This describes a method I'm looking at for expressing price swings with mathematical functions, projecting those functions two bars in the future, and trading based on the model parameters and predictions.
Steps:
Example:
Fitted curves and regression lines for iShares Semiconductor ETF (SOXX) for daily price bars from 20230728 through 20231011 covering three price waves and projecting two bars ahead:
Functions found:
Parameters for the asymmetric triangle waves are amplitude, period, phase, peak phase, bars from 20230728. To find the functions, software does simple linear regression and a modified version of the Goertzel algorithm.
Rules in pseudocode to decide whether or not to go long at next bar's open and exit at the following bar's open:
To create the rules, I used daily price data adjusted for splits and dividends for 20000915 through 20230929 for
The rules generator used genetic programming on the first 70% of the data (102,896 instances) as training data. The rules are the same for all the symbols.
Without applying the rules on the 30% of out-of-sample data (44,098 instances), going long at the next bar's open and exiting at the following bar's close resulted in a simulated mean result of 0.0309% and simulated median result of 0.0787% with 53.42% positive. Of the 26 symbols, only EWM and TLT had negative overall results.
With the rules, the results on the out-of-sample data had 18,380 simulated one day trades (41.67% of the total) with simulated mean 0.0569% and simulated median 0.0867% with 53.91% positive. Of the 26 symbols, only EEM had negative overall results.
Comments or questions?
Steps:
- Find price waves similar to those from here. These can have different numbers of bars depending on the movement of prices.
- With the series of opens, highs, lows, and closes of price bars surrounding the swings up to the present, fit curves as the sum of a least squares regression line plus one or more asymmetric triangle waves.
- Using parameters from the fitted curves and predicting two bars ahead, use derived rules to decide whether to trade the two predicted bars.
Example:
Fitted curves and regression lines for iShares Semiconductor ETF (SOXX) for daily price bars from 20230728 through 20231011 covering three price waves and projecting two bars ahead:
Functions found:
Code:
SOXX_20231011_opy = 514.119567871094 + -0.914557695388794 * x
+ atri(14.172266960144, 25.8231048583984, 0.452290117740631, 0.486637502908707, x)
+ atri(3.80764317512512, 8.71776962280273, 0.503233969211578, 0.468089550733566, x)
+ atri(3.35887813568115, 3.48830699920654, 0.876859784126282, 0.490426868200302, x)
+ atri(3.13291811943054, 6.46492099761963, 0.540566146373749, 0.479657083749771, x)
+ atri(3.11210489273071, 34.8243064880371, 0.589635968208313, 0.537295401096344, x) ;
SOXX_20231011_hiy = 518.401733398438 + -0.891234874725342 * x
+ atri(14.2325096130371, 25.5988388061523, 0.462638199329376, 0.493019610643387, x)
+ atri(3.16329288482666, 8.58524894714355, 0.472705543041229, 0.501196682453156, x)
+ atri(2.88916540145874, 6.64841079711914, 0.768346667289734, 0.579576730728149, x)
+ atri(2.60541749000549, 32.3064155578613, 0.589038550853729, 0.560829341411591, x)
+ atri(2.38103032112122, 3.48830699920654, 0.985737383365631, 0.55763828754425, x) ;
SOXX_20231011_loy = 507.585632324219 + -0.875757277011871 * x
+ atri(14.8584051132202, 25.7925224304199, 0.451266527175903, 0.476266592741013, x)
