table for calculating the first six autocorrelation coefficients and significance

Produces data table of autocorrelation coefficients \(\rho\) and corresponding Q(6)-statistic for each column in R.

table.Autocorrelation(R, digits = 4)

Arguments

R

an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns
digits

number of digits to round results to for display

Note

To test returns for autocorrelation, Lo (2001) suggests the use of the Ljung-Box test, a significance test for the auto-correlation coefficients. Ljung and Box (1978) provide a refinement of the Q-statistic proposed by Box and Pierce (1970) that offers a better fit for the \(\chi^2\) test for small sample sizes. Box.test provides both.

References

Lo, Andrew W. 2001. Risk Management for Hedge Funds: Introduction and Overview. SSRN eLibrary.

See also

Box.test, acf

Examples


data(managers)
t(table.Autocorrelation(managers))
#>                rho1    rho2    rho3    rho4    rho5    rho6 Q(6) p-value
#> HAM1         0.1890 -0.0847 -0.0602 -0.1842 -0.0035  0.0492       0.0788
#> HAM2         0.1975  0.3046  0.0719  0.0770  0.0626  0.1574       0.0011
#> HAM3         0.0071  0.1970  0.0413  0.1237 -0.0717  0.2022       0.0286
#> HAM4         0.1954 -0.0840 -0.1694 -0.0923 -0.0041 -0.0065       0.0812
#> HAM5        -0.0579 -0.1714 -0.0330  0.1371 -0.1462 -0.1148       0.2989
#> HAM6         0.0982  0.1816 -0.0274 -0.1711 -0.0501 -0.1248       0.3885
#> EDHEC LS EQ  0.2119  0.0834  0.0254 -0.0435 -0.0533  0.1758       0.0872
#> SP500 TR    -0.0134 -0.0336  0.0514 -0.0878  0.0853  0.0776       0.7487
#> US 10Y TR    0.0398 -0.1739  0.1049 -0.0355 -0.1116 -0.0602       0.2199
#> US 3m TR     0.9224  0.9081  0.8968  0.8746  0.8363  0.8127       0.0000

result = t(table.Autocorrelation(managers[,1:8]))

textplot(result, rmar = 0.8, cmar = 2,  max.cex=.9, halign = "center",
         valign = "top", row.valign="center", wrap.rownames=15,
         wrap.colnames=10, mar = c(0,0,3,0)+0.1)

title(main="Autocorrelation")