
@testset "White's covariance estimators" begin
    # using data from Nerlove Cobb-Douglas model from https://github.com/mcreel/Econometrics/blob/master/Examples/Data/nerlove.csv
    cost = [0.082, 0.661, 0.99, 0.315, 0.197, 0.098, 0.949, 0.675, 0.525, 0.501, 1.194, 0.67, 0.349, 0.423, 0.501, 0.55, 0.795, 0.664, 0.705, 0.903, 1.504, 1.615, 1.127, 0.718, 2.414, 1.13, 0.992, 1.554, 1.225, 1.565, 1.936, 3.154, 2.599, 3.298, 2.441, 2.031, 4.666, 1.834, 2.072, 2.039, 3.398, 3.083, 2.344, 2.382, 2.657, 1.705, 3.23, 5.049, 3.814, 4.58, 4.358, 4.714, 4.357, 3.919, 3.442, 4.898, 3.584, 5.535, 4.406, 4.289, 6.731, 6.895, 5.112, 5.141, 5.72, 4.691, 6.832, 4.813, 6.754, 5.127, 6.388, 4.509, 7.185, 6.8, 7.743, 7.968, 8.858, 8.588, 6.449, 8.488, 8.877, 10.274, 6.024, 8.258, 13.376, 10.69, 8.308, 6.082, 9.284, 10.879, 8.477, 6.877, 15.106, 8.031, 8.082, 10.866, 8.596, 8.673, 15.437, 8.211, 11.982, 16.674, 12.62, 12.905, 11.615, 9.321, 12.962, 16.932, 9.648, 18.35, 17.333, 12.015, 11.32, 22.337, 19.035, 12.205, 17.078, 25.528, 24.021, 32.197, 26.652, 20.164, 14.132, 21.41, 23.244, 29.845, 32.318, 21.988, 35.229, 17.467, 22.828, 33.154, 32.228, 34.168, 40.594, 33.354, 64.542, 41.238, 47.993, 69.878, 44.894, 67.12, 73.05, 139.422, 119.939]
    output = [2, 3, 4, 4, 5, 9, 11, 13, 13, 22, 25, 25, 35, 39, 43, 63, 68, 81, 84, 73, 99, 101, 119, 120, 122, 130, 138, 149, 196, 197, 209, 214, 220, 234, 235, 253, 279, 290, 290, 295, 299, 324, 333, 338, 353, 353, 416, 420, 456, 484, 516, 550, 563, 566, 592, 671, 696, 719, 742, 795, 800, 808, 811, 855, 860, 909, 913, 924, 984, 991, 1000, 1098, 1109, 1118, 1122, 1137, 1156, 1166, 1170, 1215, 1279, 1291, 1290, 1331, 1373, 1420, 1474, 1497, 1545, 1649, 1668, 1782, 1831, 1833, 1838, 1787, 1918, 1930, 2028, 2057, 2084, 2226, 2304, 2341, 2353, 2367, 2451, 2457, 2507, 2530, 2576, 2607, 2870, 2993, 3202, 3286, 3312, 3498, 3538, 3794, 3841, 4014, 4217, 4305, 4494, 4764, 5277, 5283, 5668, 5681, 5819, 6000, 6119, 6136, 7193, 7886, 8419, 8642, 8787, 9484, 9956, 11477, 11796, 14359, 16719]
