About this article: The main goal of this article is to apply a Hidden Markov Model to asset returns for “regime” detection. TWO regimes are defined based on asset mean returns and volatility (standard deviation of the returns). The “bullish” regime has higher mean and lower volatility while the “bearish” regime has lower mean and higher volatility.
Generally speaking, various “regimes” in financial markets lead to different asset mean returns, volatilities (or variances), correlations with other assets, or even self serial correlations. Changing correlations (coupling of decoupled assets and/or decoupling of coupled assets), negative skew / excess kurtosis (due to drawdowns, i.e., negative “fat tails”), and heteroskedasticity (clustering of serial correlation) impact the effectiveness of portfolio optimization which usually relies on long-term time-series stationarity. We have to effectively detect which regimes we are in and then dynamically optimize our portfolios accordingly. (e.g., defensive portfolios during “bearish” periods)
To carry out a regime detection, I am using a statistical time-series technique, Hidden Markov Model (HMM). Observed past asset returns are considered to be influenced by regimes (or states). “Hidden” means the model only needs the number of regimes to be defined; it is an autonomous process.
Markov Models (in general)
Markov Models, in general, are stochastic state models with random transitions between states where the probability of the transition is only dependent on the current state, not the previous states. It is called “Markov Property” or memoryless. Random Walk models are famous example of a Markov Model.
Markov Models can be categorized into four broad classes:
| Fully Observable (*1) | Partially Observable (*1) | |
| Autonomous (*2) | Markov Chain | Hidden Markov Model (*3) |
| Controlled (*2) | Markov Decision Process | Partially Observable Markov Decision Process |
(*1) whether all or part of the information about the system can be observed at each state - If it’s fully observable, then all information is available from the model at any state.
(*2) Autonomy of the system - If it’s controlled, then it can be modified by actions of an “agent”. If it’s autonomous, then it cannot be modified.
(*3) There are underlying latent regimes (and probability transitions between them), but they are not directly observable and instead influence the “observations.”
Hidden Markov Models
Hidden Markov Models are Markov Models where the regimes (or states) are "hidden" from view, rather than being directly observable. Instead, there are a set of output observations (e.g., mean returns, standard deviations, correlations, etc.), related to the regimes, which are directly visible.
Filtering of Hidden Markov Models
- Prediction - Forecasting subsequent values of the regime
- Filtering - Estimating the current values of the regime from past and current observations
- Smoothing - Estimating the past values of the regime given the observations
Filtering and smoothing are similar, but not identical. Smoothing is concerned with wanting to understand what has happened to regimes in the past given current knowledge, whereas filtering is concerned with what is happening with the regime right now.
The conditional probability of the regime at time t given the sequence of observations up to time t is the object of interest. Thus, this is a filtering problem, determining p(zt ∣ x1:T) where z is a regime and a series of x is observations.
Market Regimes
Various regimes lead to adjustments of asset returns via shifts in their means, volatilities/variances, serial correlation and covariances, which impact the effectiveness of time series methods (e.g., portfolio optimization) that rely on stationarity of asset returns, volatilities, correlations, etc. You have to modify your investment strategies throughout the strategy lifecycle depending on a regime you’re in.
Within this article, a simulation of streamed market returns across TWO separate regimes - "bullish" and "bearish" - will be carried out. An HMM will be fitted to the returns stream to identify the probability of being in a particular regime.
Applying HMM to regime detection is tricky, since the problem is actually a form of unsupervised learning. That is, there is no "ground truth" or labelled data on which to "train" the model. In particular, it is not clear how many regime regimes exist a priori. Are there two, three, four or more "true" hidden market regimes? You have to guess and specify the number of regimes by yourself.
A guideline to specify the number of regimes depends heavily on the asset class being modelled, the choice of time frame, and the nature of data utilized. For instance, daily returns data in equities markets often exhibits (1) normal periods of lower volatility, even over a number of years, and (2) exceptional periods of high volatility, which are called "panic" or “correction" periods. Is it natural to consider modelling equity indices with two regimes? Might there be a third intermediate state representing more volatility than very calm periods, but not outright panic? Utilizing HMM requires careful research analysis and a solid understanding of the asset class being modelled.
Reproduction of the Results
Please prepare the following environment and files:
[1] R Console
My environment on MacOS goes like this:
> version$version.string
[1] "R version 3.3.2 (2016-10-31)"
[2] hmm.r
Copy the entire part of the “Full R Code (hmm.r)” section in this article, paste it to your editor, and save as “hmm.r” onto your R Console working directory. All the explanations are written in the code as well.
[3] y.csv
Copy the entire part of the “Asset Returns (y.csv) - S&P 500 in this case” section in this article, paste it to your editor, and save as “y.csv” onto your R Console working directory.
After finishing the preparation above, then run the following script on your R Console:
source(“hmm.r”)
Full R Code (hmm.r)
# Hidden Markov Model (HMM) for asset returns
#
# In this R code, asset returns are classified into TWO market regimes by using the HMM.
# (You can specify three, four, or any other number you prefer.)
#
# Source:
# The Financial Journal
# http://thefjg.blogspot.com
# install the depmixS4 and quantmod libraries
# This part has to be done ONLY ONCE. After that, you can comment these two lines out.
### install.packages(‘depmixS4')
### install.packages(‘quantmod’)
# import the depmixS4 and quantmod libraries
library('depmixS4') # Hidden Markov Model
library('quantmod') # returns stream
# Applying the HMM to real world historical financial data, asset returns in this case.
# The HMM can be specified and fit using the Expectation Maximization (EM) algorithm, the details of which are beyond the scope of this code.
# Also, asset returns are considered to be normally distributed.
##### [1] fitting asset returns to the HMM with TWO regime states
#
# Asset returns are classified into either ”bullish" or "bearish" market regime. (i.e., the number of regimes = 2)
# The number is arbitrary, so it can be three, or more, depending on an asset you choose.
# The "bullish" periods have higher mean returns and low volatilities, while the "bearish" periods have lower mean returns and higher volatilities.
# The goal of the HMM is to identify when the regime has switched from bullish to bearish and vice versa.
# The problem of Regime Detection is actually an unsupervised learning challenge since the number of regimes is not known a priori, nor is there any "ground truth" on which to "train" the HMM.
