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Part IIBayesian Statistics11
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Page 2 and 3: ContentsI Introduction 11 Introduct
Page 4 and 5: 38.2 Correlation . . . . . . . . .
Page 6 and 7: 513.2 The Kalman Filter . . . . . .
Page 8 and 9: 719 Support Vector Machines . . . .
Page 10 and 11: 928 Kalman Filter-Based Pairs Tradi
Page 12 and 13: Limit of Liability/Disclaimer ofWar
Page 14: Part IIntroduction1
Page 17 and 18: 4The aim of this book is to provide
Page 19 and 20: 61.3 How Is The Book Laid Out?The b
Page 21 and 22: 81.5 How Does This Book Differ From
Page 23: 101.7.1 AlternativesThere are many
Page 27 and 28: 14This is in contrast to another fo
Page 29 and 30: 16P (B)P (A|B) = P (A ∩ B) (2.2)B
Page 31 and 32: 18• P (θ|D) is the posterior. Th
Page 33 and 34: 20Thus it can be seen that Bayesian
Page 35 and 36: 22
Page 37 and 38: 243.1 The Bayesian ApproachWhile we
Page 39 and 40: 26k = 0 represents a tail, then the
Page 41 and 42: 28P (θ|α, β) = θ α−1 (1 −
Page 43 and 44: 30Using a beta distribution for the
Page 45 and 46: 32P (θ|z, N) = P (z, N|θ)P (θ)/P
Page 47 and 48: 34
Page 49 and 50: 364.2 Why Markov Chain Monte Carlo?
Page 51 and 52: 38We then generate a uniform random
Page 53 and 54: 404.5.2 Inferring a Binomial Propor
Page 55 and 56: 42plt.plot(x, stats.beta.pdf(x, alp
Page 57 and 58: 44# Parameter values for prior and
Page 59 and 60: 46
Page 61 and 62: 48find the orientation of the hyper
Page 63 and 64: 50Var(y) = V (E(y)) = V (g −1 (X
Page 65 and 66: 52Figure 5.1: Simulation of noisy l
Page 67 and 68: 54Figure 5.2: Using PyMC3 to fit a
Page 69 and 70: 565.5 Full Codeimport matplotlib.py
Page 71 and 72: 58sns.lmplot(x="x", y="y", data=df,
Page 73 and 74: 60stochastic differential equations
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62changes as the number of degrees-
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64Pandas is used to obtain the raw
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66pm.traceplot(trace, model.vars[:-
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68"""Download, calculate and plot t
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70
Page 86 and 87:
Chapter 7Introduction to Time Serie
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75We will learn R in a problem-solv
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Chapter 8Serial CorrelationIn the p
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79> set.seed(1)> x <- seq(1,100) +
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81There are two important points to
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83As with the above definitions of
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85Figure 8.3: Correlogram plotted i
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Chapter 9Random Walks and White Noi
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899.3 White NoiseWe will begin by m
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91as a confirmation that we have el
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93Figure 9.3: Correlogram of a Rand
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95Once quantmod is installed we can
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Chapter 10Autoregressive Moving Ave
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99Definition 10.2.1. Strictly Stati
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101In order to determine whether an
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103with parameter estimates for the
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105Figure 10.3: Realisation of AR(2
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107This allows us to compare "apple
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109In particular we note that the a
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111Figure 10.9: Correlogram of Firs
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113⎧1 if k = 0⎪⎨ q−k∑q∑
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115[1] 0.440208 0.764392We can see
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117Figure 10.12: Realisation of MA(
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119Let us try a MA(2) model:> amznr
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121This provided evidence of both c
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123Figure 10.17: Residuals of MA(2)
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12510.6.1 Bayesian Information Crit
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127We can start with the simplest p
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129> plot(x)The output of our ARMA(
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131residuals to determine if we hav
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133> getSymbols("^GSPC")> sp = diff
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Chapter 11Autoregressive Integrated
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137Alternatively it is possible to
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139Figure 11.2: Correlogram of the
Page 154 and 155:
https://sanet.cd/blogs/polatebooks/
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143> Box.test(resid(spfinal.arima),
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145would further depress the price
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147√ √√√α0 p∑ɛ t = w t
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149Figure 11.7: Correlogram of a si
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151> ft <- as.numeric(ftrt)> ft <-