    labor = [2.09, 2.05, 2.05, 1.83, 2.12, 2.12, 1.98, 2.05, 2.19, 1.72, 2.09, 1.68, 1.81, 2.3, 1.75, 1.76, 1.98, 2.29, 2.19, 1.75, 2.2, 1.66, 1.92, 1.77, 2.09, 1.82, 1.8, 1.92, 1.92, 2.19, 1.92, 1.52, 1.92, 2.2, 2.11, 1.92, 2.05, 1.66, 1.8, 1.77, 1.7, 2.05, 2.19, 1.85, 2.19, 2.13, 1.54, 1.52, 2.09, 1.75, 2.3, 2.05, 2.32, 2.31, 1.92, 2.05, 1.76, 1.7, 2.04, 2.24, 1.7, 1.68, 2.29, 2.0, 2.31, 1.45, 1.7, 1.76, 1.7, 2.09, 1.55, 2.11, 2.05, 2.3, 2.19, 2.04, 2.31, 1.7, 2.05, 2.19, 2.0, 2.32, 1.55, 2.13, 2.2, 2.2, 1.85, 1.76, 1.8, 2.32, 1.8, 2.13, 1.98, 1.76, 1.45, 2.24, 1.69, 1.81, 2.11, 1.76, 1.77, 2.0, 2.3, 2.04, 1.69, 1.76, 2.04, 2.2, 1.76, 2.31, 1.92, 1.76, 1.76, 2.31, 2.3, 1.61, 1.68, 2.09, 2.09, 2.05, 2.29, 2.11, 1.53, 2.11, 2.04, 2.19, 1.92, 2.04, 2.11, 1.76, 1.79, 2.11, 1.54, 1.92, 2.12, 1.61, 2.32, 2.24, 2.31, 2.11, 1.68, 2.24, 2.12, 2.31, 2.3]
    fuel = [17.9, 35.1, 35.1, 32.2, 28.6, 28.6, 35.5, 35.1, 29.1, 15.0, 17.9, 39.7, 22.6, 23.6, 42.8, 10.3, 35.5, 28.5, 29.1, 42.8, 36.2, 33.4, 22.5, 21.3, 17.9, 38.9, 20.2, 22.5, 29.1, 29.1, 22.5, 27.5, 22.5, 36.2, 24.4, 22.5, 35.1, 33.4, 20.2, 21.3, 26.9, 35.1, 29.1, 24.6, 29.1, 10.7, 26.2, 27.5, 30.0, 42.8, 23.6, 35.1, 31.9, 33.5, 22.5, 35.1, 10.3, 26.9, 20.7, 26.5, 26.9, 39.7, 28.5, 34.3, 33.5, 17.6, 26.9, 10.3, 26.9, 30.0, 28.2, 24.4, 35.1, 23.6, 29.1, 20.7, 33.5, 26.9, 35.1, 29.1, 34.3, 31.9, 28.2, 30.0, 36.2, 36.2, 24.6, 10.3, 20.2, 31.9, 20.2, 10.7, 35.5, 10.3, 17.6, 26.5, 12.9, 22.6, 24.4, 10.3, 21.3, 34.3, 23.6, 20.7, 12.9, 10.3, 20.7, 36.2, 10.3, 33.5, 22.5, 10.3, 10.3, 33.5, 23.6, 17.8, 28.8, 30.0, 30.0, 35.1, 28.5, 24.4, 18.1, 24.4, 20.7, 29.1, 29.1, 20.7, 24.4, 10.3, 18.5, 24.4, 26.2, 22.5, 28.6, 17.8, 31.9, 26.5, 33.5, 24.4, 28.8, 26.5, 28.6, 33.5, 23.6]
    capital = [183, 174, 171, 166, 233, 195, 206, 150, 155, 188, 170, 167, 213, 164, 170, 161, 210, 158, 156, 176, 170, 192, 164, 175, 180, 176, 202, 227, 186, 183, 169, 168, 164, 164, 170, 158, 177, 195, 176, 188, 187, 152, 157, 163, 143, 167, 217, 144, 178, 176, 167, 158, 162, 198, 164, 164, 161, 174, 157, 185, 157, 203, 178, 183, 168, 196, 166, 172, 158, 174, 225, 168, 177, 161, 162, 158, 176, 183, 166, 164, 207, 175, 225, 178, 157, 138, 163, 168, 158, 177, 170, 183, 162, 177, 196, 164, 158, 157, 163, 161, 156, 217, 161, 183, 167, 161, 163, 170, 174, 197, 162, 155, 167, 176, 170, 183, 190, 170, 176, 159, 157, 161, 172, 203, 167, 195, 161, 159, 177, 157, 196, 183, 189, 160, 162, 178, 199, 182, 190, 165, 203, 151, 148, 212, 162]
    ndf = DataFrame(cost=cost, output=output, labor=labor, fuel=fuel, capital=capital)

