

   kernel {ts}                                  R Documentation

   SSmmooootthhiinngg KKeerrnneell OObbjjeeccttss

   DDeessccrriippttiioonn::

        The `"tskernel"' class is designed to represent dis-
        crete symmetric normalized smoothing kernels. These
        kernels can be used to smooth vectors, matrices, or
        time series objects.

   UUssaaggee::

        kernel(coef, m, r, name)

        df.kernel(k)
        bandwidth.kernel(k)
        is.tskernel(k)

        print(k, digits = max(3,.Options$digits-3))
        plot(k)

   AArrgguummeennttss::

       coef: the upper half of the smoothing kernel coeffi-
             cients (inclusive of coefficient zero) or the name
             of a kernel (currently `"daniell"', `"dirichlet"',
             `"fejer"' or `"modified.daniell"'.

          m: the kernel dimension. The number of kernel coeffi-
             cients is `2*m+1'.

       name: the name of the kernel.

          r: the kernel order for a Fejer kernel.

     digits: the number of digits to format real numbers.

   DDeettaaiillss::

        `kernel' is used to construct a general kernel or named
        specific kernels. The modified Daniell kernel halves
        the end coefficients (as used by S-PLUS).

        `df.kernel' returns the "equivalent degrees of freedom"
        of a smoothing kernel as defined in Brockwell and
        Davies (1991), p. 362, and `bandwidth.kernel' returns
        the equivalent bandwidth as defined in Bloomfield
        (1991), p. 201, with a continuity correction.

   VVaalluuee::

        `kernel' returns a list with class `"tskernel"', and
        components the coefficients `coef' and the kernel
        dimension `m'. An additional attribute is `"name"'.

   AAuutthhoorr((ss))::

        A. Trapletti; modifications by B.D. Ripley

   RReeffeerreenncceess::

        Bloomfield, P. (1976) Fourier Analysis of Time Series:
        An Introduction. Wiley.

        Brockwell, P.J. and Davis, R.A. (1991) Time Series:
        Theory and Methods. Second edition. Springer, pp.
        350-365.

   SSeeee AAllssoo::

        `kernapply'

   EExxaammpplleess::

        data(EuStockMarkets)    # Demonstrate a simple trading strategy for the
        x <- EuStockMarkets[,1]  # financial time series German stock index DAX.
        k1 <- kernel("daniell", 50)  # a long moving average
        k2 <- kernel("daniell", 10)  # and a short one
        plot(k1)
        plot(k2)
        x1 <- kernapply(x, k1)
        x2 <- kernapply(x, k2)
        plot(x)
        lines(x1, col = "red")    # go long if the short crosses the long upwards
        lines(x2, col = "green")  # and go short otherwise

        data(sunspot)     # Reproduce example 10.4.3 from Brockwell and Davies (1991)
        spectrum(sunspot.year, kernel=kernel("daniell", c(11,7,3)), log="no")