# Load prepared asset return data
# Note: You have to save your "y.csv" file with the Date and Return columns on your R Console working directory.
y <- read.csv("y.csv", header=TRUE, sep=",")
returns = as.numeric(y[,2])
#> class(y)
#[1] "data.frame"
#> class(returns)
#[1] "numeric"
# A TWO-regime HMM is fitted using the EM algorithm.
# The returns and posterior probabilities of each regime (which are derived by the HMM) are plotted.
#
# nstates = 2: the number of regimes (arbitrary)
# post_probs: the posterior probabilities of being in a particular regime
hmm <- depmix(returns ~ 1, family = gaussian(), nstates = 2, data=data.frame(returns=returns))
hmmfit <- fit(hmm, verbose = FALSE)
post_probs <- posterior(hmmfit)
tmp <- post_probs
tmp$Date <- y[,1][1:nrow(y)]
tmp2 <- tmp[c(4, 2, 3)]
# Pepare three plotting areas for (1) the returns stream, (2) the posterior probability of the regime 1, and (3) the posterior probability of the regime 2.
layout(1:3)
# The time series object y is plotted first, showing the volatile periods around 2008 and 2011.
# (1) the returns stream
plot(y, type='l', main='Regime Detection', xlab='Date', ylab='Returns')
# (2) the posterior probability of the regime 1
plot(tmp2$Date, tmp2$S1, type='l', main='Regime 1 Posterior Probabilities', xlab='Date', ylab='Probability')
# (3) the posterior probability of the regime 2
plot(tmp2$Date, tmp2$S2, type='l', main='Regime 2 Posterior Probabilities', xlab='Date', ylab='Probability')
# Note: Regime 1 and 2 in the following description could be flipped; in that case, please replace 1 by 2 accordingly and vice versa.
#
# Notice that within 2004 and 2007 the markets were calmer and hence the HMM has given high posterior probability to Regime 1 (indicated by the figure in the middle) for this period. It is considered to be the "bullish" periods.
# However, between 2007-2009 the markets were incredibly volatile due to the sub-prime crisis.
# This has the initial effect of rapidly changing the posterior probabilities between the two regimes.
# During 2008, the regime is consistently in Regime 2 (indicated by the bottom figure), which is the "bearish" period.
# The markets became calmer in 2010 but additional volatility occurred in 2011, leading once again for the HMM to give high posterior probability to Regime 2.
# Subsequent to 2011 the markets became calmer once again and the HMM is consistently giving high probability to Regime 1.
# In 2015 the markets once again became choppier and this is reflected in the increased switching between regimes for the HMM.
# export as csv
#
# Regime 1 (S1)
write.csv(tmp2[,c(1,2)], "S1.csv", quote=FALSE, row.names=TRUE)
#
# Regime 2 (S2)
write.csv(tmp2[,c(1,3)], "S2.csv", quote=FALSE, row.names=TRUE)
Figure
Asset Returns (y.csv) - S&P 500 in this case
Date,Return
,
2004-01-05,0.0123191510002796
2004-01-06,0.00129131274622907
2004-01-07,0.0023643673236684
2004-01-08,0.0049508242382883
2004-01-09,-0.00892733601663309
2004-01-12,0.00477526936492989
2004-01-13,-0.00534592581046223
2004-01-14,0.00826036924201468
2004-01-15,0.00135247014374329
2004-01-16,0.00684889817607015
2004-01-20,-0.000930339759163346
2004-01-21,0.00774147817345483
2004-01-22,-0.00321183583791296
2004-01-23,-0.00209136148618594
2004-01-26,0.0120336036991393
2004-01-27,-0.00984599354004345
2004-01-28,-0.0137030643717377
2004-01-29,0.00497661238385483
2004-01-30,-0.00263105166094135
2004-02-02,0.00364457092045178
2004-02-03,0.000678045530318805
2004-02-04,-0.00840650133647447
2004-02-05,0.00183578326039768
2004-02-06,0.012477361910177
2004-02-09,-0.002584764150245
2004-02-10,0.00501454198374862
2004-02-11,0.0106109368260423
2004-02-12,-0.00489208161539523
2004-02-13,-0.005483168833881
2004-02-17,0.00970993451588864
2004-02-18,-0.00447854330565001
2004-02-19,-0.00414105459324166
2004-02-20,-0.00257516951918024
2004-02-23,-0.00273073123532708
2004-02-24,-0.00166662965901843
2004-02-25,0.00401276010244533
2004-02-26,0.0010836327146766
2004-02-27,2.61213619481282e-05
2004-03-01,0.00958761091381533
2004-03-02,-0.00596078687364798
2004-03-03,0.0016782124912833
2004-03-04,0.00333056031019829
2004-03-05,0.00172164613406878
2004-03-08,-0.00838527718056437
2004-03-09,-0.00578728177171861
2004-03-10,-0.0147409711185587
2004-03-11,-0.0153409704027805
2004-03-12,0.012382511370979
2004-03-15,-0.0144537553158806
2004-03-16,0.00560672216204683
2004-03-17,0.0116809037290793
2004-03-18,-0.00127338348993344
2004-03-19,-0.0112360997002678
2004-03-22,-0.013042208336203
2004-03-23,-0.00132466095288386
2004-03-24,-0.00239785873375986
2004-03-25,0.01623287042956
2004-03-26,-0.00101917429049792
2004-03-29,0.0129207966536313
2004-03-30,0.00402764667430144
2004-03-31,-0.000701256470591716
2004-04-01,0.00527820546042079
2004-04-02,0.00847859023578845
2004-04-05,0.00764265053758972
2004-04-06,-0.00209673420006506
2004-04-07,-0.00666759854513099
2004-04-08,-0.00106154626567889
2004-04-12,0.00514770564456413
2004-04-13,-0.0138573690277894
2004-04-14,-0.00112499248530096
2004-04-15,0.000593636728862812
2004-04-16,0.00509843965960854
2004-04-19,0.00106584316743241
2004-04-20,-0.0156792541427349
2004-04-21,0.00529823383904748
2004-04-22,0.0139931151900266
2004-04-23,0.00058751431505577
2004-04-26,-0.00445489086627759
2004-04-27,0.00226945082900798
2004-04-28,-0.013890789123403
2004-04-29,-0.00761978270960029
2004-04-30,-0.00593374285476322
2004-05-03,0.00916042599735256
2004-05-04,0.00184177265173435
2004-05-05,0.00176698774363437
2004-05-06,-0.00674569453905072
2004-05-07,-0.0138205377008429
2004-05-10,-0.0105956250957391
2004-05-11,0.00763319999081791
