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375Figure 26.1: Equity curve of ARIMA+GARCH strategy vs "Buy & Hold" for the S&P500 from1952Figure 26.2: Equity curve of ARIMA+GARCH strategy vs "Buy & Hold" for the S&P500 from2005 until todaysense because there is likely to be a significant serial correlation in this period and it will bewell-captured by the ARIMA and GARCH models. Once the market recovered post-2009 and
376enters what looks to be more a stochastic trend, the model performance begins to suffer onceagain.Note that this strategy can be easily applied to different stock market indices, equities orother asset classes. I strongly encourage you to try researching other instruments, as you mayobtain substantial improvements on the results presented here.26.4 Full CodeHere is the full listing for the indicator generation, backtesting and plotting:# Import the necessary librarieslibrary(quantmod)library(lattice)library(timeSeries)library(rugarch)# Obtain the S&P500 returns and truncate the NA valuegetSymbols("^GSPC", from="1950-01-01")spReturns = diff(log(Cl(GSPC)))spReturns[as.character(head(index(Cl(GSPC)),1))] = 0# Create the forecasts vector to store the predictionswindowLength = 500foreLength = length(spReturns) - windowLengthforecasts <- vector(mode="character", length=foreLength)for (d in 0:foreLength) {# Obtain the S&P500 rolling window for this dayspReturnsOffset = spReturns[(1+d):(windowLength+d)]# Fit the ARIMA modelfinal.aic <- Inffinal.order <- c(0,0,0)for (p in 0:5) for (q in 0:5) {if ( p == 0 && q == 0) {next}arimaFit = tryCatch( arima(spReturnsOffset, order=c(p, 0, q)),error=function( err ) FALSE,warning=function( err ) FALSE )if( !is.logical( arimaFit ) ) {current.aic <- AIC(arimaFit)if (current.aic < final.aic) {
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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
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Chapter 4Markov Chain Monte CarloIn
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374.2.1 Markov Chain Monte Carlo Al
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39We discussed the fact that we cou
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41Finally we specify the Metropolis
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43we do not need to compute 100,000
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45x, stats.beta.pdf(x, alpha, beta)
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Chapter 5Bayesian Linear Regression
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49non-informative priors.• Poster
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51# Use a linear model (y ~ beta_0
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53# Use the No-U-Turn Samplerstep =
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55plt.show()We can see the sampled
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57"""Calculates the Markov Chain Mo
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Chapter 6Bayesian Stochastic Volati
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61plt.show()Figure 6.1: Different r
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63( )yilog ∼ t(ν, 0, exp(−2s i
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656.3.2 Model Specification in PyMC
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67Figure 6.5: Overlay of samples fr
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69plt.xlabel(’Time’)plt.ylabel(
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Part IIITime Series Analysishttps:/
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74• Seasonal Variation - Many tim
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767.5 How Does This Relate to Other
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78Definition 8.1.1. Expectation. Th
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808.2 CorrelationCorrelation is a d
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82Definition 8.3.4. Stationary in t
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84Figure 8.2: Correlogram plotted i
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868.6 Next StepsNow that we’ve di
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88• Use our knowledge of time ser
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909.3.2 CorrelogramWe can also plot
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929.4.2 CorrelogramThe autocorrelat
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94created the difference series, we
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96there are a few that are marginal
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9810.1 How Will We Proceed?In this
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10010.4.1 RationaleIn the previous
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10210.4.4 Simulations and Correlogr
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104Figure 10.2: Realisation of AR(1
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10610.4.5 Financial DataAmazon Inc.
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108Figure 10.6: Correlogram of Firs
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110> plot(gspcrt)Figure 10.8: First
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112model, as well as the conditiona
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114Figure 10.10: Realisation of MA(
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116Coefficients:ma1 intercept-0.729
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118> require(quantmod)> getSymbols(
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120> amznrt.maCall:arima(x = amznrt
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122Figure 10.16: Residuals of MA(1)
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124Figure 10.18: Residuals of MA(3)
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12610.6.3 RationaleTo date we have
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128Figure 10.20: Correlogram of an
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130Figure 10.22: Correlogram of an
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132Figure 10.23: Correlogram of the
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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
Page 338 and 339: Chapter 23Natural Language Processi
Page 340 and 341: 327The Reuters 21578 dataset can be
Page 342 and 343: 329for export as shippers are now e
Page 344 and 345: 331tungtung-oilveg-oilwheatwoolwpiy
Page 346 and 347: 333in order to minimise memory usag
Page 348 and 349: 335’The Tokyo Grain Exchange said
Page 350 and 351: 337for t in d[0]:if t in topics:d_t
Page 352 and 353: 339This would mean that we are givi
Page 354 and 355: 341partitions into the training and
Page 356 and 357: 3430.660194174757[[21 0 0 0 2 3 0 0
Page 358 and 359: 345self.encoding = encodingdef _res
Page 360 and 361: 347"""topics = open("data/all-topic
Page 362: Part VQuantitative Trading Techniqu
Page 365 and 366: 352While vectorised backtests are s
Page 367 and 368: 354• Backtest - Encapsulates the
Page 369 and 370: 356The second strategy provides a 3
Page 371 and 372: 35825.4.1 MonthlyLiquidateRebalance
Page 373 and 374: 360"""Size the order to reflect the
Page 375 and 376: 362Figure 25.1: US Equities/Bonds 6
Page 377 and 378: 364five years relative to US equiti
Page 379 and 380: 366# Use the monthly liquidate and
Page 381 and 382: 368import datetimefrom qstrader imp
Page 383 and 384: 37026.2 Strategy ImplementationTo i
Page 385 and 386: 372final.order[1],final.order[3]),
Page 387: 374> spIntersect = merge( spArimaGa
Page 391 and 392: 378# Output the CSV file to "foreca
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Page 395 and 396: 382natural gas.The hypothesis prese
Page 397 and 398: 384## Carry out linear regression o
Page 399 and 400: 38627.5 Python QSTrader Implementat
Page 401 and 402: 388that arrive out of order in the
Page 403 and 404: 390if self.invested is not None:if
Page 405 and 406: 392take into account commission dif
Page 407 and 408: 394adf.test(comb$residuals, k=1)# c
Page 409 and 410: 396def go_short_units(self):"""Go s
Page 411 and 412: 398from qstrader.trading_session.ba
Page 413 and 414: 400default=’’,help=’Pickle (.
Page 415 and 416: 402Hence we can "long the spread" i
Page 417 and 418: 404class KalmanPairsTradingStrategy
Page 419 and 420: 406if all(self.latest_prices > -1.0
Page 421 and 422: 408It also changes the FixedPositio
Page 423 and 424: 410’--testing/--no-testing’, de
Page 425 and 426: 412• Asset Selection - Choosing a
Page 427 and 428: 414if self.R is not None:self.R = s
Page 429 and 430: 416)self.events_queue.put(SignalEve
Page 431 and 432: 418@click.option(’--testing/--no-
Page 433 and 434: 420• Short-Term Trend - Predict m
Page 435 and 436: 422It takes the CSV file path as an
Page 437 and 438: 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
Page 489 and 490:
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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