"Frontmatter". In: Analysis of Financial Time Series

More documents

Recommendations

Info

98 CONDITIONAL HETEROSCEDASTIC MODELSsigma-sq0.0 0.01 0.031940 1960 1980yearstd-res-4 -2 0 21940 1960 1980Figure 3.7. (a) Time series plot of estimated volatility for the monthly excess returns of S&P500 index, and (b) the standardized shocks of the monthly excess returns of S&P 500 index.Both plots are based on the GARCH(1, 1) model in Eq. (3.18).yearσ 2 h (1) = 0.00014 + 0.822σ 2 h + 0.1352a2 h ,where a h is the residual of the mean equation at time h and σh 2 is obtained fromthe volatility equation. The starting value σ0 2 is fixed at either zero or the unconditionalvariance of a t . For multistep ahead forecasts, we use the recursive formulain Eq. (3.16). Table 3.1 shows some mean and volatility forecasts for themonthly excess return of S&P500 index with forecast origin h = 792 based onthe GARCH(1, 1) model in Eq. (3.18).t InnovationAssuming that ɛ t follows a standardized Student-t distribution with 5 degrees offreedom, we reestimate the GARCH(1, 1) model and obtainr t = 0.0085 + a t , σ 2t = 0.00018 + 0.1272a 2 t−1 + 0.8217σ 2t−1 , (3.19)where the standard errors of the parameters are 0.0014, 0.55×10 −4 , 0.0349, and0.0382, respectively. This model is essentially an IGARCH(1, 1) model as ˆα 1 + ˆβ 1 ≈0.96, which is close to 1. The Ljung–Box statistics of the standardized residuals giveQ(10) = 10.45 with p value 0.40 and those of the {ãt 2 } series give Q(10) = 9.33
THE GARCH MODEL 99Series : stdatACF0.0 0.2 0.4 0.6 0.8 1.00 5 10 15 20 25LagSeries : stdat * stdatACF0.0 0.2 0.4 0.6 0.8 1.00 5 10 15 20 25LagFigure 3.8. Model checking of the GARCH(1, 1) model in Eq. (3.18) for monthly excessreturns of S&P 500 index: (a) Sample ACF of standardized shocks, and (b) sample ACF of thesquared standardized shocks.with p value 0.50. Thus, the fitted GARCH(1, 1) model with Student-t distributionis adequate.Estimation of Degrees of FreedomIf we further extend the GARCH(1, 1) model by estimating the degrees of freedomof the Student-t distribution used, we obtain the modelr t = 0.0083 + a t , σ 2t = 0.00017 + 0.1227a 2 t−1 + 0.8193σ 2t−1 , (3.20)Table 3.1. Volatility Forecasts for the Monthly Excess Returns of S&P500 Index. TheForecast Origin Is h = 792, Which Corresponds to December, 1991. Here VolatilityDenotes Conditional Variance.Horizon 1 2 3 4 5 ∞Return 0.0065 0.0065 0.0065 0.0065 0.0065 0.0065Volatility 0.00311 0.00312 0.00312 0.00313 0.00314 0.00324
Page 1 and 2:
Analysis of FinancialTime SeriesFin
Page 3 and 4:
ContentsPrefacexi1. Financial Time
Page 5 and 6:
CONTENTSix6.6 Black-Scholes Pricing
Page 7 and 8:
PrefaceThis book grew out of an MBA
Page 9 and 10:
Analysis of Financial Time Series.