2004-05-12,0.00166922369979172
2004-05-13,-0.000765902715529343
2004-05-14,-0.000675130296937887
2004-05-17,-0.0106432561620098
2004-05-18,0.00679359855309869
2004-05-19,-0.00257772329608397
2004-05-20,0.000468243752369979
2004-05-21,0.00400423670981276
2004-05-24,0.00169027018355905
2004-05-25,0.015975285487694
2004-05-26,0.00169649994996313
2004-05-27,0.00567037686173588
2004-05-28,-0.000535223636560112
2004-06-01,0.000463804492801145
2004-06-02,0.00337464123370079
2004-06-03,-0.00744994811915944
2004-06-04,0.00523415091441137
2004-06-07,0.0158383135566673
2004-06-08,0.00154211011410421
2004-06-09,-0.00954487143369498
2004-06-10,0.00453304874071758
2004-06-14,-0.0098861267391559
2004-06-15,0.00595400762516718
2004-06-16,0.00136835250700695
2004-06-17,-0.00133298330392861
2004-06-18,0.00262009784316852
2004-06-21,-0.00416716197845446
2004-06-22,0.00362959439525046
2004-06-23,0.00847066874432834
2004-06-24,-0.00298509430806781
2004-06-25,-0.00546792665217399
2004-06-28,-0.000952542193138228
2004-06-29,0.00251149046260934
2004-06-30,0.00407548535952174
2004-07-01,-0.0104857162558556
2004-07-02,-0.00315832627531076
2004-07-06,-0.00818177748270443
2004-07-07,0.00189747842045218
2004-07-08,-0.00827858339768817
2004-07-09,0.00333052256332067
2004-07-12,0.00138285280015449
2004-07-13,0.000708717272790871
2004-07-14,-0.00329653360637572
2004-07-15,-0.00430991234974876
2004-07-16,-0.00480049299260443
2004-07-19,-0.000444983176064895
2004-07-20,0.00703308950528481
2004-07-21,-0.0134301250593714
2004-07-22,0.00270227399246714
2004-07-23,-0.00974796582573667
2004-07-26,-0.00196289474119826
2004-07-27,0.00987663311930564
2004-07-28,0.00053883165326063
2004-07-29,0.00456317004332885
2004-07-30,0.00117150705708724
2004-08-02,0.00443775153920889
2004-08-03,-0.00628205192538722
2004-08-04,-0.000964314665901966
2004-08-05,-0.0164550196009143
2004-08-06,-0.0156017662091763
2004-08-09,0.00117415559687828
2004-08-10,0.012890469720781
2004-08-11,-0.00301648143631983
2004-08-12,-0.0117438857456644
2004-08-13,0.00147560820429771
2004-08-16,0.0135626776029847
2004-08-17,0.00219337454497381
2004-08-18,0.0123665562714619
2004-08-19,-0.00360416046639234
2004-08-20,0.00650354975727563
2004-08-23,-0.00243380745150734
2004-08-24,0.000465252966974639
2004-08-25,0.00796862258152764
2004-08-26,0.00011764892599242
2004-08-27,0.00242225475389279
2004-08-30,-0.00781182794493596
2004-08-31,0.00462013081814039
2004-09-01,0.00151124973392047
2004-09-02,0.0111501137034251
2004-09-03,-0.00419371553438364
2004-09-07,0.006863815803829
2004-09-08,-0.00449598208584234
2004-09-09,0.00188842602057537
2004-09-10,0.00494139959124418
2004-09-13,0.00168899735978467
2004-09-14,0.00222701341659448
2004-09-15,-0.00707964105518855
2004-09-16,0.00278982921210424
2004-09-17,0.00448485367092655
2004-09-20,-0.00564266564367077
2004-09-21,0.00630701446669413
2004-09-22,-0.0140358717413074
2004-09-23,-0.0046807116287555
2004-09-24,0.00157766423404215
2004-09-27,-0.00595400717651007
2004-09-28,0.00590903224304196
2004-09-29,0.00426093951201967
2004-09-30,-0.000197447721089539
2004-10-01,0.0150665732328168
2004-10-04,0.00323827212244243
2004-10-05,-0.000608079672166362
2004-10-06,0.00665055747607557
2004-10-07,-0.0100322262042125
2004-10-08,-0.00755511994619784
2004-10-11,0.00200308985170228
2004-10-12,-0.00227051559019298
2004-10-13,-0.0073272335627923
2004-10-14,-0.00934627019218315
2004-10-15,0.00444037286133625
2004-10-18,0.00523807938303023
2004-10-19,-0.00973289000110267
2004-10-20,0.000389737596993456
2004-10-21,0.00256087371070546
2004-10-22,-0.00976290894529797
2004-10-25,-0.00085818203817567
2004-10-26,0.0147697419353232
2004-10-27,0.0127970644660502
2004-10-28,0.00181097422738041
2004-10-29,0.00244504128827394
2004-11-01,0.000274302327404108
2004-11-02,4.42701893179631e-05
2004-11-03,0.0111181673962095
2004-11-04,0.0160273580858457
2004-11-05,0.00386624977261452
2004-11-08,-0.00109823779418683
2004-11-09,-0.000695637163855345
2004-11-10,-0.00100552396323295
2004-11-11,0.00904816237815975
2004-11-12,0.00906846830622143
2004-11-15,-0.000304043942191079
2004-11-16,-0.00710401641328318
2004-11-17,0.00552302231877899
2004-11-18,0.0013613316948824
2004-11-19,-0.0112241622177605
2004-11-22,0.0058784314051552
2004-11-23,-0.000254907450083053
2004-11-24,0.00408706135557324
2004-11-26,0.000752842382866881
2004-11-29,-0.00345591017579228
2004-11-30,-0.00403845167999961
2004-12-01,0.0148405595675127
2004-12-02,-0.000873358598903806
2004-12-03,0.000705511681583282
2004-12-06,-0.000772685228792369
2004-12-07,-0.0111351152223982
2004-12-08,0.00486475948627696
2004-12-09,0.00542142586887806
2004-12-10,-0.00104321828479481
2004-12-13,0.00894977545902176
2004-12-14,0.00391327184363277
2004-12-15,0.00194260658268774
2004-12-16,-0.00208392188997752
2004-12-17,-0.00751648883671674
2004-12-20,0.000376811444867009
2004-12-21,0.00899962502048179
2004-12-22,0.00341197933984994
2004-12-23,0.000462916081615639
2004-12-27,-0.00431458477176161
2004-12-28,0.00712852906964656
2004-12-29,-7.42384603258373e-05
2004-12-30,8.24870210607287e-05
2004-12-31,-0.00134407367057854
2005-01-03,-0.00815256213846549
2005-01-04,-0.0117400041945519
2005-01-05,-0.00363443953594444
2005-01-06,0.00349972738333815
2005-01-07,-0.00143219632203273
2005-01-10,0.0034169287261907
2005-01-11,-0.00611824567050245
2005-01-12,0.00397349911985856
2005-01-13,-0.00866758099535048
2005-01-14,0.0059866045736392
2005-01-18,0.00962827013776835
2005-01-19,-0.00953542249290162
2005-01-20,-0.00781344193665934
2005-01-21,-0.00643547926792731
2005-01-24,-0.00353402295127658
2005-01-25,0.00399632969782715