    f = @formula(log(cost) ~ 1 + log(output) + log(labor) + log(fuel) + log(capital))
    lr2 = regress(f, ndf, cov=[:hc0, :hc1, :hc2, :hc3, :nw])

    @test [:hc0, :hc1, :hc2, :hc3] == lr2.white_types
    @test [:nw] == lr2.hac_types

    @test isapprox([1.6887096637865764, 0.03203057017940859, 0.2413635423569017, 0.07416986820706634, 0.3181801843194431], lr2.white_stderrors[1])
    @test isapprox([-2.088282503859893, 22.490828975090466, 1.807817355217008, 5.750542145660426, -0.6910812225036552], first(lr2.white_t_values))
    @test isapprox([0.03858351163194079, 2.515671235586196e-48, 0.07278163877804528, 5.358556751845478e-8, 0.4906588080040115], lr2.white_p_values[1])

    @test isapprox([1.718600650948449, 0.03259752694088162, 0.24563579513121173, 0.07548271115809448, 0.3238121292347976], lr2.white_stderrors[2])
    @test isapprox([-2.0519617765991467, 22.099654283167162, 1.7763746548274086, 5.650525087387196, -0.6790615017279884], lr2.white_t_values[2])
    @test isapprox([0.04203687115328462, 1.7165028470144865e-47, 0.07784320772633291, 8.6256319578862e-8, 0.49821998002922296], lr2.white_p_values[2])

    @test isapprox([1.7404789466388655, 0.033024377914589426, 0.24759483158894688, 0.07606559302904324, 0.327665011037017], lr2.white_stderrors[3])
    @test isapprox([-2.0261680566690297, 21.814008964615727, 1.762319503962301, 5.607225765004714, -0.6710766891466415], lr2.white_t_values[3])
    @test isapprox([0.04464696168598006, 7.061145309349196e-47, 0.0801976916093005, 1.0583954671852304e-7, 0.5032773613193346], lr2.white_p_values[3])

    @test isapprox([1.794226207499838, 0.03405163218075088, 0.25404375612619956, 0.07802173599290865, 0.3375082813724026], lr2.white_stderrors[4])
    @test isapprox([-1.96547282067551, 21.155933790655254, 1.717582858335255, 5.466642694307393, -0.6515050530368971], lr2.white_t_values[4])
    @test isapprox([0.05133862483580867, 1.909213828296015e-45, 0.08808381706940926, 2.0436000920232382e-7, 0.5157885588309656], lr2.white_p_values[4])

    @test isapprox([1.5413337169817793, 0.04558343812215214, 0.250278670841928, 0.07289639728036612, 0.2651138982712092], lr2.hac_stderrors[1])
    @test isapprox([-2.287955428555851, 15.803855644877787, 1.7434214402754615, 5.851001818682364, -0.8294108765696443], lr2.hac_t_values[1])
    @test isapprox([0.02363824106367065, 6.252423796307023e-33, 0.08345530926614206, 3.306228013288088e-8, 0.4082838999795607], first(lr2.hac_p_values))

end

@testset "Newey-West covariance estimators" begin
    # using Data from https://raw.githubusercontent.com/mcreel/Econometrics/master/Examples/Data/sp500.csv
    # based on the Econometrics code from https://github.com/mcreel/Econometrics/blob/master/Examples/TimeSeries/SP500.jl

