Variance Ratio tests and other tests for Martingale Difference Hypothesis

Description

A collection of variance ratio and spectral shapte tests

Details

Author(s)

Jae H. Kim

Maintainer: Jae H. Kim <J.Kim@latrobe.edu.au>

Adjustment for thinly-traded returns

Description

The adjustment based on AR(1) fitting as proposed by Miller et al. (1994)

Usage

Adjust.thin(y)

Arguments

Value

Adjusted return

Author(s)

Jae H. Kim

References

Miller et al. (1994), Mean Reversion of Standard & Poor's 500 Index Base Changes: Arbitrage Induced or Statistical Illusion Journal of Finance, XLIX, 479-513.

Examples

data(exrates)
y <- exrates$ca                           
nob <- length(y)
r <- log(y[2:nob])-log(y[1:(nob-1)]) 
Adjust.thin(r)

Automatic Portmanteau Test

Description

A robustified portmanteau test with automatic lag selection

Usage

Auto.Q(y,lags)

Arguments

Value

Author(s)

Jae H. Kim

References

Escanciano, J.C., Lobato, I.N. 2009a. An automatic portmanteau test for serial correlation. Journal of Econometrics 151, 140-149.

Charles, A. Darne, O. Kim, J.H. 2011, Small Sample Proeprties of Alternative Tests for Martingale Difference Hypothesis, Economics Letters, 110(2), 151-154.

Examples

data(exrates)
y <- exrates$ca                          
nob <- length(y)
r <- log(y[2:nob])-log(y[1:(nob-1)])    
Auto.Q(r)

Automatic Variance Ratio Test

Description

A variance ratio test with holding period value chosen by a data dependent procedure

Usage

Auto.VR(y)

Arguments

Value

Note

R code translated from Choi's GAUSS code

Author(s)

Jae H. Kim

References

Choi, I. 1999, Testing the random walk hypothesis for real exchange rates Journal of Applied Econometrics, 14, 293-308.

Examples

data(exrates)
y <- exrates$ca                           
nob <- length(y)
r <- log(y[2:nob])-log(y[1:(nob-1)])      
Auto.VR(r)

Wild Bootstrapping of Automatic Variance Ratio Test

Description

This function returns wild bootstrap test results for the Automatic Variance Ratio Test of Choi (1999)

Usage

AutoBoot.test(y, nboot, wild,prob=c(0.025,0.975))

Arguments

Value

Author(s)

Jae H. Kim

References

Kim, J. H., 2009, Automatic Variance Ratio Test under Conditional Heteroskedascity, Finance Research Letters, 6(3), 179-185.

Charles, A. Darne, O. Kim, J.H. 2011, Small Sample Proeprties of Alternative Tests for Martingale Difference Hypothesis, Economics Letters, 110(2), 151-154.

Examples

                                
r <- rnorm(100)          
AutoBoot.test(r,nboot=500,wild="Normal")

Average Exponential Tests

Description

Average exponential tests of Andrews and Ploberger (1996)

Usage

Ave.Ex(y)

Arguments

Value

Note

Traslated from Choi's Gauss codes

Author(s)

Jae H. Kim

References

Choi, I. 1999, Testing the random walk hypothesis for real exchange rates, Journal of Applied Econometrics, 14, 293-308.

Examples

data(exrates)
y <- exrates$ca                      
nob <- length(y)
r <- log(y[2:nob])-log(y[1:(nob-1)])   
Ave.Ex(r)

Bootstrap Variance Ratio Tests

Description

This function returns bootstrap p-values of the Lo-MacKilay (1988) and Chow-Denning (1993) tests.

Users can choose between iid bootstrap and wild bootstrap

Usage

Boot.test(y, kvec, nboot, wild, prob=c(0.025,0.975))

Arguments

Value

Author(s)

Jae H. Kim

References

Kim, J.H., 2006, Wild Bootstrapping Variance Ratio Tests. Economics Letters, 92, 38-43.

Examples

data(exrates)
y <- exrates$ca                   
nob <- length(y)
r <- log(y[2:nob])-log(y[1:(nob-1)])    
kvec <- c(2,5,10)
Boot.test(r,kvec,nboot=500,wild="Normal")

Power Transformed Joint Variance Ratio Test

Description

See equation (15) of Chen and Deo (2006)

Usage

Chen.Deo(x, kvec)

Arguments

Value

Author(s)

Jae H. Kim

References

Chen, W. W., and Deo, R.S., 2006, The Variance Ratio Statistic at Large Horizons, Econometric Theory, 22, 206-234.

Examples

data(exrates)
y <- exrates$ca                         
nob <- length(y)
r <- log(y[2:nob])-log(y[1:(nob-1)])    
kvec <- c(2,5,10)
Chen.Deo(r,kvec)

Chow-Denning Multiple Variance Ratio Tests

Description

This function returns Chow-Denning test statistics.

