advanced-algorithmic-trading

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85Figure 8.3: Correlogram plotted in R of a sequence of integers from 1 to 100Figure 8.4: Correlogram plotted in R of a sequence of integers from 1 to 10, repeated 10 times
868.6 Next StepsNow that we’ve discussed autocorrelation and correlograms in some depth, in subsequent chapterswe will be moving on to linear models and begin the process of forecasting.While linear models are far from the state of the art in time series analysis, we need to developthe theory on simpler cases before we can apply it to the more interesting non-linear models thatare in use today.
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ContentsI Introduction 11 Introduct
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38.2 Correlation . . . . . . . . .
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513.2 The Kalman Filter . . . . . .
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719 Support Vector Machines . . . .
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928 Kalman Filter-Based Pairs Tradi
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Limit of Liability/Disclaimer ofWar
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Part IIntroduction1
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4The aim of this book is to provide
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61.3 How Is The Book Laid Out?The b
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81.5 How Does This Book Differ From
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101.7.1 AlternativesThere are many
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Chapter 2Introduction to Bayesian S
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15Table 2.1: Comparison of Frequent
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172.2 Applying Bayes’ Rule for Ba
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19the next chapter. At this stage,
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21# Create and plot a Beta distribu
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Chapter 3Bayesian Inference of a Bi
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25• The fairness of the coin does
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273.4.3 Multiple Flips of the CoinN
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29x = np.linspace(0, 1, 100)params
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31Hence, all we need to do is re-ar
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33Figure 3.3: The prior and posteri
Page 48 and 49: Chapter 4Markov Chain Monte CarloIn
Page 50 and 51: 374.2.1 Markov Chain Monte Carlo Al
Page 52 and 53: 39We discussed the fact that we cou
Page 54 and 55: 41Finally we specify the Metropolis
Page 56 and 57: 43we do not need to compute 100,000
Page 58 and 59: 45x, stats.beta.pdf(x, alpha, beta)
Page 60 and 61: Chapter 5Bayesian Linear Regression
Page 62 and 63: 49non-informative priors.• Poster
Page 64 and 65: 51# Use a linear model (y ~ beta_0
Page 66 and 67: 53# Use the No-U-Turn Samplerstep =
Page 68 and 69: 55plt.show()We can see the sampled
Page 70 and 71: 57"""Calculates the Markov Chain Mo
Page 72 and 73: Chapter 6Bayesian Stochastic Volati
Page 74 and 75: 61plt.show()Figure 6.1: Different r
Page 76 and 77: 63( )yilog ∼ t(ν, 0, exp(−2s i
Page 78 and 79: 656.3.2 Model Specification in PyMC
Page 80 and 81: 67Figure 6.5: Overlay of samples fr
Page 82 and 83: 69plt.xlabel(’Time’)plt.ylabel(
Page 84: Part IIITime Series Analysishttps:/
Page 87 and 88: 74• Seasonal Variation - Many tim
Page 89 and 90: 767.5 How Does This Relate to Other
Page 91 and 92: 78Definition 8.1.1. Expectation. Th
Page 93 and 94: 808.2 CorrelationCorrelation is a d
Page 95 and 96: 82Definition 8.3.4. Stationary in t
Page 97: 84Figure 8.2: Correlogram plotted i
Page 101 and 102: 88• Use our knowledge of time ser
Page 103 and 104: 909.3.2 CorrelogramWe can also plot
Page 105 and 106: 929.4.2 CorrelogramThe autocorrelat
Page 107 and 108: 94created the difference series, we
Page 109 and 110: 96there are a few that are marginal
Page 111 and 112: 9810.1 How Will We Proceed?In this
Page 113 and 114: 10010.4.1 RationaleIn the previous
Page 115 and 116: 10210.4.4 Simulations and Correlogr
Page 117 and 118: 104Figure 10.2: Realisation of AR(1
Page 119 and 120: 10610.4.5 Financial DataAmazon Inc.