2005-01-26,0.00483241954052094
2005-01-27,0.00040883838825323
2005-01-28,-0.00271968312517323
2005-01-31,0.00842469371977739
2005-02-01,0.00686726661073855
2005-02-02,0.00317292891029908
2005-02-03,-0.00276946486908791
2005-02-04,0.0109825199609679
2005-02-07,-0.00108955868976057
2005-02-08,0.000482590000442151
2005-02-09,-0.00861225879705341
2005-02-10,0.00420261815707867
2005-02-11,0.00690175015196903
2005-02-14,0.000696650973425861
2005-02-15,0.00329433387381073
2005-02-16,0.000181759668946846
2005-02-17,-0.00795492221932559
2005-02-18,0.000699289897447386
2005-02-22,-0.014611960280889
2005-02-23,0.00559170012893606
2005-02-24,0.00786277743845432
2005-02-25,0.00926377764873809
2005-02-28,-0.00643490056190998
2005-03-01,0.00564212744562198
2005-03-02,-0.000272736514846272
2005-03-03,0.000322253219422919
2005-03-04,0.00957836152577585
2005-03-07,0.00260686984811986
2005-03-08,-0.00481034062232766
2005-03-09,-0.0102373453651881
2005-03-10,0.00185409735080366
2005-03-11,-0.00761214814668065
2005-03-14,0.00560886609194444
2005-03-15,-0.00755225388512493
2005-03-16,-0.00811470046945306
2005-03-17,0.00179963306360165
2005-03-18,-0.000470562985941392
2005-03-21,-0.00494643350547097
2005-03-22,-0.0102485459051298
2005-03-23,0.000699645119057735
2005-03-24,-0.000947106421556043
2005-03-28,0.00243849284066755
2005-03-29,-0.00762517922987449
2005-03-30,0.0136786298809524
2005-03-31,-0.0006943844478835
2005-04-01,-0.0065178810548403
2005-04-04,0.0027244771704602
2005-04-05,0.00447084318279245
2005-04-06,0.00226588671193184
2005-04-07,0.00595323360623201
2005-04-08,-0.00838001493224816
2005-04-11,8.47439722395649e-06
2005-04-12,0.00552988494719564
2005-04-13,-0.0118313257562006
2005-04-14,-0.0100521340618682
2005-04-15,-0.0168618622132328
2005-04-18,0.00293628196345619
2005-04-19,0.0059162929651384
2005-04-20,-0.013343569803137
2005-04-21,0.0195439866548481
2005-04-22,-0.0067731393222461
2005-04-25,0.00862497341885327
2005-04-26,-0.00887674885469281
2005-04-27,0.00394249654098555
2005-04-28,-0.0114456234155993
2005-04-29,0.0118519565604451
2005-05-02,0.0045795984127972
2005-05-03,-0.000852216453694155
2005-05-04,0.0123930511610517
2005-05-05,-0.00257211288916359
2005-05-06,-0.00109218435107561
2005-05-09,0.00637396597133755
2005-05-10,-0.0107631507675849
2005-05-11,0.00418427969235147
2005-05-12,-0.0100838884151795
2005-05-13,-0.00459057862361512
2005-05-16,0.0100355985937641
2005-05-17,0.0069332551303054
2005-05-18,0.00996889567756032
2005-05-19,0.00464513505665298
2005-05-20,-0.00151231524172246
2005-05-23,0.00384363622078965
2005-05-24,0.000175851893990497
2005-05-25,-0.00340587564136285
2005-05-26,0.00637453102292529
2005-05-27,0.000968147286756427
2005-05-31,-0.00609137960578643
2005-06-01,0.00895680597287107
2005-06-02,0.00172039052567463
2005-06-03,-0.00689081953642923
2005-06-06,0.00124501483063888
2005-06-07,-0.00020878831689064
2005-06-08,-0.00216558758301755
2005-06-09,0.00522626815216931
2005-06-10,-0.0023509989438093
2005-06-13,0.00225930913423156
2005-06-14,0.00257000971129617
2005-06-15,0.00221525341563655
2005-06-16,0.00362352634728769
2005-06-17,0.00494251244437027
2005-06-20,-0.000706916441091998
2005-06-21,-0.00204962066391534
2005-06-22,0.000222468477502069
2005-06-23,-0.0108921565721447
2005-06-24,-0.00765796852297385
2005-06-27,-0.000738798520538708
2005-06-28,0.00909606859627754
2005-06-29,-0.00143246108550166
2005-06-30,-0.00712623583205296
2005-07-01,0.00260711375851308
2005-07-05,0.0087938529494096
2005-07-06,-0.00837533431110948
2005-07-07,0.00244904989771122
2005-07-08,0.0116113816055528
2005-07-11,0.00623533154225697
2005-07-12,0.00226897491415645
2005-07-13,0.000883318806156552
2005-07-14,0.00262060240750994
2005-07-15,0.0011571321395607
2005-07-18,-0.00554505319390142
2005-07-19,0.0067088912334885
2005-07-20,0.00474730572312954
2005-07-21,-0.0066280638004681
2005-07-22,0.00539681952052717
2005-07-25,-0.00377635236741991
2005-07-26,0.0017315780306939
2005-07-27,0.00456250296792859
2005-07-28,0.00558752030965248
2005-07-29,-0.00770003958136112
2005-08-01,0.000947485613303378
2005-08-02,0.00707413735679197
2005-08-03,0.000739240570578836
2005-08-04,-0.00740061736449693
2005-08-05,-0.0076676796621209
2005-08-08,-0.00268624107494553
2005-08-09,0.00672234461007104
2005-08-10,-0.00182888963508621
2005-08-11,0.00703713069255496
2005-08-12,-0.00601253231564858
2005-08-15,0.00282436293183519
2005-08-16,-0.0118458665508321
2005-08-17,0.000737851644188936
2005-08-18,-0.00100027885237264
2005-08-19,0.000565819933967759
2005-08-22,0.00165477710676054
2005-08-23,-0.00339440341303554
2005-08-24,-0.00659203618525872
2005-08-25,0.00229568635791022
2005-08-26,-0.00601458632655394
2005-08-29,0.00594037685372228
2005-08-30,-0.00319743395179195
2005-08-31,0.00981580387853054
2005-09-01,0.00103198315429864
2005-09-02,-0.00292665513637669
2005-09-06,0.0125398820999036
2005-09-07,0.00240507859631567
2005-09-08,-0.00380055881825836
2005-09-09,0.00793319236942125
2005-09-12,-0.000741262048691738
2005-09-13,-0.00757367438896139
2005-09-14,-0.00328667946219152
2005-09-15,0.000464335271226801
2005-09-16,0.00825758163259671
2005-09-19,-0.00558139091487142
2005-09-20,-0.00789452146483782
2005-09-21,-0.00916299408897547
2005-09-22,0.00364567183870967
2005-09-23,0.000551496975285559
2005-09-26,0.000279701508945074
2005-09-27,2.47021124755165e-05
2005-09-28,0.001011268898929
2005-09-29,0.00882781738136718
2005-09-30,0.000920015980301336
2005-10-03,-0.00171867230092015
2005-10-04,-0.0100198533589886
2005-10-05,-0.0149990418851305
2005-10-06,-0.00410408552150265
2005-10-07,0.00369444371481276