Page 11 and 12:
ASSET RETURNS 3Multiperiod Simple R
Page 13 and 14:
ASSET RETURNS 5r t [k] =ln(1 + R t
Page 15 and 16:
DISTRIBUTIONAL PROPERTIES OF RETURN
Page 18 and 19:
10 FINANCIAL TIME SERIES AND THEIR
Page 20 and 21:
Page 22 and 23:
Page 24 and 25:
Page 26:
Page 29 and 30:
REFERENCES 21Federal Reserve Bank o
Page 31 and 32:
CORRELATION AND AUTOCORRELATION FUN
Page 33 and 34:
CORRELATION AND AUTOCORRELATION FUN
Page 35 and 36:
WHITE NOISE AND LINEAR TIME SERIES
Page 37 and 38:
SIMPLE AUTOREGRESSIVE MODELS 29whic
Page 39 and 40:
SIMPLE AUTOREGRESSIVE MODELS 31wher
Page 41 and 42:
SIMPLE AUTOREGRESSIVE MODELS 33wher
Page 43 and 44:
SIMPLE AUTOREGRESSIVE MODELS 35expa
Page 45 and 46:
SIMPLE AUTOREGRESSIVE MODELS 37Tabl
Page 47 and 48:
SIMPLE AUTOREGRESSIVE MODELS 39Mode
Page 49 and 50:
SIMPLE AUTOREGRESSIVE MODELS 41The
Page 51 and 52:
SIMPLE MOVING-AVERAGE MODELS 43wher
Page 53 and 54:
SIMPLE MOVING-AVERAGE MODELS 45s-rt
Page 55 and 56: SIMPLE MOVING-AVERAGE MODELS 47The
Page 57 and 58: SIMPLE ARMA MODELS 49A time series
Page 59 and 60: SIMPLE ARMA MODELS 51operator, the
Page 61 and 62: SIMPLE ARMA MODELS 53Table 2.5. Sam
Page 63 and 64: SIMPLE ARMA MODELS 55This represent
Page 65 and 66: UNIT-ROOT NONSTATIONARITY 57ˆp h (
Page 67 and 68: UNIT-ROOT NONSTATIONARITY 59log-pri
Page 69 and 70: SEASONAL MODELS 61which is commonly
Page 71 and 72: SEASONAL MODELS 63Series : xSeries
Page 73 and 74: SEASONAL MODELS 65models use the sa
Page 75 and 76: • ••• •••••••
Page 77 and 78: REGRESSION MODELS WITH TIME SERIES
Page 79 and 80: REGRESSION MODELS WITH TIME SERIES
Page 81 and 82: LONG-MEMORY MODELS 73=(k − d −
Page 83 and 84: APPENDIX A: SOME SCA COMMANDS 75est
Page 85 and 86: EXERCISES 77relation. Draw your con
Page 87 and 88: Analysis of Financial Time Series.
Page 89 and 90: STRUCTURE OF A MODEL 813.2 STRUCTUR
Page 91 and 92: THE ARCH MODEL 83corrected asset re
Page 93 and 94: THE ARCH MODEL 85Series : xACF0.0 0
Page 95 and 96: THE ARCH MODEL 87sample mean from t
Page 97 and 98: THE ARCH MODEL 89where Ɣ(x) is the
Page 99 and 100: THE ARCH MODEL 91Series : resiSerie
Page 101 and 102: THE GARCH MODEL 93other softwares a
Page 103 and 104: THE GARCH MODEL 95ahead forecast ca
Page 105: THE GARCH MODEL 97The fitted AR(3)
Page 109 and 110: THE GARCH-M MODEL 101two models. Th
Page 111 and 112: THE EXPONENTIAL GARCH MODEL 103To b
Page 113 and 114: THE EXPONENTIAL GARCH MODEL 105eros
Page 115 and 116: THE CHARMA MODEL 107ˆσ 2 864 (3)
Page 117 and 118: RANDOM COEFFICIENT AUTOREGRESSIVE M
Page 119 and 120: THE LONG-MEMORY STOCHASTIC VOLATILI
Page 121 and 122: AN ALTERNATIVE APPROACH 113where Va
Page 123 and 124: APPLICATION 115(a) IBMlog-rtn-30 -1
Page 125 and 126: APPLICATION 117equationThe fitted m
Page 127 and 128: KURTOSIS OF GARCH MODELS 119where K
Page 129 and 130: SOME RATS PROGRAMS FOR ESTIMATING V
Page 131 and 132: EXERCISES 123• Is there evidence
Page 133 and 134: REFERENCES 125Melino, A., and Turnb
Page 135 and 136: NONLINEAR TIME SERIES 127To put non
Page 137 and 138: NONLINEAR MODELS 129Example 4.1. Co
Page 139 and 140: NONLINEAR MODELS 131jumps when it b
Page 141 and 142: NONLINEAR MODELS 133the series and
Page 143 and 144: NONLINEAR MODELS 135els to the mont
Page 145 and 146: NONLINEAR MODELS 137growth-2 -1 0 1
Page 147 and 148: NONLINEAR MODELS 139average of y t
Page 149 and 150: NONLINEAR MODELS 141indicating that
Page 151 and 152: NONLINEAR MODELS 143s T,2t=1T∑K h
Page 153 and 154: NONLINEAR MODELS 145f i (.) of Eq.
