`bwf` (Series)

Conditonal Butterworth filter

Syntax

[T, C, CutOff, Lambda] = bwf(X, Order, ~Range, ...)

Syntax with output arguments swapped

[T, C, CutOff, Lambda] = bwf2(X, Order, ~Range, ...)

Input arguments marked with a ~ sign may be omitted.

Input arguments

X [ tseries ]

Input tseries object that will be filtered.

Order [ numeric ]

Order of the Butterworth filter; Order=2 reproduces the Hodrick-Prescott filter hpf, and Order=1 reproduces the local linear filter llf.

~Range [ numeric | char | *@all]

Date range on which the input data will be filtered; Range can be @all, Inf, [startdata, Inf], or [-Inf, enddate]; if omitted, @all (i.e. the entire available range of the input series) is used.

Output arguments

T [ tseries ]

Lower-frequency (trend) component.

C [ tseries ]

Higher-frequency (cyclical) component.

CutOff [ numeric ]

Cut-off periodicity; periodicities above the cut-off are attributed to trends, periodicities below the cut-off are attributed to gaps.

Lambda [ numeric ]

Smoothing parameter actually used; this output argument is useful when the option 'CutOff=' is used instead of 'Lambda='.

Options

'CutOff=' [ numeric | empty ]

Cut-off periodicity in periods (depending on the time series frequency); this option can be specified instead of 'Lambda='; the smoothing parameter will be then determined based on the cut-off periodicity.

'CutOffYear=' [ numeric | empty ]

Cut-off periodicity in years; this option can be specified instead of 'Lambda='; the smoothing parameter will be then determined based on the cut-off periodicity. 'infoSet=' [ 1 | 2 ] - Information set assumption used in the filter: 1 runs a one-sided filter, 2 runs a two-sided filter.

'Lambda=' [ numeric | @auto ]

Smoothing parameter; needs to be specified for tseries objects with indeterminate frequency. See Description for default values.

'level=' [ tseries ]

Time series with soft and hard tunes on the level of the trend.

'change=' [ tseries ]

Time series with soft and hard tunes on the change in the trend.

'log=' [ true | false ]

Logarithmise the data before filtering, de-logarithmise afterwards.

Description

Default smoothing parameters

If the user does not specify the smoothing parameter using the 'lambda=' option (or reassigns the default @auto), a default value is used. The default value is based on common practice and can be calculated using the date frequency of the input time series as \(\lambda = (10 \cdot f)^n\), where \(f\) is the frequency (yearly=1, half-yearly=2, quarterly=4, bi-monthly=6, monthly=12), and \(n\) is the order of the filter, determined by the input parameter Order.

bwf (Series)