2005-10-10,-0.00719200833527722
2005-10-11,-0.00207399201803771
2005-10-12,-0.00608661238739483
2005-10-13,-0.000713596001319594
2005-10-14,0.00823389537508135
2005-10-17,0.00297057034563952
2005-10-18,-0.0101003806392743
2005-10-19,0.0148450384576941
2005-10-20,-0.0151336417269832
2005-10-21,0.00151855851817206
2005-10-24,0.0166378691284015
2005-10-25,-0.00237066953647247
2005-10-26,-0.0043217879463695
2005-10-27,-0.0105304826211468
2005-10-28,0.0164138859023009
2005-10-31,0.00715052879394573
2005-11-01,-0.00352731121330319
2005-11-02,0.00992761049175339
2005-11-03,0.00425509419626646
2005-11-04,0.000163989708580559
2005-11-07,0.00218591864941686
2005-11-08,-0.00345711244357005
2005-11-09,0.00168909865223021
2005-11-10,0.00841079767286956
2005-11-11,0.00304987915565302
2005-11-14,-0.000777775032231531
2005-11-15,-0.00385744982389102
2005-11-16,0.00178841860670964
2005-11-17,0.00936954397321887
2005-11-18,0.00439167075994717
2005-11-21,0.00525741567848925
2005-11-22,0.00507139501568599
2005-11-23,0.00346678812071133
2005-11-25,0.00208378992597336
2005-11-28,-0.00854421513885928
2005-11-29,1.5920062085506e-05
2005-11-30,-0.00638225363234213
2005-12-01,0.0120838046180207
2005-12-02,0.000324073132591529
2005-12-05,-0.00236627649697496
2005-12-06,0.00127483699828801
2005-12-07,-0.00502165305799007
2005-12-08,-0.00121758962662799
2005-12-09,0.00280694762861167
2005-12-12,0.000841383476405611
2005-12-13,0.00553829531171779
2005-12-14,0.00418077817023566
2005-12-15,-0.00141531116280547
2005-12-16,-0.00285234579237414
2005-12-19,-0.00585613014760433
2005-12-20,-0.000238177601287859
2005-12-21,0.00251350543822859
2005-12-22,0.00421189517436371
2005-12-23,0.000425767312880687
2005-12-27,-0.00959930913800644
2005-12-28,0.0012963762616609
2005-12-29,-0.00298496981445417
2005-12-30,-0.00489870344972232
2006-01-03,0.0162969645269104
2006-01-04,0.00366596429987176
2006-01-05,1.57200408841263e-05
2006-01-06,0.00935551861859452
2006-01-09,0.00364969580898489
2006-01-10,-0.000356675616409952
2006-01-11,0.00347549801529734
2006-01-12,-0.0062940047826272
2006-01-13,0.00120444824773536
2006-01-17,-0.00364120853960248
2006-01-18,-0.00390494298220645
2006-01-19,0.00554825298848716
2006-01-20,-0.0184963225471479
2006-01-23,0.00184528372373194
2006-01-24,0.00240254836265841
2006-01-25,-0.0017222177056091
2006-01-26,0.00720890726399226
2006-01-27,0.00773401464669909
2006-01-30,0.00114443107060413
2006-01-31,-0.00398397982592158
2006-02-01,0.001857536476642
2006-02-02,-0.00910200568293007
2006-02-03,-0.00537301983661909
2006-02-06,0.000782895578486098
2006-02-07,-0.00812766661725295
2006-02-08,0.0086255616427291
2006-02-09,-0.00147859027646824
2006-02-10,0.00253674786508906
2006-02-13,-0.00326502259798911
2006-02-14,0.00998282308962573
2006-02-15,0.00349827668458325
2006-02-16,0.00730140862996187
2006-02-17,-0.00166110291484589
2006-02-21,-0.00327589298696385
2006-02-22,0.0074853901762113
2006-02-23,-0.00378227964058109
2006-02-24,0.00127270094302379
2006-02-27,0.00363062148030391
2006-02-28,-0.0104553270271914
2006-03-01,0.00822739265209638
2006-03-02,-0.00162764822199968
2006-03-03,-0.0014827337328418
2006-03-06,-0.00699282132241841
2006-03-07,-0.00186364543437012
2006-03-08,0.00202788726047753
2006-03-09,-0.00489277733035642
2006-03-10,0.00719762190468476
2006-03-13,0.00211257777561791
2006-03-14,0.0103424561240866
2006-03-15,0.0042607563016146
2006-03-16,0.00177118609475713
2006-03-17,0.00146984542331019
2006-03-20,-0.00166138622279544
2006-03-21,-0.00603310136266177
2006-03-22,0.00600251502940541
2006-03-23,-0.00258563228759812
2006-03-24,0.000982797571605687
2006-03-27,-0.00102893859319497
2006-03-28,-0.00645899881808898
2006-03-29,0.00744193612126409
2006-03-30,-0.00202833185299411
2006-03-31,-0.00414625352034292
2006-04-03,0.00226797383325295
2006-04-04,0.0062371980087752
2006-04-05,0.00430184141240186
2006-04-06,-0.00192323947380402
2006-04-07,-0.0103973529113004
2006-04-10,0.000864153721169103
2006-04-11,-0.00778115426067671
2006-04-12,0.00120406668203898
2006-04-13,0.000776024005575415
2006-04-17,-0.00294435068475796
2006-04-18,0.0169332044614796
2006-04-19,0.00202507694956999
2006-04-20,0.00116724879926267
2006-04-21,-0.000137209178926234
2006-04-24,-0.00242044562338073
2006-04-25,-0.0048815125086259
2006-04-26,0.0028153703395466
2006-04-27,0.00329615804485783
2006-04-28,0.00067931447502545
2006-05-01,-0.00414408739970362
2006-05-02,0.00612591306189714
2006-05-03,-0.0038835037805276
2006-05-04,0.00315223302642043
2006-05-05,0.0102426662994715
2006-05-08,-0.000830039046561204
2006-05-09,0.000362277150255608
2006-05-10,-0.00172964367592243
2006-05-11,-0.0128806749494901
2006-05-12,-0.0113048176844845
2006-05-15,0.00252153096591456
2006-05-16,-0.00187123131495426
2006-05-17,-0.0169844941677715
2006-05-18,-0.00672154985909224
2006-05-19,0.00412835705869607
2006-05-22,-0.00392241462054255
2006-05-23,-0.00435947742513143
2006-05-24,0.0015824030318532
2006-05-25,0.0113059406330516
2006-05-26,0.00570304313329206
2006-05-30,-0.0159765596101735
2006-05-31,0.00807920026290621
2006-06-01,0.0122233272769936
2006-06-02,0.00195033342938
2006-06-05,-0.0179600222971876
2006-06-06,-0.00113877693372721
2006-06-07,-0.00611109203425642
2006-06-08,0.00141604900577175
2006-06-09,-0.00448565606270979
2006-06-12,-0.0119372179581383
2006-06-13,-0.0111738459340129
2006-06-14,0.00517588506333855
2006-06-15,0.0210127546473835
2006-06-16,-0.00368465134786167
2006-06-19,-0.00915860732329765
2006-06-20,-8.07176695882816e-06
2006-06-21,0.00969382010163677
2006-06-22,-0.00528464292811393
2006-06-23,-0.00088347944431888
