Computes the trend and cyclical component of a macroeconomic time series using the Baxter-King fixed length symmetric filter.

## Syntax

**NxBK**(

**X**,

**Order**,

**P**,

**Q**,

**K**,

**Drift**,

**Unit-Root**,

**RetType**)

- X
- is the univariate time series data (a one dimensional array of cells (e.g. rows or columns)).
- Order
- is the time order in the data series (i.e. the first data point's corresponding date (earliest date = 1 (default), latest date = 0)).
Order Description 1 ascending (the first data point corresponds to the earliest date) (default) 0 descending (the first data point corresponds to the latest date) - P
- is the number of periods for the high pass filter (e.g. 6 for quarterly data, 18 for monthly data).
- Q
- is the number of periods for the low pass filter (e.g. 32 for quarterly data, 96 for monthly data).
- K
- is the number of points to use in the approximate optimal filter. If missing, a default value of 12 is assumed.
- Drift
- is a logical value: FALSE if there is no drift in the time series (default), TRUE if a drift exists in the time series.
- Unit-Root
- is a logical value: FALSE if there is no unit-root in the time series (default), TRUE if a unit-root exists in the time series.
- RetType
- is the integer enumeration for the filter output: (1 = trend component (default), 2 = cyclical component, 3 = noise component).

## Remarks

- The time series is homogeneous or equally spaced.
- The time series may include missing values (e.g. #N/A) at either end.
- The first and last K data points will not be filtered and are hence replaced by #N/A in the output time series as their values are not reliable.
- The recommended values of P and Q are 6 and 32/40 for quarterly data, or 18 and 96/120 for monthly data.
- Setting Q=P produces a single bandpass filter and the cyclical component will be 0.
- The noise component is simply the original data minus the trend and cyclical component.
- Proper seasonal adjustment should be carried out prior to BK filtering.

## Files Examples

## References

- Marianne Baxter, Robert G. King (1999). "Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series". The Review of Economics and Statistics 81 (4): 575–593.
- Hodrick, R., Prescott, E. (1997): "Postwar U.S. Business Cycles: An Empirical Investigation", Journal of Money, Credit, and Banking, 29(1), pp. 1-16.
- Beveridge, S., Nelson, C. R. (1981): "A New Approach to Decomposition of Economic Time Series into Permanent and Transitory Components with Particular Attention to Measurement of the Business Cycle", Journal of Monetary Economics, No. 7, pp. 151-174

## Comments

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