Page 155 and 156: NONLINEAR MODELS 1474.1.9.1 Feed-Fo
Page 157 and 158:
NONLINEAR MODELS 1494.1.9.2 Trainin
Page 159 and 160:
NONLINEAR MODELS 151prob0.0 0.2 0.4
Page 161 and 162:
NONLINEARITY TESTS 153idea behind v
Page 163 and 164:
NONLINEARITY TESTS 155C l (δ, T )
Page 165 and 166:
NONLINEARITY TESTS 157and obtain th
Page 167 and 168:
NONLINEARITY TESTS 159• Step 2: C
Page 169 and 170:
FORECASTING 161returns. In summary,
Page 171 and 172:
FORECASTING 163in m 11 and m 22 ind
Page 173 and 174:
APPLICATION 165unem. rate4 6 8 10
Page 175 and 176:
APPLICATION 167Table 4.4. Out-of-Sa
Page 177 and 178:
APPENDIX A 169compute a0 = 0.1, a1
Page 179 and 180:
REFERENCES 171P(s t = 2 | s t−1 =
Page 181 and 182:
REFERENCES 173Fan, J. (1993), “Lo
Page 183 and 184:
Page 185 and 186:
NONSYNCHRONOUS TRADING 177t − k t
Page 187 and 188:
BID-ASK SPREAD 179The lag-1 autocov
Page 189 and 190:
EMPIRICAL CHARACTERISTICS 181The ma
Page 191 and 192:
n(trades)0 20406080 1200 1000 2000
Page 193 and 194:
EMPIRICAL CHARACTERISTICS 185after-
Page 195 and 196:
MODELS FOR PRICE CHANGES 187deep un
Page 197 and 198:
MODELS FOR PRICE CHANGES 189σ 2i (
Page 199 and 200:
MODELS FOR PRICE CHANGES 191A i = 1
Page 201 and 202:
MODELS FOR PRICE CHANGES 193( )piln
Page 203 and 204:
DURATION MODELS 195For the IBM data
Page 205 and 206:
DURATION MODELS 197(a) is the avera
Page 207 and 208:
DURATION MODELS 199actions might no
Page 209 and 210:
DURATION MODELS 201Series : xACF0.0
Page 211 and 212:
DURATION MODELS 203reduces to that
Page 213 and 214:
DURATION MODELS 205Series : xACF0.0
Page 215 and 216:
THE PCD MODEL 207where w(α) denote
Page 217 and 218:
THE PCD MODEL 209(a) All transactio
Page 219 and 220:
THE PCD MODEL 2110 10 20 30 40 500
Page 221 and 222:
THE PCD MODEL 213⎧⎪⎨1f (x |
Page 223 and 224:
THE PCD MODEL 215Generalized Gamma
Page 225 and 226:
THE PCD MODEL 217smpl 2 3534compute
Page 227 and 228:
REFERENCES 219(a) Use the data to c
Page 229 and 230:
Page 231 and 232:
STOCHASTIC PROCESSES 223write a con
Page 233 and 234:
STOCHASTIC PROCESSES 2253. stationa
Page 235 and 236:
ITO’S LEMMA 2276.3.2 Stochastic D
Page 237 and 238:
ITO’S LEMMA 229This result shows