2006-06-26,0.00485765534552396
2006-06-27,-0.00912552759215224
2006-06-28,0.00547244978637984
2006-06-29,0.0213357690930982
2006-06-30,-0.0020998596482249
2006-07-03,0.00783412851872534
2006-07-05,-0.00727525226175629
2006-07-06,0.00249110892517024
2006-07-07,-0.00677283394842476
2006-07-10,0.00146870790186693
2006-07-11,0.00400831159902904
2006-07-12,-0.0109285275028554
2006-07-13,-0.0130515487607079
2006-07-14,-0.00490630567574613
2006-07-17,-0.00138419738118323
2006-07-18,0.00191797661238091
2006-07-19,0.0183850649379114
2006-07-20,-0.00851364977799207
2006-07-21,-0.00710205831115829
2006-07-24,0.0164884547879014
2006-07-25,0.00630091608035421
2006-07-26,-0.000378342950119404
2006-07-27,-0.00410813743460992
2006-07-28,0.0120785164702113
2006-07-31,-0.00147934242844361
2006-08-01,-0.00450623692865815
2006-08-02,0.00509353485047637
2006-08-03,0.00223639167653733
2006-08-04,-0.000711067643813124
2006-08-07,-0.00281000759664973
2006-08-08,-0.00336837299535553
2006-08-09,-0.0043587708080528
2006-08-10,0.00461833931718214
2006-08-11,-0.00399446585139795
2006-08-14,0.00115976346135405
2006-08-15,0.0136035174636522
2006-08-16,0.00763278389740041
2006-08-17,0.00158117821305748
2006-08-18,0.00370806335083795
2006-08-21,-0.00367720400594163
2006-08-22,0.00100135277016378
2006-08-23,-0.00449876030772955
2006-08-24,0.00237158060356979
2006-08-25,-0.000748774124203599
2006-08-28,0.00515241641914077
2006-08-29,0.00191860564318969
2006-08-30,0.000835335047501218
2006-08-31,-0.00118814591302208
2006-09-01,0.00549946439531546
2006-09-05,0.00170714070669131
2006-09-06,-0.00994072869100737
2006-09-07,-0.00481058479540764
2006-09-08,0.00377951646549501
2006-09-11,0.000477201874927502
2006-09-12,0.0103042096147172
2006-09-13,0.00385390915423578
2006-09-14,-0.00135890621400225
2006-09-15,0.00256455516568987
2006-09-18,0.00115116411233362
2006-09-19,-0.00268304850735479
2006-09-20,0.00570607098576126
2006-09-21,-0.00541012043327527
2006-09-22,-0.00246884627389488
2006-09-25,0.0087765104516917
2006-09-26,0.00749611513141435
2006-09-27,0.00017957006580982
2006-09-28,0.00171187834965369
2006-09-29,-0.00226567191281912
2006-10-02,-0.00339688470432176
2006-10-03,0.0020935009294778
2006-10-04,0.0119883017136537
2006-10-05,0.00223422283137698
2006-10-06,-0.00268609873960113
2006-10-09,0.000792569618379702
2006-10-10,0.00204136776932806
2006-10-11,-0.00256723638442402
2006-10-12,0.00949586934846458
2006-10-13,0.00204514652830667
2006-10-16,0.00251588174602357
2006-10-17,-0.00366616448921242
2006-10-18,0.00128212185790577
2006-10-19,0.000848894206158413
2006-10-20,0.00119903437267332
2006-10-23,0.00613345649331531
2006-10-24,0.000261389049363459
2006-10-25,0.00350773373296764
2006-10-26,0.00495074455464373
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2006-10-30,0.000428334068703684
2006-10-31,7.1752296140204e-06
2006-11-01,-0.00737862366151809
2006-11-02,-0.00034374202536025
2006-11-03,-0.00222570927225529
2006-11-06,0.0112825746857919
2006-11-07,0.00221524368669979
2006-11-08,0.00208050835407647
2006-11-09,-0.00534724972686718
2006-11-10,0.00186288838689208
2006-11-13,0.00254583325953206
2006-11-14,0.00633628288362242
2006-11-15,0.00240159776169246
2006-11-16,0.00228160870432426
2006-11-17,0.00102817687285928
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2006-11-21,0.00164809419883305
2006-11-22,0.00233536862224426
2006-11-24,-0.00366223559107937
2006-11-27,-0.0136477898022651
2006-11-28,0.003438472345481
2006-11-29,0.00915949927084458
2006-11-30,0.00082141420931503
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2006-12-04,0.00884594941184424
2006-12-05,0.00399451994379429
2006-12-06,-0.00131556569452762
2006-12-07,-0.00397844987343188
2006-12-08,0.00181030175523134
2006-12-11,0.0022672408073543
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2006-12-13,0.00116816744438797
2006-12-14,0.00865192222809696
2006-12-15,0.00112177480909281
2006-12-18,-0.00323556895191413
2006-12-19,0.00215592543469167
2006-12-20,-0.0014180158389232
2006-12-21,-0.00368071683454474
2006-12-22,-0.00533043250831877
2006-12-26,0.00434283016792225
2006-12-27,0.00699078151742771
2006-12-28,-0.00147987699760854
2006-12-29,-0.00452330217942265
2007-01-03,-0.00119938847141565
2007-01-04,0.00122753233161088
2007-01-05,-0.00610316791482379
2007-01-08,0.00221785716034351
2007-01-09,-0.000516809875508173
2007-01-10,0.00193847234895372
2007-01-11,0.00631986113354976
2007-01-12,0.00484142696844714
2007-01-16,0.000817460910785606
2007-01-17,-0.000894337211144069
2007-01-18,-0.00297516137600162
2007-01-19,0.00289128163640306
2007-01-22,-0.00529188648757106
2007-01-23,0.00353570706844586
2007-01-24,0.00846553667390015
2007-01-25,-0.0113337881028741
2007-01-26,-0.00120865904138245
2007-01-29,-0.00109755109730969
2007-01-30,0.00575549848782764
2007-01-31,0.00657124588094593
2007-02-01,0.00533945140583203
2007-02-02,0.00169301677588152
2007-02-05,-0.000967075207189083
2007-02-06,0.000697764098990028
2007-02-07,0.00139406927019614
2007-02-08,-0.00117996304892198
2007-02-09,-0.00710237611137199
2007-02-12,-0.00326671246215149
2007-02-13,0.00756877497695463
2007-02-14,0.0076150120189471
2007-02-15,0.00103705566021262
2007-02-16,-0.000872161682330841
2007-02-20,0.0028402780243777
2007-02-21,-0.00140543808918991
2007-02-22,-0.000857924353300454
2007-02-23,-0.00357003931719468
2007-02-26,-0.00125489304064619
2007-02-27,-0.0353426608069203
2007-02-28,0.00554548479193517
2007-03-01,-0.00259780573285351
2007-03-02,-0.0114682618293003
2007-03-05,-0.00945220963954707
2007-03-06,0.0153747806743985
2007-03-07,-0.00246831414475146