Page 121 and 122: 108Figure 10.6: Correlogram of Firs
Page 123 and 124: 110> plot(gspcrt)Figure 10.8: First
Page 125 and 126: 112model, as well as the conditiona
Page 127 and 128: 114Figure 10.10: Realisation of MA(
Page 129 and 130: 116Coefficients:ma1 intercept-0.729
Page 131 and 132: 118> require(quantmod)> getSymbols(
Page 133 and 134: 120> amznrt.maCall:arima(x = amznrt
Page 135 and 136: 122Figure 10.16: Residuals of MA(1)
Page 137 and 138: 124Figure 10.18: Residuals of MA(3)
Page 139 and 140: 12610.6.3 RationaleTo date we have
Page 141 and 142: 128Figure 10.20: Correlogram of an
Page 143 and 144: 130Figure 10.22: Correlogram of an
Page 145 and 146: 132Figure 10.23: Correlogram of the
Page 147 and 148: 134Notice that there are some signi
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136I would like to thank you for be
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138Figure 11.1: Plot of simulated A
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140> amzn = diff(log(Cl(AMZN)))As i
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142We fit an ARIMA model by looping
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144being able to create strategy in
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14611.5.2 Why Does This Model Volat
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148ɛ t = σ t w t (11.17)σ 2 t =
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1502.5 % 97.5 %a0 0.1786255 0.21726
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152Figure 11.10: Residuals of an AR
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Figure 11.13: Squared residuals of
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156mean, but due to its stationarit
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158x t = pz t + w x,t (12.1)y t = q
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160Figure 12.3: Plot of x t and y t
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162> layout(1:2)> plot(badcomb, typ
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164We then created two subsequent s
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166Figure 12.6: Backward-adjusted c
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168Coefficients:(Intercept) ewaAdj3
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170> plot(rdsaAdj, rdsbAdj,xlab="RD
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172set.seed(123)## SIMULATED DATA##
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174plot(comb1$residuals, type="l",x
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176> q <- 0.6*z + rnorm(10000)> r <
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178Figure 12.12: Plot of s t , the
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180EWA.Adjusted.l2 EWC.Adjusted.l2
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182library("quantmod")library("tser
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184
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186• Smoothing - Estimating the p
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18813.2.1 A Bayesian ApproachRecall
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190E[y t+1 |D t ] = E[Ft+1θ T t +
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192of our linear regression. The ne
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194Figure 13.1: Scatterplot of the
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196Figure 13.2: Time-varying slope
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198delta = 1e-5trans_cov = delta /
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200
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202"risk manager". They will be use
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204Figure 14.1: Two-state Markov Ch
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206Figure 14.2: Hidden Markov Model
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208> bull_var <- 0.1> bear_mean <-
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210historical financial data.14.3.3
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212The same process will now be car
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214install.packages(’quantmod’)
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216
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Chapter 15Introduction to Machine L
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22115.3.1 Linear RegressionAn eleme
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223While seemingly not a traditiona
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Chapter 16Supervised LearningSuperv
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227ŷ = ˆf(x) = argmax z∈R p(y =
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Chapter 17Linear RegressionIn this
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231if __name__ == "__main__":# Set
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23317.3 Maximum Likelihood Estimati
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235To simplify the notation the lat
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237Once the full dataset is created
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239if __name__ == "__main__":# Set
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241))lr_model.coef_[0]# Create a sc
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Chapter 18Tree-Based MethodsIn this
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245Figure 18.2: The resulting parti
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24718.3 Decision Trees for Classifi
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249In quantitative finance applicat
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251(a) Grow a tree ˆf b with k spl
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253tslag["Lag%s" % str(i+1)] = ts["
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255The same approach is carried out
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257seen whether it is feasible to p
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259amzn = create_lagged_series("AMZ
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Chapter 19Support Vector MachinesIn
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263• Non-Probabilistic - Since th
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265The key point here is that it is
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267classification. Overfitting mean
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269Figure 19.6: Addition of a singl
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27119.8 Support Vector MachinesThe
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273p∑K(x i , x k ) = (1 + x ij x
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Chapter 20Model Selection andCross-
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277This motivates the concept of a
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279Figure 20.1: Various estimates o
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281error for a particular model est
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283Figure 20.3: Amazon, Inc. - Pric
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28520.2.5 Python ImplementationWe a
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287At this stage we have the necess
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289..import pylab as plt....def plo
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291fold = 0# Loop over the k-foldsf
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293Figure 20.5: Test MSE curves for
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295return tsretdef validation_set_p
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297model = Pipeline([("polynomial_f
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299X = lags[["Lag1", "Lag2", "Lag3"
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Chapter 21Unsupervised LearningThe
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303parameters of the model, θ.Conv
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Chapter 22Clustering MethodsIn this
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3072. Iterate the following until c
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309]# Generate a list of the 2D clu
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311clustered using K-Means and then
