R/SADF.test.R

In d9d6ka/RANEPA-R: Set of unit root and cointegration tests

#' @title
#' Supremum ADF tests
#' @order 1
#'
#' @description
#' `SADF.test` is a test statistic equal to the minimum value of [ADF.test] for
#' subsamples starting at \eqn{t = 1}.
#'
#' `GSADF.test` is a generalized version of `SADF.test`. Subsamples are allowed
#' to start at any point between 1 and \eqn{T (1 - trim)}.
#'
#' @details
#' Refactored original code by Kurozumi et al.
#'
#' @param y A time series of interest.
#' @param trim A trimming parameter to determine the lower and upper bounds for
#' a possible break point.
#' @param const Whether the constant needs to be included.
#' @param add.p.value Whether the p-value is to be returned. This argument is
#' needed to suppress the calculation of p-values during the precalculation of
#' tables needed for the p-values estimating.
#'
#' @return An object of type `sadf`. It's a list of:
#' * `y`,
#' * `trim`,
#' * `const`,
#' * vector of \eqn{t}-values,
#' * the value of the corresponding test statistic,
#' * \eqn{p}-value if it was asked for.
#'
#' @references
#' Kurozumi, Eiji, Anton Skrobotov, and Alexey Tsarev.
#' “Time-Transformed Test for Bubbles under Non-Stationary Volatility.”
#' Journal of Financial Econometrics, April 23, 2022.
#' https://doi.org/10.1093/jjfinec/nbac004.
#'
#' @export
SADF.test <- function(y,
                      trim = 0.01 + 1.8 / sqrt(length(y)),
                      const = TRUE,
                      add.p.value = TRUE) {
    n.obs <- length(y)

    if (const == FALSE) {
        y <- y - y[1]
    }

    t.values <- c()
    m <- 1
    for (j in (floor(trim * n.obs)):n.obs) {
        model <- ADF.test(y[1:j], const = const)
        t.values[m] <- model$t.alpha
        m <- m + 1
    }

    ## Take the maximum of the calculated t-statistics.
    SADF.value <- max(t.values)

    if (add.p.value) {
        if (const == TRUE) {
            cr.values <- .cval_SADF_with_const
        } else {
            cr.values <- .cval_SADF_without_const
        }

        p.value <- get.p.values.SADF(SADF.value, n.obs, cr.values)
    }

    result <- c(
        list(
            y = y,
            trim = trim,
            const = const,
            t.values = t.values,
            SADF.value = SADF.value
        ),
        if (add.p.value) {
            list(p.value = p.value)
        } else {
            NULL
        }
    )

    class(result) <- "sadf"

    return(result)
}


#' @rdname SADF.test
#' @order 2
#'
#' @export
GSADF.test <- function(y,
                       trim = 0.01 + 1.8 / sqrt(length(y)),
                       const = TRUE,
                       add.p.value = TRUE) {
    n.obs <- length(y)

    if (const == FALSE) {
        y <- y - y[1]
    }

    t.values <- c()
    m <- 1
    for (i in 1:(n.obs - floor(trim * n.obs) + 1)) {
        for (j in (i + floor(trim * n.obs) - 1):n.obs) {
            model <- ADF.test(y[i:j], const = const)
            t.values[m] <- model$t.alpha
            m <- m + 1
        }
    }

    ## Take the maximum of the calculated t-statistics.
    GSADF.value <- max(t.values)

    if (add.p.value) {
        if (const == TRUE) {
            cr.values <- .cval_GSADF_with_const
        } else {
            cr.values <- .cval_GSADF_without_const
        }

        p.value <- get.p.values.SADF(GSADF.value, n.obs, cr.values)
    }

    result <- c(
        list(
            y = y,
            trim = trim,
            const = const,
            t.values = t.values,
            GSADF.value = GSADF.value
        ),
        if (add.p.value) {
            list(p.value = p.value)
        } else {
            NULL
        }
    )

    class(result) <- "sadf"

    return(result)
}