In the following code box there are the results from the temporal clustering routine of my last few posts on the four forex majors pairs of EUR_USD, GBP_USD, USD_CHF and USD_JPY.
###### EUR_USD 10 minute bars #######
## In the following order
## Both Delta turning point filter and "normal" TPF combined ##
## Delta turning point filter only ##
## "Normal" turning point filter only
###################### Monday ##############################################
K_opt == 8, ix values == 13 38 63 89 112 135 162 186 ## averaged over all 15 n_bars 1 to 15 inclusive
00 4:10 8:20 12:40 16:30 20:20 00:50 4:50
K_opt == 8, ix values == 13 39 64 89 112 135 161 186 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt == 5, ix_values == 21 60 97 134 175 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
K == 6, ix values == 21 59 94 125 158 184
K_opt == 11, ix values == 9 26 43 60 78 95 113 132 151 169 185 ## averaged over all 15 n_bars 1 to 15 inclusive
K_opt == 8, ix values == 13 36 61 86 111 136 161 186 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt == 8, ix values == 13 34 61 87 110 137 164 187 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
K_opt == 8, ix values == 13 38 63 88 112 137 162 186 ## averaged over all 15 n_bars 1 to 15 inclusive
K_opt == 10, ix values == 10 31 52 72 91 112 131 150 169 188 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt == 8, ix values == 12 35 62 88 112 137 164 187 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
###################### Tuesday #############################################
K_opt == 6, ix values == 131 169 206 244 283 322 ## averaged over all 15 n_bars 1 to 15 inclusive
19:40 02:00 8:10 14:30 21:00 03:30
K_opt == 6, ix values == 131 170 207 245 284 323 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt == 7, ix values == 131 168 206 243 274 305 330 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
K_opt == 11, ix values == 124 143 164 184 205 226 247 268 289 310 331 ## averaged over all 15 n_bars 1 to 15 inclusive
K_opt == 11, ix values == 124 144 164 185 204 225 246 267 288 309 332 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt == 7, ix values = 133 169 206 241 273 304 329 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
K_opt == 9, ix values == 127 152 175 202 228 253 278 305 330 ## averaged over all 15 n_bars 1 to 15 inclusive
K_opt == 9, ix values == 127 152 177 202 228 253 278 304 329 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt == 7, ix values == 132 168 205 242 273 304 329 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
###################### Wednesday ###########################################
K_opt == 6, ix values == 275 312 351 389 426 465 ## averaged over all 15 n_bars 1 to 15 inclusive
19:40 01:50 08:20 14:40 20:50 03:20
K_opt == 6, ix values == 275 313 352 391 428 466 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt == 6, ix values == 274 312 350 389 424 463 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
K_opt == 9, ix values == 272 299 322 347 372 397 422 449 474 ## averaged over all 15 n_bars 1 to 15 inclusive
K_opt == 11, ix values == 268 288 308 329 348 369 390 411 432 453 476 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt == 6, ix values == 275 312 351 388 424 463 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
K_opt == 9, ix values == 272 297 322 348 373 398 423 449 474 ## averaged over all 15 n_bars 1 to 15 inclusive
K_opt == 9, ix values == 271 297 322 348 373 398 423 448 473 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt == 6, ix values == 276 311 350 389 426 465 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
####################### Thursday ###########################################
K_opt == 6, ix values == 420 457 495 532 570 609 ## averaged over all 15 n_bars 1 to 15 inclusive
19:50 02:00 08:20 14:30 20:50 03:20
K_opt == 6, ix values == 420 457 494 531 570 610 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt == 6, ix values == 420 457 495 532 568 607 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
K_opt == 9, ix values == 416 443 466 492 518 543 568 593 618 ## averaged over all 15 n_bars 1 to 15 inclusive
K_opt == 10, ix values == 414 437 460 483 506 527 550 573 596 619 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt == 9, ix values == 416 443 466 493 520 543 568 595 618 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
K_opt == 9, ix values == 415 440 465 492 518 543 568 593 618 ## averaged over all 15 n_bars 1 to 15 inclusive
K_opt == 9, ix values == 415 440 465 492 518 543 568 593 618 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt == 7, ix values == 420 457 494 529 561 592 617 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
####################### Friday #############################################
K_opt == 5, ix values == 564 599 635 670 703 ## averaged over all 15 n_bars 1 to 15 inclusive
19:50 01:40 07:40 13:30 19:00
K_opt == 6, ix values == 563 596 627 654 680 707 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K == 5, ix values == 564 599 635 668 703
K_opt == 5, ix values == 564 601 639 674 705 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
