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add Baxter King filter #223

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3 changes: 2 additions & 1 deletion src/QuantEcon.jl
Original file line number Diff line number Diff line change
Expand Up @@ -147,7 +147,8 @@ export

# filter
hp_filter,
hamilton_filter
hamilton_filter,
bk_filter


include("sampler.jl")
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31 changes: 31 additions & 0 deletions src/filter.jl
Original file line number Diff line number Diff line change
Expand Up @@ -85,3 +85,34 @@ function hamilton_filter(y::AbstractVector, h::Integer)
y_trend = y - y_cycle
return y_cycle, y_trend
end

@doc doc"""
This function applies "Baxter King filter" to `y <:AbstractVector`.

Reference: https://www.mitpressjournals.org/doi/abs/10.1162/003465399558454?casa_token=pfn7A97wi0QAAAAA:78AlfSOyiz__a6_snyH7jwydLu8uGZV-U3ZVY5Vo3dTi0r7da5uuVtUyUR87-uZBAuarQAYMiywJ76o

##### Arguments
- `y::AbstractVector` : data to be filtered
- `wu::Real` : upper cutoff frequencies
- `wl::Real` : lower cutoff frequencies
- `K::Integer` : number of lead and lag of the moving average
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Should be leads and lags


##### Returns
- `y_cycle::Vector` : cyclical component
- `y_trend::Vector` : trend component
"""
function bk_filter(y::AbstractVector, wu::Real, wl::Real, K::Integer)
T = length(y)
w1 = 2pi/wu
w2 = 2pi/wl
b = vcat((w2-w1)/pi, [(sin(w2*i)-sin(w1*i))/(i*pi) for i=1:K])
theta = (b[1] + 2*sum(b[2:end]))/(2K+1)
B = b .- theta
y_cycle = Vector{Union{Missing, Float64}}(undef, T)
for t = K+1:T-K
y_cycle[t] = y[t]*B[1] +
dot(y[t-1:-1:t-K], B[2:end]) + dot(y[t+1:t+K], B[2:end])
end
y_trend = y - y_cycle
return y_cycle, y_trend
end
7 changes: 7 additions & 0 deletions test/test_filter.jl
Original file line number Diff line number Diff line change
Expand Up @@ -20,4 +20,11 @@
@test isapprox(data["ham_c"], data["ham_c_mat"], nans=true, rtol=1e-7, atol=1e-7)
@test isapprox(data["ham_rw_c"], data["ham_rw_c_mat"], nans=true)
end

@testset "test baxter king filter" begin
bk_cyc, _ = bk_filter([1,5,4,7,3,2,4,8], 24, 6, 2)
cyc_py = [missing, missing, 0.5401001384504593, 0.34785164507573785,
-0.05672021307788492, -0.887951783526198, missing, missing]
@test all((ismissing.(bk_cyc) .& ismissing.(cyc_py)).| isapprox.(bk_cyc, cyc_py))
end
end