CD1: test for iid series; CD2: test for uncorrelated series with possible heteroskedasticity.

Usage

Chow.Denning(y, kvec)

Arguments

Value

Note

See Chow and Denning (1993) for the details of critical value calculation

Author(s)

Jae H. Kim

References

Chow,K. V., K. C. DENNING, 1993, A Simple Multiple Variance Ratio Test, Journal of Econometrics, 58, 385-401.

Examples

data(exrates)
y <- exrates$ca                  
nob <- length(y)
r <- log(y[2:nob])-log(y[1:(nob-1)])      
kvec <- c(2,5,10)
Chow.Denning(r,kvec) 

Dominguez-Lobato Test for Martingale Difference Hypothesis

Description

Dominguez-Lobato Test

Usage

DL.test(y,B,p)

Arguments

Value

Author(s)

Jae H. Kim

References

Domingues M.A. and Lobato, I. N., 2003, Testing the Martingale Difference Hypothesis, Econometrics Reviews, 22, p351-377.

Charles, A. Darne, O. Kim, J.H. 2011, Small Sample Proeprties of Alternative Tests for Martingale Difference Hypothesis, Economics Letters, 110(2), 151-154.

Examples

r <- rnorm(50)           
DL.test(r,B=100)
# B=100 is used for fast execution in the example. 
# Use a higher number in actual application

Generalized spectral Test

Description

Generalized spectral Test

Usage

Gen.Spec.Test(y,B)

Arguments

Value

Author(s)

Jae H. Kim

References

Escanciano, J.C. and Velasco, C., 2006, Generalized Spectral Tests for the martigale Difference Hypothesis, Journal of Econometrics, 134, p151-185.

Charles, A. Darne, O. Kim, J.H. 2011, Small Sample Proeprties of Alternative Tests for Martingale Difference Hypothesis, Economics Letters, 110(2), 151-154.

Examples

r <- rnorm(100)        
Gen.Spec.Test(r)

Critical Values for the joint versions of Wright's rank and sign tests

Description

This function runs a simulation to calculate the critical values of the joint versions of Wright's tests.

Usage

JWright.crit(n, kvec, nit)

Arguments

Value

Author(s)

Jae H. Kim

References

Belaire-Franch G, Contreras D. Ranks and signs-based multiple variance ratio tests, Working paper, University of Valencia 2004.

Kim, J. H. and Shamsuddin, A., 2008, Are Asian Stock Markets Efficient? Evidence from New Multiple Variance Ratio Tests, Journal of Empirical Fiance 15(8), 518-532.

Examples

kvec <- c(2,5,10)
JWright.crit(n=100,kvec,nit=50)

# nit is set to 50 for fast execution in the example. 
# nit=10000 is recommended as in Wright (2000)

A Joint Version of Wight's Rank and Sign Test

Description

This function returns joint or multiple version of Wright's rank and sign tests. The test takes the maximum value of the individual rank or sign tests, in the same manner as Chow-Denning test

Usage

Joint.Wright(y, kvec)

Arguments

Value

Author(s)

Jae H. Kim

References

Belaire-Franch G, Contreras D. Ranks and signs-based multiple variance ratio tests, Working paper, University of Valencia 2004.

Kim, J. H. and Shamsuddin, A., 2008, Are Asian Stock Markets Efficient? Evidence from New Multiple Variance Ratio Tests, Journal of Empirical Fiance 15(8), 518-532.

Examples

data(exrates)
y <- exrates$ca                           
nob <- length(y)
r <- log(y[2:nob])-log(y[1:(nob-1)])    
kvec <- c(2,5,10)
Joint.Wright(r,kvec) 

Lo-MacKinlay variance Ratio Tests

Description

The function returns M1 and M2 statistics of Lo and MacKinlay (1998).

M1: tests for iid series; M2: for uncorrelated series with possible heteroskedasticity.

Usage

Lo.Mac(y, kvec)

Arguments

Value

Author(s)

Jae H. Kim

References

LO, A. W., and A. C. MACKINLAY (1988): "Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, 1, 41-66.

Examples

data(exrates)
y <- exrates$ca                 
nob <- length(y)
r <- log(y[2:nob])-log(y[1:(nob-1)])       
kvec <- c(2,5,10)
Lo.Mac(r,kvec) 

Panel Variance Ratio Tests

Description

Panel variance tatio tests based on Maximum Absloute Value, Sum of Squares, and Mean of each cross-sectional units

Usage

Panel.VR(dat, nboot = 500)

Arguments

Details

The component statistics are based on the automatic variance ratio test The set of returns are wild bootstrapped to conserve cross-sectional dependency

Value

Author(s)

Jae H. Kim

References

Kim, J. H., & Shamsuddin, A. (2015). A closer look at return predictability of the US stock market: evidence from new panel variance ratio tests. Quantitative Finance, 15(9), 1501-1514.