+ atri(3.45638751983643, 32.8059158325195, 0.548395812511444, 0.554247796535492, x)
+ atri(3.37502837181091, 8.90125846862793, 0.663182616233826, 0.527323365211487, x)
+ atri(2.64485692977905, 6.43433952331543, 0.552761316299438, 0.437974035739899, x)
+ atri(2.58983421325684, 3.85528683662415, 0.0773146748542786, 0.561826586723328, x) ;
SOXX_20231011_cly = 512.796081542969 + -0.868771910667419 * x
+ atri(15.5449867248535, 25.5274848937988, 0.46088045835495, 0.489230245351791, x)
+ atri(3.52759599685669, 5.46592044830322, 0.347266614437103, 0.400878101587296, x)
+ atri(3.15372681617737, 8.70757484436035, 0.599749982357025, 0.470881700515747, x)
+ atri(2.80252599716187, 30.8792724609375, 0.553648114204407, 0.380335748195648, x)
+ atri(2.4834132194519, 2.38736772537231, 0.821252465248108, 0.434782981872559, x) ;Rules in pseudocode to decide whether or not to go long at next bar's open and exit at the following bar's open:
Code:
# types_for_runtime_checking [Ff]itProp lpr ^bars$
R1 = R0 = undef
R0 = 0.828438 * lpr01op
R1 = 0.388818 * lpr01cl
if lpr12hi > R1 if hifitProp > clfitProp if R0 > cldtwFitProp if bars <= 36 if hifitProp > clfitProp R1 = 0.0973804 * lpr01lo
R0 = 0.979132 * cldtwFitProp
if opfitProp <= R0 if clfitProp >= 0.894782 R1 = 0.230463 * opdtwFitProp
if bars <= 38 if lpr12lo <= R1 return 1
R0 = R1 = undef
R0 = 0.139022 * lpr12lo
R1 = 0.595785 * lpr12op
if lpr12cl >= lpr01op if bars < 37 R1 = 0.435886 * lpr01op
if R0 > R1 if lofitProp >= 0.854828 if lpr12op >= lpr01hi return 1
R0 = R1 = undef
if bars < 37 R0 = 0.965308 * lpr12lo
R1 = 0.603325 * lpr12hi
if lpr01cl > lpr01lo if R1 <= lpr12hi if clfitProp > hifitProp if cldtwFitProp <= hidtwFitProp if lpr01lo >= R1 if lpr01cl < lpr12hi if bars < 37 if lpr12lo <= -0.0554865 if clfitProp > 0.845599 if lpr01hi >= lpr01op if lpr12op >= R0 R0 = 0.283999 * lpr12op
if cldtwFitProp <= hidtwFitProp R1 = 0.0450815 * lpr12lo
if R0 <= R1 if hifitProp >= 0.773191 return 1
R1 = R0 = undef
R1 = 0.973247 * clfitProp
if lpr01hi >= 0.783447 R1 = 0.849232 * hidtwFitProp
R0 = 0.0974599 * hifitProp
if R0 >= hifitProp R1 = 0.461475 * clfitProp
if bars < 33 if lofitProp >= R1 return 1
R0 = R1 = undef
if R1 <= R0 if hidtwFitProp > 0.869307 if lpr12lo < R0 if bars < 37 if lodtwFitProp > R1 R1 = 0.404841 * lpr12cl
if lpr12lo < R0 if bars < 37 if R1 > lpr01hi R0 = 0.52052 * lpr01lo
if bars < 41 R0 = 0.266953 * lpr12hi
if lpr12lo < R0 if hifitProp >= clfitProp return 1
R1 = R0 = undef
R1 = 0.0152074 * lpr12cl
R0 = 0.778812 * lpr01hi
if R0 >= lpr01op if bars < 37 if bars < 34 R1 = 0.771484 * lpr12op
if bars < 37 R0 = 0.795779 * lpr01op
if R0 < R1 if bars < 37 if R0 <= R1 if lodtwFitProp >= R0 if bars < 37 R1 = 0.194692 * lofitProp
if R0 <= R1 if R0 < R1 if bars < 53 if bars < 37 return 1
R0 = R1 = undef
R0 = 0.889307 * lpr12op
R1 = 0.986241 * lpr12op
if R0 <= lpr01op if R1 <= R0 if hidtwFitProp >= clfitProp if lpr01cl <= lpr01hi if lpr01lo <= R0 if opfitProp <= 0.902505 R0 = 0.248328 * lpr01cl
if R1 <= R0 if lpr01lo < R0 if lofitProp >= 0.863728 if R1 <= R0 return 1
R0 = undef
R0 = 0.716964 * lpr12op
if clfitProp < lodtwFitProp R0 = 0.0372142 * lpr01cl
if bars <= 36 if R0 >= lpr01op if R0 >= lpr01op return 1
R1 = undef
R1 = 0.391735 * lpr01op
if opdtwFitProp >= 0.938459 if R1 <= hifitProp if lofitProp >= 0.915739 if bars > R1 R1 = 0.842392 * lpr01op
if lodtwFitProp < cldtwFitProp R1 = 0.879626 * lofitProp
if hifitProp >= R1 R1 = 0.667925 * lpr01hi