Page 239 and 240:
DISTRIBUTIONS OF PRICE AND RETURN 2
Page 241 and 242:
BLACK-SCHOLES EQUATION 233and G t =
Page 243 and 244:
BLACK-SCHOLES FORMULA 235risk prefe
Page 245 and 246:
BLACK-SCHOLES FORMULA 237The stock
Page 247 and 248:
BLACK-SCHOLES FORMULA 239(a) Call o
Page 249 and 250:
AN EXTENSION OF ITO’S LEMMA 2410
Page 251 and 252:
STOCHASTIC INTEGRAL 243using the It
Page 253 and 254:
JUMP DIFFUSION MODELS 245where w t
Page 255 and 256:
JUMP DIFFUSION MODELS 247where it i
Page 257 and 258:
JUMP DIFFUSION MODELS 249sudden jum
Page 259 and 260:
APPENDIX A 251Pricing formulas for
Page 261 and 262:
EXERCISES 253which involves the CDF
Page 263 and 264:
REFERENCES 255Bakshi, G., Cao, C.,
Page 265 and 266:
VALUEATRISK 257log return-0.2 -0.1
Page 267 and 268:
RISKMETRICS 259we use log returns r
Page 269 and 270:
RISKMETRICS 261investor is$10,000,0
Page 271 and 272:
ECONOMETRIC APPROACH TO VAR 263Cons
Page 273 and 274:
ECONOMETRIC APPROACH TO VAR 265The
Page 275 and 276:
QUANTILE ESTIMATION 267Using the fo
Page 277 and 278:
QUANTILE ESTIMATION 269ˆx 0.01 = p
Page 279 and 280:
EXTREME VALUE THEORY 271= 1 −= 1
Page 281 and 282:
EXTREME VALUE THEORY 273shows that
Page 283 and 284:
EXTREME VALUE THEORY 275{ [] }r n(i
Page 285 and 286:
EXTREME VALUE THEORY 2777.5.3 Appli
Page 287 and 288:
EXTREME VALUE TO VAR 2797.6 AN EXTR
Page 289 and 290:
EXTREME VALUE TO VAR 281VaR =−2.5
Page 291 and 292:
EXTREME VALUE TO VAR 283stock. The
Page 293 and 294:
A NEW APPROACH TO VAR 285series (e.
Page 295 and 296:
A NEW APPROACH TO VAR 287In Eq. (7.
Page 297 and 298:
A NEW APPROACH TO VAR 289Example 7.
Page 299 and 300:
A NEW APPROACH TO VAR 291feature is
Page 301 and 302:
A NEW APPROACH TO VAR 293(a) Homoge
Page 303 and 304:
A NEW APPROACH TO VAR 295Table 7.4.
Page 305 and 306:
REFERENCES 297a Gaussian GARCH(1, 1
Page 307 and 308:
Page 309 and 310:
CROSS-CORRELATION 301correlation co
Page 311 and 312:
CROSS-CORRELATION 303where ̂D is t
Page 313 and 314:
CROSS-CORRELATION 305Table 8.1. Sum
Page 315 and 316:
30yr20yr10yr5yr1yr-10 0 510-10 0 51
Page 317 and 318:
VAR MODELS 3098.2 VECTOR AUTOREGRES
Page 319 and 320:
VAR MODELS 311where G = Cov(b t ).