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153Figure 11.12: Residuals of a GAR
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Chapter 12Cointegrated Time SeriesI
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15712.3.1 Augmented Dickey-Fuller T
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159autocorrelation:> layout(1:2)> a
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161library:> library("tseries")> ad
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163section we are going to consider
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165firms paired with an ETF that tr
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167Figure 12.7: Scatter plot of bac
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169We can replicate the above steps
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171Figure 12.11: Residuals of the f
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173## Plot the residuals of the fir
Page 188 and 189:
175∆x t = µ + Ax t−1 + Γ 1
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177p.d -0.1381095 -0.771055116 -0.0
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179> library("quantmod")We now need
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181Test type: trace statistic , wit
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183spyAdj = unclass(SPY$SPY.Adjuste
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Chapter 13State Space Models and th
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187Where F T is the transpose of F
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189This says that the likelihood fu
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19113.3 Dynamic Hedge Ratio Between
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193Note: You will likely need to ru
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195Utilise the Kalman Filter from t
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197from __future__ import print_fun
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199prices = pd.DataFrame(index=etf_
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Chapter 14Hidden Markov ModelsA con
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203team at OpenAI spend significant
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205Model will tend to stay in a par
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20714.3.1 Market RegimesApplying Hi
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209Figure 14.3: Simulated market re
Page 224 and 225:
211> # Fit a Hidden Markov Model wi
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213highly volatile state. Subsequen
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215# Obtain S&P500 data from 2004 o
Page 230:
Part IVStatistical Machine Learning
Page 233 and 234:
Page 235 and 236:
22215.4 Machine Learning Applicatio
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224disadvantages are the need to ha
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226to machine learning, which is th
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228However, a significant concern a
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230variance σ 2 . ɛ represents th
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232Figure 17.1:(2012)[71]Plot of p(
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234N∑NLL(θ) = − log p(y i | x
Page 249 and 250:
236The goal of the exercise will be
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238lr_model.predict(X_test),color=
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240from sklearn import linear_model
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242
Page 257 and 258:
244Where w m is the mean response i
Page 259 and 260:
246The first task is to sum across
Page 261 and 262:
24818.4 Advantages and Disadvantage
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250Unfortunately this gain in predi
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252import datetimeimport matplotlib
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254X = amzn[["Lag1", "Lag2", "Lag3"
Page 269 and 270:
256plt.plot(estimators, bagging_mse
Page 271 and 272:
258"""# Obtain stock information fr
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260)rf = RandomForestRegressor(n_es
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262between categories.Formally, in
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264b 0 + b 1 x 1 + ... + b p x p =
Page 279 and 280:
266andb · x i + b 0 < 0, if y i =
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268Maximise M ∈ R, by varying b 1
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270andy i (b · x + b 0 ) ≥ M(1
Page 285 and 286:
272p∑〈u, v〉 = u j v j (19.14)
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274
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276y = f(x) + ɛ (20.1)This states
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278the following day, we are only c
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280However if we plot the test MSE,
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28220.2.1 Overview of Cross-Validat
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284Secondly, note that in the 50-50
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286tslag["Volume"] = ts["Volume"]#
Page 301 and 302:
288# Increase degree of linear# reg
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290Figure 20.4: Test MSE curves for
Page 305 and 306:
292..We can plot these curves with
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294Trading volume, as well as the D
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296sample_dict["seed_%s" % i] = np.