if R1 > lpr01op if bars < 37 return 1
R1 = R0 = undef
if bars < R1 if R0 < lpr12hi if R1 <= R0 R0 = 0.79406 * lpr12op
if clfitProp < lodtwFitProp if bars <= 45 R0 = 0.370069 * lpr01cl
R1 = 0.201226 * lpr01cl
if R0 > R1 if R1 >= R0 if lpr12lo <= -0.00832105 R0 = 0.610872 * lpr12cl
if R1 >= lpr01hi if lpr01lo <= R0 if lpr12lo <= -0.00832105 return 1
R1 = R0 = undef
R0 = 0.256056 * lpr12hi
if hidtwFitProp <= cldtwFitProp R0 = 0.564842 * lpr12hi
if R1 > R0 if opdtwFitProp <= lofitProp if R1 >= lpr01op if lpr01op < R0 if R0 <= lpr01cl if R1 < R0 if R1 < lpr12cl R0 = 0.784858 * lpr01hi
if bars <= 37 if lpr01hi <= R0 if bars <= 36 return 1
R1 = R0 = undef
R1 = 0.933817 * lpr12hi
if bars <= 42 R0 = 0.0337586 * lpr01op
if lpr01hi < 1.50224 if bars < 37 if bars < 32 if bars <= 32 if R0 > R1 if bars >= 69 R0 = 0.279611 * clfitProp
R1 = 0.942037 * lpr12lo
if R1 >= lpr12lo if lpr01lo <= R0 if lpr01hi < R0 return 1
R0 = R1 = undef
R0 = 0.298353 * lpr01op
R1 = 0.0150169 * lpr01cl
if R0 >= lpr01lo if lpr01hi > -0.422588 R0 = 0.827824 * lpr12cl
if R1 < lpr12lo if R1 < R0 if lpr12lo >= -0.980803 if R0 >= R1 if R1 >= cldtwFitProp R0 = 0.306634 * lpr12lo
if R1 >= R0 if lpr12hi > -0.62418 if lpr01hi < lpr12op if lofitProp > 0.85289 return 1
R0 = R1 = undef
R0 = 0.671082 * lpr12hi
if opfitProp > 0.779704 if bars < 33 R0 = 0.964064 * lpr12cl
R1 = 0.961604 * lpr01cl
if R1 <= R0 if R0 > lpr12hi if R0 < lpr12cl return 1
R1 = undef
R1 = 0.693783 * lpr12op
if lpr01hi <= R1 if opfitProp < 0.911767 R1 = 0.252478 * lpr12lo
if bars <= 44 if bars <= 44 if lpr01lo <= R1 if clfitProp > 0.763084 if lpr12lo < R1 if bars <= 44 return 1To create the rules, I used daily price data adjusted for splits and dividends for 20000915 through 20230929 for
Code:
DIA SPDR Dow Jones Industrial Average ETF Trust
EEM iShares MSCI Emerging Markets ETF
EFA iShares MSCI EAFE ETF
EWG iShares MSCI Germany ETF
EWM iShares MSCI Malaysia ETF
EWS iShares MSCI Singapore ETF
EWW iShares MSCI Mexico ETF
GLD SPDR Gold Shares
IWM iShares Russell 2000 ETF
MDY SPDR S&P Midcap 400 ETF Trust
QQQ Invesco QQQ Trust Series I
SLYV SPDR S&P 600 Small Cap Value ETF
SPTM SPDR Portfolio S&P 1500 Composite Stock Market ETF
SPY SPDR S&P 500 ETF Trust
SPYG SPDR Portfolio S&P 500 Growth ETF
SPYV SPDR Portfolio S&P 500 Value ETF
TLT iShares 20+ Year Treasury Bond ETF
XLB Materials Select Sector SPDR Fund
XLE Energy Select Sector SPDR Fund
XLF Financial Select Sector SPDR Fund
XLI Industrial Select Sector SPDR Fund
XLK Technology Select Sector SPDR Fund
XLP Consumer Staples Select Sector SPDR Fund
XLU Utilities Select Sector SPDR Fund
XLV Health Care Select Sector SPDR Fund
XLY Consumer Discretionary Select Sector SPDR FundThe rules generator used genetic programming on the first 70% of the data (102,896 instances) as training data. The rules are the same for all the symbols.
Without applying the rules on the 30% of out-of-sample data (44,098 instances), going long at the next bar's open and exiting at the following bar's close resulted in a simulated mean result of 0.0309% and simulated median result of 0.0787% with 53.42% positive. Of the 26 symbols, only EWM and TLT had negative overall results.
With the rules, the results on the out-of-sample data had 18,380 simulated one day trades (41.67% of the total) with simulated mean 0.0569% and simulated median 0.0867% with 53.91% positive. Of the 26 symbols, only EEM had negative overall results.
Comments or questions?
