List of figures
Effect of no intercept on a regression line 5.2 Graphical illustration of heteroscedasticity 5.3 Plot of uˆ t against uˆ t−1 , showing positive autocorrelation 5.4 Plot of uˆ t over time, showing positive autocorrelation 5.5 Plot of uˆ t against uˆ t−1 , showing negative autocorrelation 5.6 Plot of uˆ t over time, showing negative autocorrelation 5.7 Plot of uˆ t against uˆ t−1 , showing no autocorrelation 5.8 Plot of uˆ t over time, showing no autocorrelation 5.9 Rejection and non-rejection regions for DW test 5.10 Regression residuals from stock return data, showing large outlier for October 1987 5.11 Possible effect of an outlier on OLS estimation 5.12 Plot of a variable showing suggestion for break date 6.1 Autocorrelation function for sample MA(2) process 6.2 Sample autocorrelation and partial autocorrelation functions for an MA(1) model: yt = −0.5ut−1 + ut 6.3 Sample autocorrelation and partial autocorrelation functions for an MA(2) model: yt = 0.5ut−1 − 0.25ut−2 + ut 6.4 Sample autocorrelation and partial autocorrelation functions for a slowly decaying AR(1) model: yt = 0.9yt−1 + ut 6.5 Sample autocorrelation and partial autocorrelation functions for a more rapidly decaying AR(1) model: yt = 0.5yt−1 + ut 6.6 Sample autocorrelation and partial autocorrelation functions for a more rapidly decaying AR(1) 5.1
181 6.7
182 191 6.8
191 192 6.9
192 7.1
193 193 7.2
196 8.1
212 213 8.2
231 259 8.3 8.4
270 8.5
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8.6 9.1
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9.2 9.3
271 9.4
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model with negative coefficient: yt = −0.5yt−1 + ut Sample autocorrelation and partial autocorrelation functions for a non-stationary model (i.e. a unit coefficient): yt = yt−1 + ut Sample autocorrelation and partial autocorrelation functions for an ARMA(1, 1) model: yt = 0.5yt−1 + 0.5ut−1 + ut Use of in-sample and out-ofsample periods for analysis Impulse responses and standard error bands for innovations in unexpected inflation equation errors Impulse responses and standard error bands for innovations in the dividend yields Value of R2 for 1,000 sets of regressions of a non-stationary variable on another independent non-stationary variable Value of t-ratio of slope coefficient for 1,000 sets of regressions of a non-stationary variable on another independent non-stationary variable Example of a white noise process Time series plot of a random walk versus a random walk with drift Time series plot of a deterministic trend process Autoregressive processes with differing values of φ (0, 0.8, 1) Daily S&P returns for August 2003–August 2013 The problem of local optima in maximum likelihood estimation News impact curves for S&P500 returns using coefficients implied from GARCH and GJR model estimates Three approaches to hypothesis testing under maximum likelihood
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