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298label=’Avg Test MSE’)ax.lege
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300
Page 315 and 316:
30221.1 High Dimensional DataQuanti
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304The canonical algorithm for clus
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306Figure 22.1: K-Means Clustering
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30822.1.3 Simulated DataIn this sec
Page 323 and 324:
310Figure 22.2: K-Means Algorithm o
Page 325 and 326:
312["Open", "High", "Low","Close",
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314alldays = DayLocator()weekFormat
Page 329 and 330:
316# Plot the full OHLC candles re-
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318changes. Clearly this motivates
Page 333 and 334:
320Obtains a pandas DataFrame conta
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322ax.xaxis.set_major_locator(monda
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Page 339 and 340:
326• Continually monitor the syst
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328... 1049566 Dec 4 1996 reut2-020
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330of a quant researchers day is sp
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332import pprintimport retry:from h
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334self.docs.append( (self.topics,
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336’90,000 yen per 15 tonne lot f
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33823.4 VectorisationAt this stage
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340# Open the first Reuters data se
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34223.7 Performance MetricsThe two
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344print(svm.score(X_test, y_test))
Page 359 and 360:
346def handle_endtag(self, tag):"""
Page 361 and 362:
348def train_svm(X, y):"""Create an
Page 364 and 365:
Chapter 24Introduction to QSTraderI
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353The design calls for the infrast
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Chapter 25Introductory Portfolio St
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357Ticker Name Period LinkSPY SPDR
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359):ticker = event.tickerif self.t
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361from qstrader import settingsfro
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363Figure 25.2: "Strategic" Weight
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36525.6 Full Code# monthly_rebalanc
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367import datetimefrom qstrader imp
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Chapter 26ARIMA+GARCH Trading Strat
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371We use the same procedure as in
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373value would represent data not k
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375Figure 26.1: Equity curve of ARI
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377}final.aic <- current.aicfinal.o
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379new_str = "%s,%s\n" % (strpf, ol
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Chapter 27Cointegration-Based Pairs
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383Figure 27.1: Backward-adjusted p
Page 398 and 399:
385By definition a mean-reverting s
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387ues of the market value of a "un
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389commands, so that the positions
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391thresholds are set to 1.5 and 0.
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393surprising since no statisticall
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395self.bars_elapsed = 0def _set_co
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397self.invested = Nonedef calculat
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399# Use the ExampleCompliance comp
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Chapter 28Kalman Filter-Based Pairs
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403• TLT - For the period 3rd Aug
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405self.time = event.time# Set the
Page 420 and 421:
407print("LONG: %s" % event.time)se
Page 422 and 423:
409# Use the Naive Position Sizer (
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411Figure 28.1: Kalman Filter-Based
Page 426 and 427:
413"""Sets the correct price and ev
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415))self.invested = "long"elif et
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417strategy = Strategies(strategy,
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Chapter 29Supervised Learning for I
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42129.2 Building a Prediction Model
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423The next steps consist of filter
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425if __name__ == "__main__":random
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427from sklearn.externals import jo
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429SignalEvent(self.tickers[0], "BO
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431)# Use the ExampleCompliance com
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433Figure 29.1: Tearsheet for Linea
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435total return. The Sharpe Ratio i
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437)# Create the lookback and lookf
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439#model = LinearDiscriminantAnaly
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441self.minutes += 1# Allow enough
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443# Use the Tearsheet Statisticsst
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Chapter 30Sentiment Analysis via Se
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447sentiment").This sample file for
Page 462 and 463:
449Ticker Name Period LinkXOM Exxon
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451tuples, it is useful to create a
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453if event.type == EventType.TICK
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455threshold, then it closes the po
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457Figure 30.1:is mostly down or fl
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459Figure 30.3:Defence stocks provi
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461if (self.invested[ticker] is Fal
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Page 478 and 479:
Chapter 31Market Regime Detection w
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467Ticker Name Period LinkSPY SPDR
Page 482 and 483:
469def obtain_prices_df(csv_filepat
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471adjusted closing prices are plot
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473# short and long window barspric
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475# Determine the HMM predicted re
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477pickle_path = "/path/to/your/mod
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479The underlying strategy is desig
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481Obtain the prices DataFrame from
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483Requires:tickers - The list of t
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485)hidden_state = self.hmm_model.p
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487)csv_dir, events_queue, tickers,
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Chapter 32Strategy DecayIn this cha
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491It should be well remembered tha
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493)label=’Backtest’, ax=ax, **
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495Figure 32.1: Kalman Filter Pairs
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497Figure 32.3: Sentiment Sentdex S
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Bibliography[1] Wikipedia: Standard
Page 514 and 515:
501[39] Efron, B. Bootstrap methods
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503[74] O’Mahony, A. Online linea
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