Time Series Classification Synthetic vs Real Financial Time Series – Part VIII

Learn which R packages and data sets you need by reviewing Part I, Part II ,Part III, Part IV, Part V , Part VI and Part VII of this series.

That’s enough data analysis I could probably fit the PACF plots also along with a few more exploratory data analysis but I move on to generating the financial time series features using the tsfeatures package.

What I do in the below code is to take a random sample of 5 groups (Using the whole data set takes too long to calculate the time series features) and then apply all the functions in the tsfeatures package to each of the time series assets data which is does by mapping over each assets data and computing the time series features.

This section takes some time to process and compute (especially on the whole sample) and I already saved the results as a csv which I will just work from and load in the pre-computed time series features.

################# Generate Time Series Features ######################

# I create some time series features from the package “tsfeatures”. There are 40+ functions in the “tsfeatures” package
# which can generate approximately 106 time series features.
# Due to memory issues I am only able to create a few of the features, therefore I randomly sample 10 features from the
# “tsfeatures” package. We could also add in technical indicators from the “PerformanceAnalytics” or “TTR” packages (I omit these
# here, however creating ‘functions2 <- ls("package:TTR")' and adding it to the 'summarise' command will work.)

functions <- ls("package:tsfeatures")[1:42]
# functions <- sample(functions, 20)

Stats <- df %>%
group_by(row_id, class) %>%
nest() %>%
ungroup() %>%
sample_n(5) %>%
unnest() %>%
nest(-row_id, -class) %>%
group_by(row_id, class) %T>%
{options(warn = -1)} %>%
summarise(Statistics = map(data, ~ data.frame(
bind_cols(
tsfeatures(.x$value, functions))))) %>%
unnest(Statistics)

# I saved to whole dataset as “Stats” next I split it between training and test.
Stats <- read.csv("C:/Users/Matt/Desktop/Data Science Challenge/TSfeatures_train_val.csv")

Note: Again, bad practice by me. I just called the df data Stats which consists of only the time series features. This still only refers to the train_val.csv data and not the test.csv data.

The training data looks like: (after computing the time series features). Now each asset has been collapsed from ~260 days down to 1 signal time series feature observation.

Recall the goal here was to classify synthetic time series vs real time series and not what the next days price is going to be. For each asset I have a signal observation and based on this I can train a classifying algorithm to distinguish between real vs synthetic time series.

How the training data looks:

Table 4: tsfeatures package features

X	row_id	class	ac_9_ac_9	acf_features_x_acf1	acf_features_x_acf10	acf_features_diff1_acf1	acf_features_diff1_acf10	acf_features_diff2_acf1	acf_features_diff2_acf10	ARCH.LM	autocorr_features_embed2_incircle_1	autocorr_features_embed2_incircle_2	autocorr_features_ac_9	autocorr_features_firstmin_ac	autocorr_features_trev_num	autocorr_features_motiftwo_entro3	autocorr_features_walker_propcross	binarize_mean_binarize_mean	binarize_mean_NA	compengine_embed2_incircle_1	compengine_embed2_incircle_2	compengine_ac_9	compengine_firstmin_ac	compengine_trev_num	compengine_motiftwo_entro3	compengine_walker_propcross	compengine_localsimple_mean1	compengine_localsimple_lfitac	compengine_sampen_first	compengine_std1st_der	compengine_spreadrandomlocal_meantaul_50	compengine_spreadrandomlocal_meantaul_ac2	compengine_histogram_mode_10	compengine_outlierinclude_mdrmd	compengine_fluctanal_prop_r1	crossing_points	dist_features_histogram_mode_10	dist_features_outlierinclude_mdrmd	embed2_incircle	entropy	firstmin_ac	firstzero_ac	flat_spots	fluctanal_prop_r1_fluctanal_prop_r1	arch_acf	garch_acf	arch_r2	garch_r2	histogram_mode	alpha	beta	hurst	hw_parameters_hw_parameters	hw_parameters_NA	localsimple_taures	lumpiness	max_kl_shift	time_kl_shift	max_level_shift	time_level_shift	max_var_shift	time_var_shift	motiftwo_entro3	nonlinearity	outlierinclude_mdrmd	x_pacf5	diff1x_pacf5	diff2x_pacf5	pred_features_localsimple_mean1	pred_features_localsimple_lfitac	pred_features_sampen_first	sampen_first_sampen_first	sampenc	scal_features_fluctanal_prop_r1	spreadrandomlocal_meantaul	stability	station_features_std1st_der	station_features_spreadrandomlocal_meantaul_50	station_features_spreadrandomlocal_meantaul_ac2	std1st_der_std1st_der	nperiods	seasonal_period	trend	spike	linearity	curvature	e_acf1	e_acf10	trev_num	tsfeatures_frequency	tsfeatures_nperiods	tsfeatures_seasonal_period	tsfeatures_trend	tsfeatures_spike	tsfeatures_linearity	tsfeatures_curvature	tsfeatures_e_acf1	tsfeatures_e_acf10	tsfeatures_entropy	tsfeatures_x_acf1	tsfeatures_x_acf10	tsfeatures_diff1_acf1	tsfeatures_diff1_acf10	tsfeatures_diff2_acf1	tsfeatures_diff2_acf10	unitroot_kpss	unitroot_pp	walker_propcross
1	1	0	-0.0675275	0.0097094	0.0526897	-0.5005299	0.3297018	-0.6772403	0.6124739	0.0627825	0.3929961	0.6147860	-0.0675275	1	0.1208750	2.071663	0.5405405	1	1	0.3929961	0.6147860	-0.0675275	1	0.1208750	2.071663	0.5405405	1	1	1.788841	1.408737	1.68	1.43	-0.25	-0.2865385	0.1627907	132	-0.25	-0.2865385	0.3929961	0.9840151	1	3	4	0.1627907	0.0652585	0.0154406	0.0627825	0.0253367	-0.25	0.0013330	0.0013330	0.5000458	NA	NA	1	0.3556536	1.783636	103	1.297736	97	2.819828	46	2.071663	0.0752319	-0.2865385	0.0108653	0.4457792	1.0525222	1	1	1.788841	1.788841	1.788841	0.1627907	1.76	0.0562693	1.408737	1.74	1.36	1.408737	0	1	0.0043052	0.0000261	0.8421403	-0.7069160	0.0052389	0.0588324	0.1208750	1	0	1	0.0043052	0.0000261	0.8421403	-0.7069160	0.0052389	0.0588324	0.9840151	0.0097094	0.0526897	-0.5005299	0.3297018	-0.6772403	0.6124739	0.0993829	-249.7732	0.5405405
2	2	0	-0.0421577	-0.0075902	0.0387481	-0.5171529	0.3129147	-0.6727897	0.5379301	0.0558032	0.4285714	0.6563707	-0.0421577	1	-0.4765229	2.077581	0.5019305	1	1	0.4285714	0.6563707	-0.0421577	1	-0.4765229	2.077581	0.5019305	1	1	1.780390	1.419266	1.95	1.00	0.50	0.2615385	0.1627907	123	0.50	0.2615385	0.4285714	0.9864332	1	1	4	0.1627907	0.0664358	0.0657859	0.0558032	0.0554355	0.50	0.0001000	0.0001000	0.5000458	NA	NA	1	0.4636768	1.733008	247	1.311861	141	2.625772	221	2.077581	0.0273335	0.2615385	0.0256032	0.4606850	1.0171377	1	1	1.780390	1.780390	1.780390	0.1627907	2.05	0.0892206	1.419266	2.12	1.00	1.419266	0	1	0.0177460	0.0000399	0.9249561	0.7665407	-0.0218053	0.0411861	-0.4765229	1	0	1	0.0177460	0.0000399	0.9249561	0.7665407	-0.0218053	0.0411861	0.9864332	-0.0075902	0.0387481	-0.5171529	0.3129147	-0.6727897	0.5379301	0.0414599	-256.0485	0.5019305
3	3	1	0.0099598	-0.0405929	0.0449036	-0.5026683	0.3471209	-0.6718885	0.6109006	0.0325470	0.4671815	0.7065637	0.0099598	1	-0.8755173	2.069233	0.5328185	1	0	0.4671815	0.7065637	0.0099598	1	-0.8755173	2.069233	0.5328185	1	1	1.706841	1.443315	1.38	1.00	-0.50	-0.2538462	0.1395349	132	-0.50	-0.2538462	0.4671815	0.9868568	1	1	6	0.1395349	0.0388513	0.0039162	0.0325470	0.0041902	-0.50	0.0014557	0.0014557	0.5000458	NA	NA	1	1.2670493	7.746711	95	1.403784	87	5.235499	84	2.069233	0.2436499	-0.2538462	0.0223069	0.5356408	0.9954919	1	1	1.706841	1.706841	1.706841	0.1395349	1.42	0.0716499	1.443315	1.42	1.00	1.443315	0	1	0.0141368	0.0000929	0.8414359	-0.0259311	-0.0547484	0.0492987	-0.8755173	1	0	1	0.0141368	0.0000929	0.8414359	-0.0259311	-0.0547484	0.0492987	0.9868568	-0.0405929	0.0449036	-0.5026683	0.3471209	-0.6718885	0.6109006	0.0775698	-258.1295	0.5328185
4	4	0	-0.0428748	-0.0443619	0.0615867	-0.4571442	0.3184053	-0.5906478	0.4361178	0.1275576	0.4555985	0.7027027	-0.0428748	2	-0.9943808	2.068744	0.4903475	0	0	0.4555985	0.7027027	-0.0428748	2	-0.9943808	2.068744	0.4903475	1	1	1.660825	1.445807	1.24	1.00	0.25	0.0153846	0.1395349	127	0.25	0.0153846	0.4555985	0.9790521	2	1	7	0.1395349	0.0694296	0.0112709	0.0579144	0.0123884	0.25	0.0480021	0.0001000	0.5000458	NA	NA	1	1.0068624	4.994753	132	1.258758	173	5.886911	156	2.068744	0.3840091	0.0153846	0.0503205	0.5402603	1.1070217	1	1	1.660825	1.660825	1.660825	0.1395349	1.10	0.1065111	1.445807	1.14	1.00	1.445807	0	1	0.0283540	0.0000482	-1.2297854	0.2921899	-0.0728152	0.0752389	-0.9943808	1	0	1	0.0283540	0.0000482	-1.2297854	0.2921899	-0.0728152	0.0752389	0.9790521	-0.0443619	0.0615867	-0.4571442	0.3184053	-0.5906478	0.4361178	0.2129633	-262.0781	0.4903475
5	5	0	0.0259312	-0.2447835	0.1469130	-0.5810073	0.4796508	-0.6799229	0.6232529	0.2014861	0.6563707	0.7992278	0.0259312	1	-0.7167079	2.059764	0.5289575	1	0	0.6563707	0.7992278	0.0259312	1	-0.7167079	2.059764	0.5289575	1	1	1.347789	1.580825	1.08	0.98	-0.50	0.7961538	0.1627907	133	-0.50	0.7961538	0.6563707	0.9723766	1	1	9	0.1627907	0.2718058	0.2229375	0.1765130	0.1330761	-0.50	0.0001000	0.0001000	0.5000458	NA	NA	1	2.8846415	11.474426	80	1.772392	229	8.468236	236	2.059764	0.2143595	0.7961538	0.1008392	0.7538746	1.2926800	1	1	1.347789	1.347789	1.347789	0.1627907	1.08	0.0797924	1.580825	1.06	0.98	1.580825	0	1	0.0121072	0.0001568	-0.5488436	0.2255538	-0.2599764	0.1558209	-0.7167079	1	0	1	0.0121072	0.0001568	-0.5488436	0.2255538	-0.2599764	0.1558209	0.9723766	-0.2447835	0.1469130	-0.5810073	0.4796508	-0.6799229	0.6232529	0.1506344	-323.5672	0.5289575
6	6	0	-0.0761166	0.0468556	0.0858348	-0.5253131	0.3438031	-0.6901570	0.6130725	0.0432628	0.4352941	0.6627451	-0.0761166	1	0.0898648	2.068914	0.5250965	1	1	0.4352941	0.6627451	-0.0761166	1	0.0898648	2.068914	0.5250965	1	1	1.751575	1.381854	2.69	1.71	-0.25	-0.0846154	0.3488372	134	-0.25	-0.0846154	0.4352941	0.9806218	1	5	5	0.3488372	0.0500806	0.0502154	0.0627968	0.0620877	-0.25	0.0286244	0.0001000	0.5188805	NA	NA	1	0.2189481	3.145763	141	1.447883	80	2.077936	84	2.068914	0.0137733	-0.0846154	0.0172321	0.4345976	1.0881798	1	1	1.751575	1.751575	1.751575	0.3488372	2.61	0.1479673	1.381854	2.63	1.81	1.381854	0	1	0.0077481	0.0000329	-0.5473782	0.4505809	0.0410068	0.0873468	0.0898648	1	0	1	0.0077481	0.0000329	-0.5473782	0.4505809	0.0410068	0.0873468	0.9806218	0.0468556	0.0858348	-0.5253131	0.3438031	-0.6901570	0.6130725	0.0259414	-262.3484	0.5250965

