forecast Chinese stock market return

Class 9 Bootstrapping and Data Mining/Snooping

Professor David Rapach

ECON 6520

Forecasting Macroeconomic and Financial Variables

Spring Semester 2019

[This Version: 04-01-2019]

Data mining/snooping

I Concern ⇒ we consider many potential predictors

I More likely to find ‘significant’ evidence of predictability

I Even when target variable is unpredictable

I Conventional tests assume researcher conducts single test

I But researcher actually conducts multiple tests

I Focus on ‘best’ results ⇒ size distortion

I 5% nominal critical value 6= actual 5% critical value

Data mining/snooping

I Need to control for data mining/snooping

I White (2000) ‘reality check’ bootstrap

I Controls test size for multiple model comparisons

I Based on maximum statistic

I Data-mining bootstrap procedures for nested models

I Inoue & Kilian (2005) ⇒ asymptotic results

I Rapach & Wohar (2006) ⇒ US stock returns

I Clark & McCracken (2012) ⇒ fixed-regressor wild bootstrap

Fixed-regressor wild bootstrap

I Out-of-sample asset return forecasting ⇒ yt = Rxt

I Constant expected return (prevailing mean) benchmark

I yt+1 = α + εt+1

I Competing predictive regression model forecasts

I yt+1 = α + βxj,t + εt+1 for j = 1, . . . , J

I T ⇒ # of observations in full sample

I First M1 observations ⇒ initial in-sample period I Last M2 observations ⇒ out-of-sample period

I Prevailing mean benchmark ⇒ MSFE0

I Predictive regression forecasts ⇒ MSFEj for j = 1, . . . , J

Fixed-regressor wild bootstrap

I Max of Clark & McCracken (2001) MSE-F statistics

I maxMSE-F = max j=1,...,J

MSE-Fj

I MSE-Fj = M2(MSFE0 − MSFEj)/MSFEj for j = 1, . . . , J

I Compute OLS residuals for ‘kitchen sink’ model

I yt = α + J∑

j=1

βjxj,t−1 + εt

I ε̂t = yt −

( α̂ +

J∑ j=1

β̂jxj,t−1

) for t = 2, . . . , T

Fixed-regressor wild bootstrap

I Generate pseudo observations under H0: no predictability

I y (b) t =

1

T

T∑ t=1

yt︸ ︷︷ ︸ ȳ

+ε̂tu (b) t for t = 2, . . . , T

I u (b) t ⇒ draw from N(0, 1) distribution

I Simply set y (b) 1 = y1

I Bootstrap pseudo observations ⇒ { y (b) t

}T t=1

I Wild bootstrap ⇒ accounts for conditional heteroskedasticity

Fixed-regressor wild bootstrap

I Use { y (b) t

}T t=1

& original xj,t observations to compute

I Prevailing mean benchmark forecast

I Predictive regression model forecasts for j = 1, . . . , J

I MSE-F (b) j for j = 1, . . . , J

I maxMSE-F(b) = max j=1,...,J

MSE-F (b) j ⇒ store

Fixed-regressor wild bootstrap

I Repeat B times ⇒ {

maxMSE-F(b) }B b=1

I Bootstrap p-value = 1 B

B∑ b=1

I(maxMSE-F(b) > maxMSE-F)

I I(x) = 1 when x is true, 0 otherwise

I Significant results readily explained by chance?

I Neely et al (2014) ⇒ equity premium forecasting

I Significant evidence not easily attributable to chance

Forecasting macro variables

I Proceed similarly with usual benchmark/competitors

I AR ⇒ yt+1 = α0 + p∑

k=1

αkyt−(k−1) + εt+1

I ARDL for j = 1, . . . , J

I yt+1 = α0 + p1∑ k=1

αkyt−(k−1) + p2∑ k=1

βkxj,t−(k−1) + εt+1

I General model needed for wild bootstrap

I Could consider ARDL model based on first PC

I yt+1 = α0 + p1∑ k=1

αkyt−(k−1) + p2∑ k=1

βk f̂t−(k−1) + εt+1

I Relatively straightforward extension for h > 1

I Need to account for serial correlation in general model residuals

__MACOSX/out sample/._Class09Slides6520_04-01-2019.pdf