Cowan's CAR test.

Source: R/car_nonparametric_tests.R

A nonparametric test proposed by Cowan 1992 as an extension of the rank test proposed by Corrado 1989.

car_rank_test(list_of_returns, car_start, car_end, percentage = 90)

Arguments

list_of_returns

a list of objects of S3 class returns, each element of which is treated as a security.
car_start

an object of Date class giving the first date of the CAR period.
car_end

an object of Date class giving the last date of the CAR period.
percentage

a lowest allowed percentage of non-missing observation for each day to be incorporated into CAR. The default value is 90 percent.

  • name: a name of the test, i.e. "car_brown_warner_1985"

  • car_start: the first date of the CAR period

  • car_end: the last date of the CAR period

  • average_percentage: an average share of non-missing observations over the CAR period

  • statistic: a test's statistic

  • number_of_days: the number of days in the CAR period

  • significance: a significance of the statistic

Details

This function performs a test proposed by Cowan 1992 to investigate the significance of the CAR for a given period. In order to get ranks of corresponding abnormal returns, the procedure uses regular R function rank with parameter ties.method = "average" and na.last = "keep". For this test the estimation period and the event period must not overlap, otherwise an error will be thrown. The test statistic is assumed to have a normal distribution (as an approximation). The test is well-specified for the case, when cross-sectional abnormal returns are not symmetric. The test is stable to variance increase during given period. This test ignores the dependence of abnormal returns' ranks of different days (i.e., a serial dependence). The critical values are standard normal. The significance levels of \(\alpha\) are 0.1, 0.05, and 0.01 (marked respectively by *, **, and ***).

References

  • Corrado C.J. A Nonparametric Test for Abnormal Security-Price Performance in Event Studies. Journal of Financial Economics 23:385-395, 1989.

  • Cowan A.R. Nonparametric Event Study Tests. Review of Quantitative Finance and Accounting, 2:343-358, 1992.

See also

car_nonparametric_tests.

Examples

if (FALSE) {
library("magrittr")
rates_indx <- get_prices_from_tickers("^GSPC",
                                      start = as.Date("2019-04-01"),
                                      end = as.Date("2020-04-01"),
                                      quote = "Close",
                                      retclass = "zoo") %>%
    get_rates_from_prices(quote = "Close",
                          multi_day = TRUE,
                          compounding = "continuous")
tickers <- c("AMZN", "ZM", "UBER", "NFLX", "SHOP", "FB", "UPWK")
get_prices_from_tickers(tickers,
                        start = as.Date("2019-04-01"),
                        end = as.Date("2020-04-01"),
                        quote = "Close",
                        retclass = "zoo") %>%
    get_rates_from_prices(quote = "Close",
                          multi_day = TRUE,
                          compounding = "continuous") %>%
    apply_market_model(regressor = rates_indx,
                       same_regressor_for_all = TRUE,
                       market_model = "sim",
                       estimation_method = "ols",
                       estimation_start = as.Date("2019-04-01"),
                       estimation_end = as.Date("2020-03-13")) %>%
    car_rank_test(car_start = as.Date("2020-03-16"),
                  car_end = as.Date("2020-03-20"))
}
## The result of the code above is equivalent to:
data(securities_returns)
car_rank_test(
    list_of_returns = securities_returns,
    car_start = as.Date("2020-03-16"),
    car_end = as.Date("2020-03-20")
)

#>            name  car_start    car_end average_percentage statistic
#> 1 car_rank_test 2020-03-16 2020-03-20                100    3.0537
#>   number_of_days significance
#> 1              5          ***