Examples

ret=matrix(rnorm(200),nrow=100)
Panel.VR(ret)

Spectral shape tests for random walk

Description

Spectral Shape tests proposed by Durlauf (1991) and Choi (1999)

Usage

Spec.shape(x)

Arguments

Value

Note

Traslated from Choi's Gauss codes

Author(s)

Jae H. Kim

References

Choi, I. 1999, Testing the random walk hypothesis for real exchange rates, Journal of Applied Econometrics, 14, 293-308. Durlauf, S. N., 1991, Spectral based testing of the martingale hypothesis, Journal of Econometrics, 50, 355-376.

Examples

data(exrates)
y <- exrates$ca                   
nob <- length(y)
r <- log(y[2:nob])-log(y[1:(nob-1)])     
Spec.shape(r)

Subsampling test of Whang and Kim (2003)

Description

The function returns the p-values of the subsampling test.

Usage

Subsample.test(y, kvec)

Arguments

Details

The block lengths are chosen internally using the rule proposed in Whang and Kim (2003)

Value

Author(s)

Jae H. Kim

References

WHANG,Y.-J., J. KIM, 2003, A Multiple Variance Ratio Test Using Subsampling, Economics Letters, 79, 225-230.

Examples

data(exrates)
y <- exrates$ca                  
nob <- length(y)
r <- log(y[2:nob])-log(y[1:(nob-1)])   
kvec <- c(2,5,10)
Subsample.test(r,kvec)

Absolute Value of (VR - 1)

Description

This value is sometimes used to measure the degree of market efficiency

Usage

VR.minus.1(y, kvec)

Arguments

Value

Note

see Auto.VR function for automatic selection of holding periods

Author(s)

Jae H. Kim

Examples

data(exrates)
y <- exrates$ca             
nob <- length(y)
kvec <- c(2,5,10)
r <- log(y[2:nob])-log(y[1:(nob-1)])          
VR.minus.1(r,kvec)

Variance Ratio Plot

Description

Plotting unstandadized variance ratios against holding periods with 95percent confidence band

Standard errors under iid returns are used.

Usage

VR.plot(y, kvec)

Arguments

Value

Author(s)

Jae H. Kim & Alexios Ghalanos

Examples

data(exrates)
y <- exrates$ca                                 
nob <- length(y)
r <- log(y[2:nob])-log(y[1:(nob-1)])
kvec <- c(2,5,10)
VR.plot(r,kvec)

Wald Test of Richardson and Smith (1991)

Description

This function returns the Wald test statistic with critical values

Usage

Wald(y, kvec)

Arguments

Value

Note

The statistic asymptotically follows the chi-squared distribution with the degrees of freedom same as the number of holding periods used

Author(s)

Jae H. Kim

References

Richardson, M., T. Smith, 1991, "Tests of Financial Models in the Presence of Overlapping Observations," The Review Financial Studies, 4, 227-254.

Examples

data(exrates)
y <- exrates$ca                        
nob <- length(y)
r <- log(y[2:nob])-log(y[1:(nob-1)])     
kvec <- c(2,5,10)
Wald(r,kvec) 

Wright's Rank and Sign Tests

Description

The function returns R1, R2 and S1 tests statistics detailed in Wright (2000)

Usage

Wright(y, kvec)

Arguments

Details

Nonparametric tests

Value

Author(s)

Jae H. Kim

References

WRIGHT,J.H.,2000,Alternative Variance-Ratio Tests Using Ranks and Signs, Journal of Business & Economic Statistics, 18, 1-9.

Examples

data(exrates)
y <- exrates$ca                    
nob <- length(y)
r <- log(y[2:nob])-log(y[1:(nob-1)])  
kvec <- c(2,5,10)
Wright(r,kvec) 

Critical Values for Wright's rank and sign tests

Description

This function returns critical values of Wright's tests based on the simulation method detailed in Wright (2000)

Usage

Wright.crit(n, k, nit)

Arguments

Value

Author(s)

Jae H. Kim

References

WRIGHT,J.H.,2000,Alternative Variance-Ratio Tests Using Ranks and Signs, Journal of Business & Economic Statistics, 18, 1-9.

Examples

Wright.crit(n=10,k=2,nit=50)  

# nit is set to 50 for fast execution in the example. 
# nit=10000 is recommended as in Wright (2000)

wright's Exchange Rates Data

Description

The data set used in Wright (2001) as an application, weekly from August, 7, 1974 to May 29 1996

Usage

data(exrates)

Format

A data frame with 1139 observations on the following 5 variables.

ca

a numeric vector, Canadian Dollar

dm

a numeric vector, Deutch Mark

ff

a numeric vector, French Franc

uk

a numeric vector, UK Pound

jp

a numeric vector, Japanese Yen

References

WRIGHT,J.H.,2000,Alternative Variance-Ratio Tests Using Ranks and Signs, Journal of Business & Economic Statistics, 18, 1-9.

Examples

data(exrates)