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313ax.set_axis_bgcolor((1,1,0.9))ax
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315ClusterTomorrow to contain tomor
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317Figure 22.4: 3D scatterplot of n
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319# Apply the K-Means Algorithm fo
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321# up days and red for down daysc
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323sp500["ClusterMatrix"] = list(zi
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Chapter 23Natural Language Processi
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327The Reuters 21578 dataset can be
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329for export as shippers are now e
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331tungtung-oilveg-oilwheatwoolwpiy
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333in order to minimise memory usag
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335’The Tokyo Grain Exchange said
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337for t in d[0]:if t in topics:d_t
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339This would mean that we are givi
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341partitions into the training and
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3430.660194174757[[21 0 0 0 2 3 0 0
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345self.encoding = encodingdef _res
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347"""topics = open("data/all-topic
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Part VQuantitative Trading Techniqu
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352While vectorised backtests are s
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354• Backtest - Encapsulates the
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356The second strategy provides a 3
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35825.4.1 MonthlyLiquidateRebalance
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360"""Size the order to reflect the
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362Figure 25.1: US Equities/Bonds 6
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364five years relative to US equiti
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366# Use the monthly liquidate and
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368import datetimefrom qstrader imp
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37026.2 Strategy ImplementationTo i
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372final.order[1],final.order[3]),
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374> spIntersect = merge( spArimaGa
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376enters what looks to be more a s
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378# Output the CSV file to "foreca
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380
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382natural gas.The hypothesis prese
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384## Carry out linear regression o
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38627.5 Python QSTrader Implementat
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388that arrive out of order in the
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390if self.invested is not None:if
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392take into account commission dif
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394adf.test(comb$residuals, k=1)# c
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396def go_short_units(self):"""Go s
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398from qstrader.trading_session.ba
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400default=’’,help=’Pickle (.
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402Hence we can "long the spread" i
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404class KalmanPairsTradingStrategy
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406if all(self.latest_prices > -1.0
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408It also changes the FixedPositio
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410’--testing/--no-testing’, de
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412• Asset Selection - Choosing a
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414if self.R is not None:self.R = s
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416)self.events_queue.put(SignalEve
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418@click.option(’--testing/--no-
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420• Short-Term Trend - Predict m
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422It takes the CSV file path as an
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424produce a final truth column whe
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426bias-variance trade-off of the m
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428used by the machine learning mod
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430IQFeedIntradayCsvBarPriceHandler
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432’--filename’,default=’’,
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Figure 29.2: Tearsheet for Random F
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436):lookforward_minutes=5,up_down_
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438#ts["UpDown"] = down_tot & up_to
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440events_queue - A handle to the s
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442from intraday_ml_strategy import
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444if __name__ == "__main__":main()
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446sentiment.In recent years there
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448Ticker Name Period LinkMSFT Micr
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450self.statistics.update(event.tim
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452if self.end_date is not None:sen
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454a sent_sell corresponding exit t
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456sentiment_handler = SentdexSenti
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458Figure 30.2:volatile, posting mo
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460fication by adding many more sto
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462events_queue = queue.Queue()csv_
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464def main(config, testing, ticker
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466In quantitative trading this pro
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468self.tickers[ticker]["timestamp"
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470df["Adj Close"][mask],".", lines
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472from qstrader.event import (Sign
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474class RegimeHMMRiskManager(Abstr
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476# If in the undesirable regime,
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47831.5 Strategy Results31.5.1 Tran
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480Figure 31.3: Trend Following Reg
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482ax.grid(True)plt.show()if __name
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484elif short_sma < long_sma and se
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486elif action == "SLD":if self.inv
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488backtest = Backtest(price_handle
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490holding an instrument representi
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492rolling_sharpe_s = np.sqrt(self.
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494In order to use the annualised r
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496Figure 32.2: Aluminum Smelting S
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498
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500[18] Wikipedia: Viterbi algorith
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502[56] Investor, S. Regime detecti
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504[92] Sinclair, E. Volatility Tra
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