White Test for Heteroskedasticity

Performs the White test for heteroskedasticity by regressing the squared residuals of a linear model on the original regressors and their squared terms. The null hypothesis is homoskedasticity.

Usage

eda_white_test(data, years, alpha = 0.05)

Arguments

data: Numeric vector of observed annual maximum series values. Must be strictly positive, finite, and not missing.
years: Numeric vector of observation years corresponding to data. Must be the same length as data and strictly increasing.
alpha: Numeric scalar in \([0.01, 0.1]\). The significance level for confidence intervals or hypothesis tests. Default is 0.05.

Value

A list containing the results of the White test:

data: The data argument.
years: The years argument.
alpha: The significance level as specified in the alpha argument.
null_hypothesis: A string describing the null hypothesis.
alternative_hypothesis: A string describing the alternative hypothesis.
statistic: White test statistic based on sample size and r_squared.
p_value: The p-value derived from a Chi-squared distribution with df = 2.
reject: If TRUE, the null hypothesis was rejected at significance alpha.

Details

The White test regresses the squared residuals from a primary linear model lm(data ~ years) against both the original regressor and its square. The test statistic is calculated as \(nR^2\), where \(R^2\) is the coefficient of determination from the auxiliary regression and \(n\) is the number of elements in the time series. Under the null hypothesis, the test statistic has the \(\chi^2\) distribution with 2 degrees of freedom.

References

White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica, 48(4), 817–838.

Examples

data <- rnorm(n = 100, mean = 100, sd = 10)
years <- seq(from = 1901, to = 2000)
eda_white_test(data, years)
#> $data
#>   [1] 107.85550 103.97192 106.98846 104.50714 106.40800 112.20660 110.78431
#>   [8]  96.80989  87.26127  93.49333  92.57200  87.74771  96.87723 110.71671
#>  [15]  98.46020  91.09966  84.26416 105.62013  94.57179 111.64665 103.88534
#>  [22] 108.28514 100.32738  93.51255  98.24003  91.33492 102.79443  74.37330
#>  [29] 105.36249 117.23348  98.92870 105.61287  89.23935 100.82991 101.78167
#>  [36]  91.55114 117.67981  82.68244 112.11189 107.36570 111.29951  90.78180
#>  [43] 101.56818  80.14524 110.30039 112.91148 105.00442 110.39921  87.44111
#>  [50]  98.86676 101.12835 111.51733  85.58585 103.89748 107.29353  86.04344
#>  [57]  96.94657 110.95199  88.58207  91.29411 109.85239  91.61905  91.71838
#>  [64] 110.01256 111.97043  95.29367  84.88836 103.47476  95.94925  96.50217
#>  [71]  84.59143  95.90070  89.02645 100.54988  90.44008 109.84374 109.39418
#>  [78]  87.61338  86.89788  92.04935  93.35320 108.44849  94.79207 103.34544
#>  [85]  93.20054  96.88521 113.29437 103.96915  98.51686  92.26959 118.54612
#>  [92] 111.78232 105.47654 106.94876 108.49706 103.51722 104.15862  84.53482
#>  [99]  87.53159 104.64329
#> 
#> $years
#>   [1] 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915
#>  [16] 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930
#>  [31] 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945
#>  [46] 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960
#>  [61] 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975
#>  [76] 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990
#>  [91] 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
#> 
#> $alpha
#> [1] 0.05
#> 
#> $null_hypothesis
#> [1] "The data is homoskedastic."
#> 
#> $alternative_hypothesis
#> [1] "The data is heteroskedastic."
#> 
#> $statistic
#> [1] 1.428001
#> 
#> $p_value
#> [1] 0.4896812
#> 
#> $reject
#> [1] FALSE
#>