    y = [0.002583702575676502, 0.3079890371414663, 0.2218233792549798, 0.07975000051131587, 0.22310573843696402, 0.0016145767310154937, 0.00021506066259480462, 0.1347348238545566, 0.7244128703617047, 0.0011828566361204594, 0.07002289701258912, 0.37366185926285417, 0.0007702828176743898, 0.002139278700879984, 0.053836464007526154, 1.650675513088037, 1.16748122425437, 0.27856093459188397, 0.019058258961000864, 0.16136521150410382, 0.08224579148911378, 0.004024360208805437, 0.7653817220257503, 4.4510953200179815, 0.25957822569124633, 0.37137008090011087, 1.0357988095863304, 1.2389842387287384, 0.4324607874947091, 5.269593589329902, 0.5621803938941623, 0.03477934257291081, 1.4619965090681062, 1.7365164047084427, 0.028582510379680535, 1.1864719119647948, 0.00017403544878260159, 0.32998873142007473, 0.23548033193902543, 0.019210839894924763, 0.4530222091064397, 0.36620714829237433, 0.033215060313819496, 0.36313208130177793, 0.01484899619985411, 4.698840747702183e-6, 0.22943861446916383, 0.0693734390306599, 0.5194246266697191, 2.254208363566848, 0.000711991818247004, 0.03227740032396568, 0.0002067872176035323, 0.0008581956571378268, 0.25524877190609313, 0.0006603091802297528, 1.362499153127377, 0.08577309821496772, 0.8919014915087333, 0.5230148340571447, 0.3562150939685192, 0.3562150939685192, 0.1096908647583281, 0.20407089519132424, 0.1968720725392859, 0.48739080592383005, 0.04061200146027687, 0.20350016132170584, 0.6452477732061614, 0.4935279378347359, 0.08269231898382176, 0.010974942559581268, 1.6116941048352218, 1.1928108856953, 0.15213049376092777, 1.1501296327247874, 4.425046102227064, 0.8991160278122725, 0.6456958173927121, 0.4580013476284833, 1.0730853116158547, 0.02257630017653147, 0.12632124277322926, 0.19019934287306395, 0.05196206322855161, 0.02692636386162153, 0.635005506129145, 0.0972247251099256, 0.22760365264589139, 0.07938909838989823, 0.00028864197438840976, 0.014932056591780294, 0.03840574490115696, 0.8190214201900288, 0.30950765751926473, 0.01831369772284331, 0.021621005780058804, 0.9430252521456538, 0.0012103784072304167, 0.22155472706333956, 0.8627598292464865, 0.1347165223919831, 0.13961685134675358, 0.396375900478387, 0.6152459263002183, 0.061040907672904716, 0.17837935923383433, 0.3582749524196826, 0.011621160871505566, 0.2727183192294628, 0.03317357438251278, 0.005996550580435087, 0.0012854244709616827, 0.03435859450068371, 0.4084641127852834, 0.2156258703166822, 0.009693582456685656, 0.00017760650614569273, 0.11942646862758109, 0.5276094841987697, 0.09066065784318494, 0.009929957262853248, 0.052145347173973046, 0.5724172922392592, 0.014649269664895301, 0.03913792721866548, 0.0013455493423829188, 0.3953058983299156, 0.22439797677280424, 0.01227838224650002, 0.03605488081864467, 0.001879662186147144, 0.4409922694618947, 0.003946687216989506, 0.3092252935097444, 0.15935751264549847, 0.47063574021947513, 0.1922336294839871, 0.16143647680511083, 0.017894712219287973, 0.24489610764512534, 0.03229765751935813, 0.15918992781905314, 1.436885125027776, 1.0319324805303918, 0.04264171592814084, 0.2528556838239409, 0.033424334783545964, 0.0004900776090921828, 0.23388375032149153, 0.0009505823861797834, 0.1835680041079445, 5.796064815787655e-5, 4.0806986460067876, 0.08346313295260399, 0.5272289742049457, 0.9931513138005919, 1.0850581417353803e-6, 0.30014196696728745, 1.2968901911493473, 0.078242727820577, 0.02386976812780534, 0.4251328893584252, 0.1979793262794858, 