    [40] => 2.762561216
)

// Signal line
Array
(
    [0] => 3.037525869
    [1] => 1.905652229
    [2] => 1.058708435
    [3] => 0.410640325
    [4] => -0.152012994
    [5] => -0.790034732
    [6] => -1.338100413
    [7] => -2.17197458
    [8] => -3.30783451
    [9] => -4.590141099
    [10] => -5.756686181
    [11] => -6.657381376
    [12] => -7.339747023
    [13] => -7.786181541
    [14] => -7.902871931
    [15] => -7.58262469
    [16] => -6.786036054
    [17] => -5.772858515
    [18] => -4.564486166
    [19] => -3.215554283
    [20] => -1.670715865
    [21] => -0.112968661
    [22] => 1.45411119
    [23] => 2.828779714
    [24] => 3.943712008
    [25] => 4.856650871
    [26] => 5.410473066
    [27] => 5.458368269
    [28] => 5.265625568
    [29] => 4.899098327
    [30] => 4.585973432
    [31] => 4.260111317
    [32] => 3.960601297
)

// MACD histogram
Array
(
    [0] => -5.108084059
    [1] => -4.527494558
    [2] => -3.387775176
    [3] => -2.59227244
    [4] => -2.250613279
    [5] => -2.55208695
    [6] => -2.192262723
    [7] => -3.335496669
    [8] => -4.543439719
    [9] => -5.129226357
    [10] => -4.666180327
    [11] => -3.602780783
    [12] => -2.729462587
    [13] => -1.785738071
    [14] => -0.466761561
    [15] => 1.280988966
    [16] => 3.186354544
    [17] => 4.052710154
    [18] => 4.833489398
    [19] => 5.39572753
    [20] => 6.179353673
    [21] => 6.230988815
    [22] => 6.268319404
    [23] => 5.498674095
    [24] => 4.459729177
    [25] => 3.651755452
    [26] => 2.215288778
    [27] => 0.191580814
    [28] => -0.770970803
    [29] => -1.466108965
    [30] => -1.252499579
    [31] => -1.303448461
    [32] => -1.198040081
)

^{Note that the MACD requires the calculation of a 26 day moving average, so while there are 66 different data points for the close price, there are only 41 calculated MACD values. Additionally, the signal line (and therefore the MACD histogram which requires the signal line) requires a 9 day moving average of the MACD, so there are only 31 calculations for the signal line/MACD histogram.}

The above data was calculated on excel and is the correct MACD. The short script I have to calculate the MACD in PHP is:

<?php
// The array $close is the same as it is in the above example, omitted here for brevity.
$macd = trader_macd($close, 12, 26);
var_dump($macd);
?>

However, var_dump($macd) prints:

array(3) {
  [0]=>
  array(40) {
    [24]=>
    float(0)
    [25]=>
    float(4.415)
    [26]=>
    float(4.437)
    [27]=>
    float(3.652)
    [28]=>
    float(1.899)
    [29]=>
    float(0.574)
    [30]=>
    float(-0.295)
    [31]=>
    float(-1.314)
    [32]=>
    float(-2.457)
    [33]=>
    float(-3.085)
    [34]=>
    float(-3.48)
    [35]=>
    float(-3.055)
    [36]=>
    float(-2.796)
    [37]=>
    float(-2.923)
    [38]=>
    float(-3.782)
    [39]=>
    float(-3.903)
    [40]=>
    float(-5.822)
    [41]=>
    float(-8.118)
    [42]=>
    float(-9.945)
    [43]=>
    float(-10.614)
    [44]=>
    float(-10.422)
    [45]=>
    float(-10.206)
    [46]=>
    float(-9.688)
    [47]=>
    float(-8.467)
    [48]=>
    float(-6.384)
    [49]=>
    float(-3.67)
    [50]=>
    float(-1.779)
    [51]=>
    float(0.219)
    [52]=>
    float(2.138)
    [53]=>
    float(4.473)
    [54]=>
    float(6.088)
    [55]=>
    float(7.697)
    [56]=>
    float(8.306)
    [57]=>
    float(8.385)
    [58]=>
    float(8.493)
    [59]=>
    float(7.613)
    [60]=>
    float(5.639)
    [61]=>
    float(4.485)
    [62]=>
    float(3.425)
    [63]=>
    float(3.327)
  }
  [1]=>
  array(40) {
    [24]=>
    float(4.437)
    [25]=>
    float(3.652)
    [26]=>
    float(1.899)
    [27]=>
    float(0.574)
    [28]=>
    float(-0.295)
    [29]=>
    float(-1.314)
    [30]=>
    float(-2.457)
    [31]=>
    float(-3.085)
    [32]=>
    float(-3.48)
    [33]=>
    float(-3.055)
    [34]=>
    float(-2.796)
    [35]=>
    float(-2.923)
    [36]=>
    float(-3.782)
    [37]=>
    float(-3.903)
    [38]=>
    float(-5.822)
    [39]=>
    float(-8.118)
    [40]=>
    float(-9.945)
    [41]=>
    float(-10.614)
    [42]=>
    float(-10.422)
    [43]=>
    float(-10.206)
    [44]=>
    float(-9.688)
    [45]=>
    float(-8.467)
    [46]=>
    float(-6.384)
    [47]=>
    float(-3.67)
    [48]=>
    float(-1.779)
    [49]=>
    float(0.219)
    [50]=>
    float(2.138)
    [51]=>
    float(4.473)
    [52]=>
    float(6.088)
    [53]=>
    float(7.697)
    [54]=>
    float(8.306)
    [55]=>
    float(8.385)
    [56]=>
    float(8.493)
    [57]=>
    float(7.613)
    [58]=>
    float(5.639)
    [59]=>
    float(4.485)
    [60]=>
    float(3.425)
    [61]=>
    float(3.327)
    [62]=>
    float(2.951)
    [63]=>
    float(2.758)
  }
  [2]=>
  array(40) {
    [24]=>
    float(-4.437)
    [25]=>
    float(0.763)
    [26]=>
    float(2.538)
    [27]=>
    float(3.079)
    [28]=>
    float(2.194)
    [29]=>
    float(1.888)
    [30]=>
    float(2.162)
    [31]=>
    float(1.771)
    [32]=>
    float(1.023)
    [33]=>
    float(-0.03)
    [34]=>
    float(-0.684)
    [35]=>
    float(-0.133)
    [36]=>
    float(0.986)
    [37]=>
    float(0.98)
    [38]=>
    float(2.04)
    [39]=>
    float(4.215)
    [40]=>
    float(4.122)
    [41]=>
    float(2.496)
    [42]=>
    float(0.477)
    [43]=>
    float(-0.408)
    [44]=>
    float(-0.734)
    [45]=>
    float(-1.738)
    [46]=>
    float(-3.303)
    [47]=>
    float(-4.798)
    [48]=>
    float(-4.605)
    [49]=>
    float(-3.889)
    [50]=>
    float(-3.917)
    [51]=>
    float(-4.254)
    [52]=>
    float(-3.95)
    [53]=>
    float(-3.224)
    [54]=>
    float(-2.218)
    [55]=>
    float(-0.688)
    [56]=>
    float(-0.187)
    [57]=>
    float(0.772)
    [58]=>
    float(2.854)
    [59]=>
    float(3.127)
    [60]=>
    float(2.214)
    [61]=>
    float(1.159)
    [62]=>
    float(0.474)
    [63]=>
    float(0.569)
  }
}

As is above, PHP returns an array containing 3 arrays. The documentation gives little hint as to what each array is, stating only that the MACD function

Returns an array with calculated data or false on failure.