K_opt == 9, ix values == 556 575 595 614 633 652 672 691 711 ## averaged over all 15 n_bars 1 to 15 inclusive
K_opt == 11, ix values == 554 570 587 602 619 634 651 667 682 698 713 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt == 9, ix values == 556 575 595 614 633 652 671 691 711 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt == 9, ix values == 556 575 596 613 634 652 672 691 711 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
K_opt == 9, ix values == 556 575 594 613 633 652 672 691 710 ## averaged over all 15 n_bars 1 to 15 inclusive
K_opt == 9, ix values == 556 575 594 613 634 653 672 691 710 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt == 5, ix values == 564 600 637 674 705 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
############################################################################
###### GBP_USD 10 minute bars #######
## In the following order
## Both Delta turning point filter and "normal" TPF combined ##
###################### Monday ##############################################
K_opt = 8, ix_values = 13 36 61 86 111 136 162 186 ## averaged over all 15 n_bars 1 to 15 inclusive
0:00 3:50 8:00 12:10 16:20 20:30 0:50 4:50
K_opt = 9, ix_values = 12 34 56 78 99 120 141 164 187 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt = 8, ix_values = 12 35 61 86 110 136 163 186 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
###################### Tuesday #############################################
K_opt = 12, ix_values = 124 143 162 180 199 216 235 254 274 293 312 332 ## averaged over all 15 n_bars 1 to 15 inclusive
18:30 21:40 0:50 3:50 7:00 9:50 13:00 16:10 19:30 22:40 1:50 5:10
K_opt = 11, ix_values = 124 143 164 185 206 227 248 269 290 311 332 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt = 9, ix_values = 128 154 177 205 230 254 279 307 330 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
###################### Wednesday ###########################################
K_opt = 11, ix_values = 269 290 311 331 352 373 394 415 434 455 476 ## averaged over all 15 n_bars 1 to 15 inclusive
18:40 22:10 1:40 5:00 8:30 12:00 15:30 19:00 22:10 1:40 5:10
K_opt = 11, ix_values = 269 289 310 330 351 372 393 413 434 455 476 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt = 8, ix_values = 275 310 341 367 394 422 451 475 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
###################### Thursday ############################################
K_opt = 9, ix_values = 415 440 465 492 517 542 568 594 618 ## averaged over all 15 n_bars 1 to 15 inclusive
19:00 23:10 3:20 7:50 12:00 16:10 20:30 0:50 4:50
K_opt = 9, ix_values = 415 440 465 491 517 542 568 593 618 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt = 9, ix_values = 416 441 464 492 519 542 569 596 619 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
###################### Friday ##############################################
K_opt = 9, ix_values = 557 576 595 614 633 652 671 690 711 ## averaged over all 15 n_bars 1 to 15 inclusive
18:40 21:50 1:00 4:10 7:20 10:30 13:40 16:50 20:20
K_opt = 9, ix_values = 557 576 595 614 633 652 671 691 711 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt = 8, ix_values = 557 576 599 621 642 665 686 709 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
############################################################################
###### USD_CHF 10 minute bars #######
## In the following order
## Both Delta turning point filter and "normal" TPF combined ##
###################### Monday ##############################################
K_opt = 11, ix_values = 8 25 42 61 79 96 113 131 150 169 188 ## averaged over all 15 n_bars 1 to 15 inclusive
23:10 2:00 4:50 8:00 11:00 13:50 16:40 19:40 22:50 2:00 5:10
K_opt = 11, ix_values = 9 26 43 60 79 96 114 133 151 170 189 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt = 7, ix_values = 13 38 66 99 127 157 184 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
###################### Tuesday #############################################
K_opt = 9, ix_values = 127 152 177 202 228 253 279 306 330 ## averaged over all 15 n_bars 1 to 15 inclusive
19:00 23:10 3:20 7:30 11:50 16:00 20:20 0:50 4:50
K_opt = 11, ix_values = 124 144 165 185 204 225 246 267 288 309 331 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt = 7, ix_values = 133 170 205 240 270 301 328 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
###################### Wednesday ###########################################
K_opt = 10, ix_values = 270 293 316 342 365 388 411 432 454 475 ## averaged over all 15 n_bars 1 to 15 inclusive
18:50 22:40 2:30 6:50 10:40 14:30 18:20 21:50 1:30 5:00
K_opt = 12, ix_values = 268 287 308 327 346 365 384 401 420 439 458 477 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt = 7, ix_values = 276 313 349 383 414 444 471 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
###################### Thursday ############################################
K_opt = 11, ix_values = 413 432 452 471 491 512 533 554 575 598 619 ## averaged over all 15 n_bars 1 to 15 inclusive
18:40 21:50 1:10 4:20 7:40 11:10 14:40 18:10 21:40 1:30 5:00