2.6160527648452464e-7, 0.6926779466296006, 0.25803324018763996, 0.062248616253323265, 0.08765575761459778, 0.04120106917205882, 0.25067625966553186, 0.008562886172120192, 0.00022500000084360892, 0.020053628341366012, 0.1011039485999002, 0.004543950646515702, 0.004090312768752987, 0.024199736620066938, 0.23609140197946205, 0.08782228599374417, 0.4200776046483452, 0.1309926797100626, 0.006665392855877088, 0.34397553423331073, 0.006744069891373599, 0.5680539834354023, 0.015620473802026125, 0.24491747714212983, 0.0021386494864975964, 0.6407900944133236, 0.3431802914429819, 0.6204188359136701, 2.63173564256491, 0.6698705449027024, 0.054904693752213116, 0.06797321779763552, 1.767005817528848, 0.0011152537338764798, 1.2128283813183613, 0.0184390507113931, 2.3766787146086807, 3.0079507122335087, 4.258404245487947, 1.3115650352289032, 2.8165805348731867, 0.025905717699369488, 0.664907800923179, 0.0011444411916685549, 1.7241447201716487, 0.8370970621184224, 3.7284109849477085, 0.5113090444749049, 1.4257963182829891, 0.5167011440300261, 0.02526566428379101, 1.3757506587868202, 0.012755883561513673, 0.37649443520629744, 1.3193112989834972, 4.815314748655017e-5, 0.06997476757293467, 0.2934423572024434, 0.14542305380085527, 0.0015900672702848092, 0.10233979942471935, 0.005630546906068476, 0.006469621166966418, 0.002964489964671273, 0.0006010368661893317, 0.005049890932956196, 0.2841651168698957, 0.03239227448552545, 0.0437699743603815, 0.25004113429080693, 0.09896237374382906, 0.008348297582788964, 0.06578790089468022, 0.06653433188654503, 0.4642751904757431, 0.39519374748374775, 0.13476408975837945, 0.014546447433743066, 0.03048312954732133, 0.4971181043026032, 0.0018662766285030344, 2.6278158118829213, 0.1835022400764073, 2.47514809706536, 0.4902999631428375, 0.6470801794417882, 3.786416800758203, 5.710830088843509, 0.20926417831010427, 0.1581341399810609, 0.027658022936031913, 0.00026667083846736194, 0.1238659117684014, 0.0063843628083706545, 0.2568548171899579, 1.0711977658880973, 0.0013630664009920536, 3.30352005277502, 0.879937452995484, 1.3685169188596928, 3.1345899818323706, 0.6720940644275492, 0.6578195141762373, 0.07532735309925823, 0.34805685820061716, 0.842015572726283, 1.7087250120723894, 0.029488252214740676, 0.24182332479734264, 2.284138680208943, 0.31894040973928284, 0.061151112591218436, 1.7538966941844074, 1.8268492450043812, 0.8870968872656356, 1.6888231118637285, 1.6087801518278428, 2.019083717365777, 0.1684290942528512, 1.0410453692042765, 0.10908074809402096, 0.1908436042909946, 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0.0023378035023157266, 0.6465288454659239, 0.04200635699421544]

    df = DataFrame(y=y, x1=x1, x2=x2)
    f = @formula(y ~ x1 + x2)
    lr2 = regress(f, df, cov="nw")
    
    @test isapprox(0.14294512360920375, lr2.R2)
    @test isapprox(0.141222400239574, lr2.ADJR2)
    @test [] == lr2.white_types
    @test [:nw] == lr2.hac_types
    @test isapprox([0.04903317561314946, 0.06022964615347672, 0.07414158887070771], lr2.hac_stderrors[1])
    @test isapprox([6.306088088824664, 4.169867149620186, 2.8751798612414263], lr2.hac_t_values[1])
    @test isapprox([4.296835456090843e-10, 3.313459203977476e-5, 0.004124044653585188], lr2.hac_p_values[1])
    @test isapprox([0.2129872220097398, 0.13295791474690624, 0.06767857989564119], lr2.hac_ci_low[1])
    @test isapprox([0.40542782737291977, 0.3693413311103545, 0.35866222650735935], lr2.hac_ci_up[1])

end