A user contributed note (albeit one that has a score of -1) adds that the first array (index 0) is the MACD values, the second array (index 1) is the signal values, and the last array (index 2) is the divergence values.

Even if the users note is true, the returned arrays do not match my calculations (which I know to be correct). Why is trader_macd() returning incorrect values/what am I doing wrong?

PHPs documentation of the trader functions contains little more than an argument list of each function. As a side note, is there anywhere I can get more detailed documentation for the trader extension? This is not the first time I have had trouble with a function in the extension.

Answer 1

I don't know PHP, but I can explain ta-lib behavior from C/C++ perspective. I've debugged its MACD with your dataset. If you call ta-lib's C function ta_macd() for your data you'll get following.

macd     signal    hist
-3.08486 0.869685 -3.95455
-3.4801 -0.000272319 -3.47983
-3.05529 -0.611275 -2.44401
-2.79613 -1.04825 -1.74788
-2.92258 -1.42311 -1.49947
-3.78208 -1.89491 -1.88718
-3.90264 -2.29645 -1.60619
-5.82247 -3.00166 -2.82082
-8.11782 -4.02489 -4.09293
-9.9449 -5.20889 -4.73601
-10.6137 -6.28985 -4.32385
-10.4216 -7.11621 -3.30543
-10.2058 -7.73414 -2.47171
-9.68753 -8.12482 -1.56272
-8.46746 -8.19335 -0.274115
-6.38441 -7.83156 1.44715
-3.66972 -6.99919 3.32947
-1.77941 -5.95524 4.17582
0.218855 -4.72042 4.93927
2.13774 -3.34879 5.48653
4.47273 -1.78448 6.25722
6.08764 -0.210058 6.2977
7.69672 1.3713 6.32543
8.3057 2.75818 5.54752
8.38504 3.88355 4.50149
8.49283 4.80541 3.68743
7.61258 5.36684 2.24574
5.6388 5.42123 0.217565
4.48522 5.23403 -0.748811
3.42501 4.87223 -1.44722
3.32672 4.56312 -1.23641
2.95095 4.24069 -1.28974
2.75772 3.9441 -1.18637

It doesn't match your excel file bcs of following:

1. TA-Lib calculates 26-day EMA where first EMA result is average of initial 26-days period. This is a default behavior (non-Metastock).
2. TA-lib calculates 12-day EMA where first EMA result is average of initial 12-days period. But it adjusted to a day where first 26-day EMA could be got. So it uses days 15-26 to calculate average that is first value for 12-day EMA. That's a main difference with your Excel. Just put formula =AVERAGE(B19:B30) in cell C30 and the excel results will match with C function results.
3. Then TA-lib calculates signal\hist values using 9-day (default signal period) EMA over values it got on steps 2 and 3. And it returns results only for days what have both MACD, signal and hist. In other words it doesn't return first 8 MACD values. If you made the change proposed on step 2 in your Excel you'll see that the C++ function results will match with range E38-G70.

Well, that's how TA-Lib works as far as I can see. But if you compare my results with your PHP function results you'll find that they doesn't match too. But you can notice that my MACDs are equal to values in your 1st array starting from

[33]=>
    float(-3.085)

And if you compare PHP results with Excel (updated) you'll find that first elements of 1st array are equal to E30-E37. These are first 8 MACDs that TA-Libs omits as they don't have corresponding signal\hist values bcs signal is calculated with 9-days EMA. It also means following:

1. trader function authors doesn't use vanilla ta-lib. Perhaps they've rewritten TA_MACD function logic in PHP, or forked ta-lib or used very old version that I don't know. Because ta-lib just don't return MACD values that they returns (although it calculates them).
2. I don't understand their result arrays format or I don't understand how they calculate signal\hist values (bcs first array is quite explainable).

I would recommend looking inside PHP function source code. I couldn't find it. If you want to doublecheck vanilla C implementation of MACD in ta-lib, you shall refer to following pages: macd, ema.