Add modifications from Paul Soderlind

src/HypothesisTests.jl

@@ -191,5 +191,6 @@ include("wald_wolfowitz.jl")
 include("f.jl")
 include("correlation.jl")
 include("diebold_mariano.jl")
+include("clark_west.jl")
 
 end

src/clark_west.jl

@@ -24,45 +24,53 @@
 
 export ClarkWestTest
 
-struct ClarkWestTest <: TTest
-    n::Int         # number of observations
-    xbar::Real     # estimated mean
-    df::Int        # degrees of freedom
-    t::Real        # test statistic
-    stderr::Real   # empirical standard error
-    μ0::Real       # mean under h_0
+struct ClarkWestTest <: ZTest
+    n::Int       # number of observations
+    xbar::Real   # estimated mean
+    stderr::Real # population standard error
+    z::Real      # t-statistic
+    μ0::Real     # mean under h_0
 end
 
 """
-    ClarkWestTest(e1::AbstractVector{<:Real}, e2::AbstractVector{<:Real}; lookahead::Int=1)
+    ClarkWestTest(e1::AbstractVector{<:Real}, e2::AbstractVector{<:Real};lookahead::Integer=1)
 
-Perform the Clark-West test ...
+Perform the Clark-West test of equal performance of two nested predition models, in terms of the
+out-of-sample mean squared prediction errors.
 
-# References
+`e1` is a vector of forecasts from the smaller (nested) model, `e2` is a vector of forecast
+errors from the larger model, and `lookahead` is the number of steps ahead of the forecast.
+Typically, the null hypothesis is that the two models perform equally well (a two-sided test),
+but sometimes we test whether the larger model performs better, which is indicated by a
+positive test statistic, for instance, above 1.645 for the 5% significance level (right tail test).
 
- * Clark, T. E., West, K. D. 2006, Using out-of-sample mean squared prediction errors to test 
+Implements: [`pvalue`](@ref)
+# References
+ * Clark, T. E., West, K. D. 2006, Using out-of-sample mean squared prediction errors to test
    the martingale difference hypothesis. Journal of Econometrics, 135(1): 155–186.
+ * Clark, T. E., West, K. D. 2007, Approximately normal tests for equal predictive accuracy
+   in nested models. Journal of Econometrics, 138(1): 291–311.
 
- * Clark, T. E., West, K. D. 2007, Approximately normal tests for equal predictive accuracy 
-   in nested models. Journal of Econometrics, 138(1): 291–311. 
 """
-function ClarkWestTest(e1::AbstractVector{<:Real}, e2::AbstractVector{<:Real}; 
-                        lookahead::Int=1)
-
-    @assert length(e1) == length(e2)
-    n = length(e1)
-
-
-
-    return ClarkWestTest(n, xbar, n - 1, statistic_cw, stderr, 0.0)
+function ClarkWestTest(e1::AbstractVector{<:Real}, e2::AbstractVector{<:Real};
+                       lookahead::Integer=1)
+    length(e1) == length(e2) || throw(DimensionMismatch("inputs must have the same length"))
+    n            = length(e1)
+    d            = 2*e1.*(e1 - e2)
+    cw_cov       = HypothesisTests.autocov(d, collect(0:lookahead-1))
+    cw_var       = (cw_cov[1] + 2 * sum(cw_cov[2:end]))/n
+    xbar         = mean(d)
+    stderr       = sqrt(cw_var)
+    statistic_cw = xbar/stderr
+    return ClarkWestTest(n, xbar, stderr, statistic_cw, 0.0)
 end
 
 testname(::ClarkWestTest) = "Clark West test"
-population_param_of_interest(x::ClarkWestTest) = ("Mean", 0.0, x.xbar)
+population_param_of_interest(x::ClarkWestTest) = ("Mean", x.μ0, x.xbar)
 default_tail(test::ClarkWestTest) = :both
 
 function show_params(io::IO, x::ClarkWestTest, ident)
-    println(io, ident, "number of observations: $(x.n)")
-    println(io, ident, "CW statistic:           $(x.t)")
-    println(io, ident, "degrees of freedom:     $(x.df)")
+    println(io, ident, "number of observations:    $(x.n)")
+    println(io, ident, "CW statistic:              $(x.z)")
+    println(io, ident, "population standard error: $(x.stderr)")
 end

src/z.jl

@@ -55,7 +55,7 @@ struct OneSampleZTest <: ZTest
     n::Int       # number of observations
     xbar::Real   # estimated mean
     stderr::Real # population standard error
-    z::Real      # t-statistic
+    z::Real      # z-statistic
     μ0::Real     # mean under h_0
 end
 

test/clark_west.jl

@@ -1 +1,28 @@
-# Add tests
+using HypothesisTests, Test
+
+@testset "Clark-West tests" begin
+
+    e1 = [ 9.78432,  12.73500,   8.67224,   2.62740,   5.60947,
+           7.57809,   4.53774,   2.51084,   0.49290,   3.48394,
+           9.46152,   9.41220,   2.36289,   0.34495,   3.33599,
+           5.31357,   4.28219,  -3.74471,  -5.73575,  -3.71781 ]
+
+    e2 =  [ 2.82053,   4.39754,  -1.78647,  -4.30662,   3.69526,
+            3.37259,  -1.09002,  -0.50984,  -0.78973,   3.89077,
+            7.52849,   2.82373,  -3.95838,  -0.13606,   4.54444,
+            4.18216,   1.67993,  -5.38077,  -0.85686,   2.70479 ]
+
+    atol = 1e-4
+    cw_test = ClarkWestTest(e1, e2)
+    @test pvalue(cw_test) ≈ 0.0002 atol=atol
+    @test pvalue(cw_test, tail=:right) ≈ 0.0001 atol=atol
+
+    cw_test = ClarkWestTest(e1, e2; lookahead=3)
+    @test pvalue(cw_test) ≈ 0.0157 atol=atol
+    @test pvalue(cw_test, tail=:right) ≈ 0.0079 atol=atol
+
+    show(IOBuffer(), cw_test)
+
+    @test_throws DimensionMismatch ClarkWestTest(rand(3), rand(4))
+
+end

test/runtests.jl

@@ -37,3 +37,4 @@ include("wilcoxon.jl")
 include("z.jl")
 include("f.jl")
 include("diebold_mariano.jl")
+include("clark_west.jl")