Package 'corbouli'

Corbae-Ouliaris

Description

Corbae-Ouliaris (2006) Frequency Domain Filter

Usage

corbae_ouliaris(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 the filtering algorithm. low_freq and high_freq are connected with characteristics of the series, for example the business circle. low_freq and high_freq must be both 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, filtering per column is applied.

Value

Filtered object with the same length/dimensions and class as the input x.

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. doi:10.1017/CBO9781139164863.008.

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

See Also

dftse

Examples

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

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

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

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

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Remove irrelevant frequencies

Description

Remove irrelevant frequencies

Usage

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.

Value

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. doi:10.1017/CBO9781139164863.008.

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

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USgdp

Description

Quarterly US GDP in billions of chained 2017 dollars (Seasonally adjusted) series from 1947.1 to 2019.4.

number of observations : 292

observation : country

country : United States

Usage

data(USgdp)

Format

A monthly time series, in billions of chained 2017 dollars.

Value

A ts object.

Source

Bureau of Economic Analysis.

References

U.S. Bureau of Economic Analysis. (2024). Current-dollar and “real” GDP. Retrieved from BEA website. https://www.bea.gov/

Examples

# Apply on vector
data(USgdp)
USgdp

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