Page 321 and 322:
VAR MODELS 313where φ 0 and a t ar
Page 323 and 324:
VAR MODELS 315To specify the order
Page 325 and 326:
VAR MODELS 317the S&P 500 index. Th
Page 327 and 328:
VECTOR MA MODELS 319[ ] [ ] [ ] [r1
Page 329 and 330:
VECTOR MA MODELS 321turn used to co
Page 331 and 332:
VECTOR ARMA MODELS 323For the VAR(1
Page 333 and 334:
VECTOR ARMA MODELS 325log-rate0.0 0
Page 335 and 336:
VECTOR ARMA MODELS 327interest-rate
Page 337 and 338:
CO-INTEGRATION 329Series : x1ACF0.0
Page 339 and 340:
CO-INTEGRATION 331Stock Exchange; o
Page 341 and 342:
THRESHOLD CO-INTEGRATION 333ously b
Page 343 and 344:
PRINCIPAL COMPONENT ANALYSIS 3358.6
Page 345 and 346:
PRINCIPAL COMPONENT ANALYSIS 337(c
Page 347 and 348:
PRINCIPAL COMPONENT ANALYSIS 339(a)
Page 349 and 350:
FACTOR ANALYSIS 341(a) 5 stock retu
Page 351 and 352:
FACTOR ANALYSIS 343andCov(r, F) = E
Page 353 and 354:
FACTOR ANALYSIS 345matrix P to tran
Page 355 and 356:
FACTOR ANALYSIS 347Example 8.9. In
Page 357 and 358:
APPENDIX A. REVIEW OF VECTORS AND M
Page 359 and 360:
APPENDIX A. REVIEW OF VECTORS AND M
Page 361 and 362:
APPENDIX B. MULTIVARIATE NORMAL DIS
Page 363 and 364:
REFERENCES 355(b) Build a bivariate
Page 365 and 366:
Page 367 and 368:
REPARAMETERIZATION 359To illustrate
Page 369 and 370:
REPARAMETERIZATION 361where ⊥ den
Page 371 and 372:
GARCH MODELS FOR BIVARIATE RETURNS
Page 373 and 374:
Page 375 and 376:
Page 377 and 378:
Page 379 and 380:
Page 381 and 382:
Page 383 and 384:
Page 385 and 386:
VECTOR VOLATILITY MODELS 377using t
Page 387 and 388:
VECTOR VOLATILITY MODELS 379large-c
Page 389 and 390:
VECTOR VOLATILITY MODELS 381(a) S&P
Page 391 and 392:
FACTOR-VOLATILITY MODELS 383conside
Page 393 and 394:
APPLICATION 385[ ]σ11,t=σ 22,t⎡
Page 395 and 396:
MULTIVARIATE t DISTRIBUTION 387σ 1
Page 397 and 398:
APPENDIX A. SOME REMARKS ON ESTIMAT
Page 399 and 400:
APPENDIX A. SOME REMARKS ON ESTIMAT
Page 401 and 402:
REFERENCES 393(a) Compute the sampl
Page 403 and 404:
Page 405 and 406:
GIBBS SAMPLING 397mean adding auxil
Page 407 and 408:
BAYESIAN INFERENCE 399distributions
Page 409 and 410:
BAYESIAN INFERENCE 401normal with m
Page 411 and 412:
ALTERNATIVE ALGORITHMS 403distribut
Page 413 and 414:
ALTERNATIVE ALGORITHMS 40510.4.2 Me
Page 415 and 416:
REGRESSION WITH SERIAL CORRELATIONS
Page 417 and 418:
REGRESSION WITH SERIAL CORRELATIONS
Page 419 and 420:
MISSING VALUES AND OUTLIERS 411y h
Page 421 and 422:
MISSING VALUES AND OUTLIERS 413Cons
Page 423 and 424:
MISSING VALUES AND OUTLIERS 415we h
Page 425 and 426:
MISSING VALUES AND OUTLIERS 417c3t-
Page 427 and 428:
STOCHASTIC VOLATILITY MODELS 419tha
Page 429 and 430:
STOCHASTIC VOLATILITY MODELS 421whe
Page 431 and 432:
STOCHASTIC VOLATILITY MODELS 423den
Page 433 and 434:
STOCHASTIC VOLATILITY MODELS 425The
Page 435 and 436:
STOCHASTIC VOLATILITY MODELS 427(a)
Page 437 and 438:
•••MARKOV SWITCHING MODELS 42
Page 439 and 440:
MARKOV SWITCHING MODELS 431(a) GARC
Page 441 and 442:
MARKOV SWITCHING MODELS 433β i ∼
Page 443 and 444:
MARKOV SWITCHING MODELS 435(a) mont
Page 445 and 446:
MARKOV SWITCHING MODELS 437α ij ar
Page 447 and 448:
FORECASTING 439garchrtn-sq0 200 400
Page 449 and 450:
EXERCISES 441eter uncertainty in pr
Page 451 and 452:
REFERENCES 443Justel, A., Peña, D.
Page 453 and 454:
446 INDEXData (cont.)equal-weighted
Page 455:
448 INDEXPoisson process, 244inhomo
show all

"Frontmatter". In: Analysis of Financial Time Series

Create successful ePaper yourself

Delete template?

Save as template?