2007-03-08,0.00710134776828308
2007-03-09,0.000677392150231881
2007-03-12,0.00267669878877985
2007-03-13,-0.0205785759265096
2007-03-14,0.00666888032911483
2007-03-15,0.00367697970685921
2007-03-16,-0.00383565561190924
2007-03-19,0.0108355694564022
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2016-11-07,0.0219801997770315
2016-11-08,0.00376487836711892
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2016-11-29,0.00133440216881286
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2016-12-02,0.000396927698722571
2016-12-05,0.00580442703350403
2016-12-06,0.0034050842286355
2016-12-07,0.0130773591099809
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2016-12-09,0.0059214185824441
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2017-01-06,0.00351078897471435
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2017-01-10,0
2017-01-11,0.00282564238266225
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2017-01-13,0.00184813175954535
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2017-01-20,0.00336058441962539
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2017-02-01,0.00029831914579237
2017-02-02,0.000570146914003367
2017-02-03,0.0072384967582515
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2017-02-07,0.00022680323213109
2017-02-08,0.000693082257595456
2017-02-09,0.00573606360024215
2017-02-10,0.00355970705167064
2017-02-13,0.00523213343559359
2017-02-14,0.00399932714219808
2017-02-15,0.00497988871920896
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2017-02-17,0.00167714915423822
2017-02-21,0.00602985014585666
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2017-02-23,0.000418899295217656
2017-02-24,0.00149225010637011
2017-02-27,0.00101746522153245
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2017-03-01,0.0135812109313251
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2017-03-03,0.000503750237377254
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2017-03-09,0.000799575731853075
2017-03-10,0.00326333993002681
2017-03-13,0.000366565599366986
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2017-03-15,0.00833987929560642
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2017-03-28,0.00722530863054427
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2017-04-04,0.000559365981950499
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2017-04-06,0.00192765026736463
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2017-04-10,0.000687450115915311
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2017-04-17,0.00857646586468253
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2017-04-20,0.00752885035594009
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2017-04-24,0.0107817366162921
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2017-04-27,0.000552767268520604
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2017-05-01,0.00173079184664537
2017-05-02,0.00118834369042453
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2017-05-04,0.000581933405524815
2017-05-05,0.00408035918526028
2017-05-08,3.74453761029514e-05
2017-05-09,-0.00102577458278841
2017-05-10,0.00112996274343669
2017-05-11,-0.00216515162190767
2017-05-12,-0.00147953531490508
2017-05-15,0.00476514229719438
2017-05-16,-0.000687132835322402
2017-05-17,-0.0183454683491364
2017-05-18,0.00368003887865953
2017-05-19,0.00674470288589912
2017-05-22,0.00514686368861916
2017-05-23,0.00183618502869809
2017-05-24,0.00248603392791935
2017-05-25,0.00443211171771196
2017-05-26,0.000310501785349082
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2017-05-31,-0.000460074503358499
2017-06-01,0.00754259568076066
2017-06-02,0.00370087430352761
2017-06-05,-0.00121840685198027
2017-06-06,-0.00278290885876586
2017-06-07,0.00156702902118955
2017-06-08,0.000267168836597165
2017-06-09,-0.000830333647746428
2017-06-12,-0.000979242498823751
2017-06-13,0.0045013588104359
2017-06-14,-0.000996327054904711
2017-06-15,-0.00224210982241946
2017-06-16,0.000283598983087607
2017-06-19,0.00831258337364549
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2017-06-21,-0.000582814244665109
2017-06-22,-0.000455885799226508
2017-06-23,0.00155969862589878
2017-06-26,0.000315751721901236
2017-06-27,-0.00810558635083236
2017-06-28,0.00876950140260302
2017-06-29,-0.00863721674872409
2017-06-30,0.00153205763677278
2017-07-03,0.00230816812076995
2017-07-05,0.00145222391410549
2017-07-06,-0.00941298728117257
2017-07-07,0.00638271271779978
2017-07-10,0.000927336103375254
2017-07-11,-0.000782987336525487
2017-07-12,0.00727905107021787
2017-07-13,0.00187282942240685
2017-07-14,0.00466261641168053
2017-07-17,-5.29142557583739e-05
2017-07-18,0.000597678355106268
2017-07-19,0.00535825833697601
2017-07-20,-0.000153671107566922
2017-07-21,-0.000367939284998009
2017-07-24,-0.00106430101441379
2017-07-25,0.00291890763987279
2017-07-26,0.000282623879980015
2017-07-27,-0.000973161536450107
2017-07-28,-0.00134201558956093
2017-07-31,-0.00072841090403486
2017-08-01,0.0024461208441755
2017-08-02,0.000492527123482134
2017-08-03,-0.00218604173413617
2017-08-04,0.00188732141131442
2017-08-07,0.00164584465066131
2017-08-08,-0.00241735213579197
2017-08-09,-0.000363674653750756
2017-08-10,-0.0145802185645767
2017-08-11,0.00127475695514878
2017-08-14,0.00999365143761022
2017-08-15,-0.000498932542412511
2017-08-16,0.00141909552357511
2017-08-17,-0.015557342219811
2017-08-18,-0.00183705368694209
2017-08-21,0.001161975566494
2017-08-22,0.00989169543340296
2017-08-23,-0.00345957025377697
2017-08-24,-0.00207661659984471
2017-08-25,0.00167147161756898
2017-08-28,0.00048695330705506