## [1] 12000 109

The dimensions of the data as still 12,000 with 109 features (created from the tsfeatures package). That is we have 6,000 synthetic and 6,000 real financial time series (12,000 * ~260 = 3,120,000 but we applied tsfeatures to collapse the ~260 down to 1 single observation for each asset)

I collapsed this problem down from a time series expectation problem to a pure classification problem. I split the data between training and validation set next… I also split the data into X_train, Y_train… etc.

I split the df/Stats data set into a train set of 75% of the observations and an in-sample test data set of 25% of the observations.

######################################################################
################# Train and XGBoost model on the TS Features #########

#Stats <- Stats %>%
# select_if(~sum(!is.na(.)) > 0)

# Split the training set up between train and a small validation set
smp_size <- floor(0.75 * nrow(Stats))
#set.seed(123)
train_ind <- sample(seq_len(nrow(Stats)), size = smp_size)

train <- Stats[train_ind, ]
val <- Stats[-train_ind, ]
# We have 106 time series features for the model to learn from.

x_train <- train %>%
ungroup() %>%
select(-class, -row_id, -X) %>%
as.matrix()

x_val <- val %>%
ungroup() %>%
select(-class, -row_id, -X) %>%
as.matrix()

y_train <- train %>%
ungroup() %>%
pull(class)
y_val <- val %>%
ungroup() %>%
pull(class)

Stay tuned for the next installment to find out how the training X (input variables) data looks.

Visit Matthew Smith – R Blog to download the complete R code and see additional details featured in this tutorial: https://lf0.com/post/synth-real-time-series/financial-time-series/