dftse function

Remove irrelevant frequencies

dftse(x, low_freq = NULL, high_freq = NULL)

Arguments

• x: Vector, data.frame, matrix or any similar 1D/2D object containing values for filtering.

• low_freq: Number indicating the lowest period of oscillation as fractions of $\pi$. If low_freq > 1, indicating that the direct frequency of the data is provided, this is transformed internally into 2 / high_freq. The default is NULL, meaning that the ifelse(freq > 1, trunc(freq * 1.5), 2)

  will be used.

• high_freq: Number indicating the highest period of oscillation as radians of $\pi$. If high_freq > 1, indicating that the direct frequency of the data is provided, this is transformed internally into 2 / low_freq. The default is NULL, meaning that the trunc(freq * 8) will be used.

Details

This is a pure R implementation of removing the irrelevant frequencies. First, DFT is applied on the data and this result is filtered according to low_freq and high_freq. Finally, an inverse DFT is performed on these relevant frequencies. Both low_freq and high_freq must be either between 0 and 1, meaning that they are frequencies of the period as radians, or both >1, indicating that both are starting and ending periods of the cycle.

low_freq and high_freq are used for keeping the relevant frequencies. These are meant to be the ones inside the range $[ low \_ freq, high \_ freq ]$. Therefore, values outside this range are removed.

For 2-dimensional objects x, this transformation is applied per column.

Returns

Filtered object with length/dimensions same with the input x. Note that for inputs with dimensions (e.g. matrix, data.frame) a matrix

object will be returned.

References

Corbae, D., Ouliaris, S., & Phillips, P. (2002), Band Spectral Regression with Trending-Data. Econometrica 70 (3), pp. 1067-1109.

Corbae, D. & Ouliaris, S. (2006), Extracting Cycles from Nonstationary Data, in Corbae D., Durlauf S.N., & Hansen B.E. (eds.). Econometric Theory and Practice: Frontiers of Analysis and Applied Research. Cambridge: Cambridge University Press, pp. 167–177. tools:::Rd_expr_doi("10.1017/CBO9781139164863.008") .

Shaw, E.S. (1947), Burns and Mitchell on Business Cycles. Journal of Political Economy, 55 (4): pp. 281-298. tools:::Rd_expr_doi("10.1086/256533") .

See Also

corbae_ouliaris

Examples

# Apply on ts object
data(USgdp)
res <- dftse(USgdp, low_freq = 0.0625, high_freq = 0.3333)
head(res)

# Apply on vector
res <- dftse(c(USgdp), low_freq = 0.0625, high_freq = 0.3333)
head(res)

# Apply on matrix per column
mat <- matrix(USgdp, ncol = 4)
res <- dftse(mat, low_freq = 0.0625, high_freq = 0.3333)
head(res)

# Apply on data.frame per column
dfmat <- as.data.frame(mat)
res <- dftse(dfmat, low_freq = 0.0625, high_freq = 0.3333)
head(res)