2017-08-29,0.000842466928157037
2017-08-30,0.00460453176230669
2017-08-31,0.0057046734011319
2017-09-01,0.0019805782508131
2017-09-05,-0.00757945848168795
2017-09-06,0.00312384232793672
2017-09-07,-0.000178451880057828
2017-09-08,-0.00148996013690184
2017-09-11,0.0107809748815884
2017-09-12,0.00335830257667524
2017-09-13,0.000756834360798209
2017-09-14,-0.00110132385091077
2017-09-15,0.00184547743380836
2017-09-18,0.00145486204172762
2017-09-19,0.00110957955448043
2017-09-20,0.000634146746002706
2017-09-21,-0.00305056571600559
2017-09-22,0.000647583976344457
2017-09-25,-0.00222452286230723
2017-09-26,7.21642135088629e-05
2017-09-27,0.00407682233325257
2017-09-28,0.00120389081571659
2017-09-29,0.00369826273919749
2017-10-02,0.00386651892302847
2017-10-03,0.00215651120947946
2017-10-04,0.00124594361807606
2017-10-05,0.00563090398283173
2017-10-06,-0.00107421107345562
2017-10-09,-0.00180606400318517
2017-10-10,0.00231971998008174
2017-10-11,0.00180188267254078
2017-10-12,-0.00168817688774858
2017-10-13,0.000877721912925011
2017-10-16,0.00174922264829469
2017-10-17,0.000672352575650237
2017-10-18,0.000742059767674164
2017-10-19,0.000327944157669791
2017-10-20,0.005103796075133
2017-10-23,-0.00398039552001705
2017-10-24,0.00161660113028983
2017-10-25,-0.00467395589466868
2017-10-26,0.00127013925077257
2017-10-27,0.00804060997474831
2017-10-30,-0.00319757728609016
2017-10-31,0.000944013076273897
2017-11-01,0.00159084385333585
2017-11-02,0.000189948066468659
2017-11-03,0.00309228923533578
2017-11-06,0.00127044391487363
2017-11-07,-0.00018912071459809
2017-11-08,0.00144261384148603
2017-11-09,-0.00376898148418636
2017-11-10,-0.000898046836950606
2017-11-13,0.000983150887048367
2017-11-14,-0.00231228067530242
2017-11-15,-0.00554099874252767
2017-11-16,0.00816265301924357
2017-11-17,-0.0026294170087624
2017-11-20,0.00127486991887604
2017-11-21,0.00651983860214589
2017-11-22,-0.000750542637235618
2017-11-24,0.00205398437439541
2017-11-27,-0.000384331586785081
2017-11-28,0.00980033212495268
2017-11-29,-0.000369293995849063
2017-11-30,0.00815758675244727
2017-12-01,-0.00202658277623424
2017-12-04,-0.0010527108155598
2017-12-05,-0.00374639050870762
2017-12-06,-0.000114111855581633
2017-12-07,0.00292806665406786
2017-12-08,0.00549120221327826
2017-12-11,0.00319684203358417
2017-12-12,0.00154772365184641
2017-12-13,-0.000473068682704358
2017-12-14,-0.00407916777147754
2017-12-15,0.00893431347358931
2017-12-18,0.00534847838711716
2017-12-19,-0.00323549789174749
2017-12-20,-0.000828236184285736
2017-12-21,0.00198368687879125
2017-12-22,-0.000458271463486426
2017-12-26,-0.00105897574081926
2017-12-27,0.000790628240348035
2017-12-28,0.00183231904955861
2017-12-29,-0.00519663242728541
2018-01-02,0.00826907852688752
2018-01-03,0.00637843324297815
2018-01-04,0.00402054261954721
2018-01-05,0.007009145849314
2018-01-08,0.00166096391535486
2018-01-09,0.00130208347183558
2018-01-10,-0.00111284595936834
2018-01-11,0.00700902608623633
2018-01-12,0.00672692616818527
2018-01-16,-0.00353071313246112
2018-01-17,0.00937100630643606
2018-01-18,-0.00161769774853138
2018-01-19,0.00437564815425073
2018-01-22,0.00803436442584715
2018-01-23,0.00217200492947089
2018-01-24,-0.000560132635300192
2018-01-25,0.000602439420859469
2018-01-26,0.0117716380408188
2018-01-29,-0.00675473632363577
2018-01-30,-0.0109586425739705
2018-01-31,0.000488865875231781
2018-02-01,-0.000648298661995561
2018-02-02,-0.0214366802827097
2018-02-05,-0.0418425411596273
2018-02-06,0.0172905736588325
2018-02-07,-0.00501413842107024
2018-02-08,-0.0382590522050155
2018-02-09,0.0148256452651365
2018-02-12,0.0138186656125736
2018-02-13,0.00260952182772112
2018-02-14,0.0133134400309336
2018-02-15,0.0119968616443646
2018-02-16,0.000373399821508968
2018-02-20,-0.00585851712920782
2018-02-21,-0.00551166461587016
2018-02-22,0.000973077554965229
2018-02-23,0.0159012782845682
2018-02-26,0.0116884386817349
2018-02-27,-0.0127883116733161
2018-02-28,-0.0111578060215365
2018-03-01,-0.0134139657621342
2018-03-02,0.0050587854385169
2018-03-05,0.0109716174612213
2018-03-06,0.00263538301257338
2018-03-07,-0.000483991693956298
2018-03-08,0.00445314825424248
2018-03-09,0.0172295465038514
2018-03-12,-0.00127479704060018
2018-03-13,-0.00638391043583741
2018-03-14,-0.00574097014258435
2018-03-15,-0.000782236274108783
2018-03-16,0.00170199807789562
2018-03-19,-0.0143060405804629
2018-03-20,0.00148070846611859
2018-03-21,-0.00184569184358807
2018-03-22,-0.0254848872590383
2018-03-23,-0.0211898070675298
2018-03-26,0.0267950406801321
2018-03-27,-0.0174272857817392
2018-03-28,-0.0029209188276953
2018-03-29,0.0136757774228435
2018-04-02,-0.0225906821998745
2018-04-03,0.0125359611773792
2018-04-04,0.0115001022585774
2018-04-05,0.00683942159633499
2018-04-06,-0.0221640669841525
2018-04-09,0.00333099481175125
2018-04-10,0.0165885989675969
2018-04-11,-0.00554068585564416
2018-04-12,0.00821689876343346
2018-04-13,-0.00289079967402373
2018-04-16,0.00807633677770347
2018-04-17,0.0106050717289028
2018-04-18,0.000831020407423999
2018-04-19,-0.00574258188196275
2018-04-20,-0.00857317709997663
2018-04-23,5.62299297808266e-05
2018-04-24,-0.013470887828869
2018-04-25,0.00183537394838584
2018-04-26,0.0103801441652864
2018-04-27,0.00111300538272641
2018-04-30,-0.00822119244304886
2018-05-01,0.00254580217086176
2018-05-02,-0.00723195121871711
2018-05-03,-0.00225621781074015
References
https://www.quantstart.com/articles/hidden-markov-models-an-introduction
https://www.quantstart.com/articles/hidden-markov-models-for-regime-detection-using-r
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