K_opt = 12, ix_values = 412 431 450 469 488 507 526 545 563 582 601 621 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt = 9, ix_values = 415 440 463 491 518 543 570 597 619 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
###################### Friday ##############################################
K_opt = 9, ix_values = 557 576 596 615 634 653 672 691 710 ## averaged over all 15 n_bars 1 to 15 inclusive
18:40 21:50 1:10 4:20 7:30 10:40 13:50 17:00 20:10
K_opt = 9, ix_values = 556 575 595 614 633 652 671 690 710 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt = 7, ix_values = 558 579 602 629 652 677 705 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
############################################################################
###### USD_JPY 10 minute bars #######
## In the following order
## Both Delta turning point filter and "normal" TPF combined ##
###################### Monday ##############################################
K_opt = 12, ix_values = 8 24 41 58 73 90 107 124 141 158 173 190 ## averaged over all 15 n_bars 1 to 15 inclusive
23:10 1:50 4:40 7:30 10:00 12:50 15:40 18:30 21:20 0:10 2:40 5:30
K_opt = 12, ix_values = 8 24 41 56 73 90 107 124 141 158 173 190 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt = 5, ix_values = 20 60 99 136 175 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
###################### Tuesday #############################################
K_opt = 9, ix_values = 128 154 179 204 229 254 279 306 331 ## averaged over all 15 n_bars 1 to 15 inclusive
19:10 23:30 3:40 7:50 12:00 16:10 20:20 0:50 5:00
K_opt = 9, ix_values = 128 153 178 203 228 254 279 305 330 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt = 7, ix_values = 133 168 205 240 271 302 329 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
###################### Wednesday ###########################################
K_opt = 11, ix_values = 269 289 310 331 352 373 394 414 433 454 476 ## averaged over all 15 n_bars 1 to 15 inclusive
18:40 22:00 1:30 5:00 8:30 12:00 15:30 18:50 22:00 1:30 5:10
K_opt = 9, ix_values = 272 297 322 348 374 399 424 449 474 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt = 10, ix_values = 269 288 309 331 352 376 398 423 450 475 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
###################### Thursday ############################################
K_opt = 9, ix_values = 416 442 467 492 518 543 568 593 618 ## averaged over all 15 n_bars 1 to 15 inclusive
19:10 23:30 3:40 7:50 12:10 16:20 20:30 0:40 4:50
K_opt = 12, ix_values = 412 431 450 469 488 507 526 545 564 583 602 621 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt = 7, ix_values = 420 455 492 527 560 591 618 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
###################### Friday ##############################################
K_opt = 7, 8 or 9
ix_values 7 = 561 588 613 638 663 686 709 ## averaged over all 15 n_bars 1 to 15 inclusive
ix_values 8 = 557 578 599 622 643 666 687 710
ix_values 9 = 557 576 596 616 635 653 672 691 711 ## timings are for this bottom row
18:40 21:50 1:10 4:30 7:40 10:40 13:50 17:00 20:20
K_opt = 8, ix_values = 558 579 600 621 644 665 687 709 ## averaged over n_bars 1 to 6 inclusive ( upto and include 1 hour )
K_opt = 6, ix_values = 563 594 621 646 676 705 ## averaged over n_bars 7 to 15 inclusive ( over 1 hour )
############################################################################This is based on 10 minute bars over the last year or so. Readers should read my last few previous posts for background.
The first set of results, EUR_USD, are what the charts of my previous posts were based on and include combined results of my “Delta Turning Point Filter” and “Normal Turning Point Filter” and the results for each filter separately. Since there doesn't appear to be significant differences between these, the other three pairs' results are the combined filter results only.
The K_opt variable is the optimal number of clusters (see my temporal-clustering-part-3 post for how “optimal” is decided) and the ix_values are also described in this post. For convenience the first set of ix_values per day have the relevant times anotated underneath and therefore it is a simple matter to count forwards/backwards in 10 minute increments to place times to the other ix_values. The variable n_bars is an input to the turning point filter functions and essentially indicates the lookback/lookforward period (n_bar == 2 would mean 2 x 10 minute periods) used for determining a local high/low according to each function's logic.
As to how to interpret this, a typical sequence of times per day might look like this:
18:40 22:00 1:30 5:00 8:30 12:00 15:30 18:50 22:00 1:30 5:10
where the highlighted times represent the BST times for the period covering the London session open to the New York session close for one day. The preceding and following times are the two “book-ending” Asian sessions.
Close inspection of these results reveals some surprising regularities. In even just the above single example (an actual copy and paste of a code box example) there appear to be definite times per day at which a local high/low occurs. I hopefully will be able to incorporate this into some type of chart for a nice visual presentation of the data.
More in due course. Enjoy.
