Difference between VAR and Structural VAR and Cholesky Estimation in R

2

I'm studying the Autoregressive Vectors (VAR) method. The pet part I understand, but there is one question that intrigues me. Is there a differentiation between VAR and Structural Var? Is not the same thing? Why is this division?

Once estimated the coefficients I "recover" the true betas of the "true" VAR that would be the Structural? Is that it?

 data=structure(list(y = c(0.364282642384806, -3.01119851776461, -8.66579826331936, 
-3.65240790618631, -2.25772100857938, -1.32788331062106, -3.93453431873129, 
1.61851595577216, -0.0835810964347372, 2.95763072440725, 6.7345949418983, 
6.7746614478806, 10.04066940684, 6.27227040071725, 14.56115309833, 
15.0810480320631, 11.5063029741632, 6.80750487347931, -1.18833072016655, 
-5.79184160479651, -6.02697184281142, -0.909063160559842, 7.1570192501252, 
7.25446483355088, 4.60134038275206, 1.60503179253466, 2.58786679843029, 
3.19993398488766, 4.01612468480688, 2.39049742365532, 3.57305840142054, 
5.28113597392619, 4.6193383395236, 9.81570376258964, 7.67053263166053, 
8.7462971767163, -2.41101583519383, -5.72144301967394, -3.34962429953772, 
2.42469686950135, 6.88605537277944, 2.3304084911685, 1.64473176724599, 
2.096376463845, 3.13301905274572, 6.49356088547929, -1.86209170829409, 
0.969247579474031, 0.228136448905347, 7.3057673851306, 5.72526458055773, 
6.70822912575443, 5.79347633054322, 9.53916273996297, 7.03489385261224, 
8.83071554382293, 6.35608662968355, 7.49570813361414, 10.37816202928, 
-6.51787198449831, -9.32547734768995, -17.5503959550318, -5.77635109284904, 
-12.8389156697705, -7.84899871564035, -7.28868533949256, -2.06863126318557, 
-6.80742307126607, -2.55789582062076, 1.99805564554255, 2.93018799594101, 
-1.95382266713475, -9.38935251294901, -1.80342802394376, -3.89266430829278, 
3.91169092161552, -1.0597772435936, 5.72213942249839, 5.93973186475869, 
3.73136750684378, -2.43841298366497, -7.43642386549835, -7.55480288130688, 
-8.06420698959456, -9.23742969086161, -5.26098891655298, -0.360621818814133, 
4.27609325342668, -0.202264121414653, -0.739790826736958, -7.88395645160394, 
-11.1613743624087, -14.9077940939956, -2.72760839139119, 2.89510238654891, 
-0.0264076206382358, -6.00045133715453, -3.58206296383663, 9.90965977455895, 
9.39892106396294, 8.8500742386703, 1.03004327160894, -3.39139346236547, 
-9.45297995984866, -6.71754724732234, 1.07856171317046, 5.86275416364693, 
7.06192113166803, 3.54834901654426, 10.4151183234618, 8.42649396178409, 
1.37215941378174, -0.095908187061583, -4.14146697690086, 5.45774132871071, 
0.223119681519052, 0, -6.25895663105755, -7.34996687943651, -2.05362102615002, 
2.44037956419783, 0.75559692077275, -5.71923441693524, -12.6550626632576, 
-12.0927223707412, -7.10441235443739, -4.41694182999975, -2.46514623415841, 
-2.89484145252672, -1.07496393286225, 1.51846109153434, 9.79837511377407, 
13.1724396478228, 11.7638714073689, 7.75715439394167, 2.22971449546022, 
1.06575344772809, -7.95668538743414, -3.38527597974283, -4.96296878836012, 
-6.30387499070715, -2.63245107781988, 0.538790612129314, 7.20385490322102, 
0.785855160264248, -4.07327342173986, -9.19404535084919, -7.85306631326661, 
-8.40195847478381, 6.76518882540079, 20.6044483431751, 27.3376364755518, 
16.1950373814053, 5.05297216901036, 6.27092973657019, 0.26593751035297, 
-5.50084864000119, -9.32908406147996, 1.06569212227401, 5.53500950831649, 
4.83724572553634, -0.201759108367133, -0.215557373390085, 0.106993204250799, 
1.24439442613878, -0.823381993220523, -0.1545825094528, -0.70727210353681, 
-0.750059996605623, -1.63317292685484, -3.97351005316506, -1.94637375483417, 
-1.58806068447527, -1.83603210646961, -5.88746009143947, -1.98437987405322, 
0.667994656613069, 3.32686055849901, -1.07920100252718, -3.29642432801328, 
-1.7308231755863, -0.158526372350115, 1.77637675120452, 0.692732317051481, 
2.23096071532342, 0.694227095544098, 1.088686144766, 1.38211640569414, 
1.65885963402311, 4.6014062772581, -0.116364540323033, 1.77382780449352, 
0.305983492555839, -1.13705870323273, -1.73499737648262, -3.30793271880242, 
-0.751234198131978, -0.795139830134706, -4.53643385672045, -7.45247812161643, 
-8.97687022091052, 1.64834018202805, 3.21911768954841, 4.02245558153151, 
-1.16766371252042, -0.447267358966252, -1.21963830943122, -1.15359574347951, 
0.963862883776873, 3.25319828757088, -2.39992279960699, -4.12163514399823, 
-1.90534640281392, 2.78430274536803, 2.59174694319815, -2.03619623396279, 
-2.4324139141488, 0.88454114048393, 0.418249651921709, 2.28537908942337, 
-2.7344162155999, -1.78212198491062, -2.33222611800354, 1.65554036309925, 
2.18366538205943, 1.67446390265718, 2.81681294535392, 2.9782046488222, 
2.2858974878044, 0.0432640314403709, 2.35121048901689, -0.755634498802804, 
-0.410961681565353, -4.29551925868059, -1.33625737104313, 0.943018059528516, 
1.88295709348439, 1.49172550710409, 0.978402254843047, 1.42235310313777, 
3.91914606208345, 5.28314584575616, 5.10122307869, 3.77881596936092, 
3.07312894929215, 2.29296833894587, 3.24166264400179, 2.12263652776999, 
-1.1286952595831, -0.74105148659504, -1.55670242261214, 5.2509895915329, 
2.12250977552116, 1.80365467630413, 0.798540025499012, 0.378396196333453, 
-2.33620973303545, -4.26936625532945, -1.95877284189546, 1.77329245651049, 
1.01295182388557, 2.88936841049213, 0.888415363261474, 2.03553984999003, 
-3.1032473376593, -3.44980743173678, -6.74926487149525, -7.02400101528008, 
-5.65598277237218, -2.94091069139391, -0.0328178844786753, -0.496463722957785, 
-2.4845307388898, -5.10144588653887, -1.17648415795863, 1.91298814782697, 
2.76261110928593, -4.08423218492677, -4.57481047338545, -0.561573878563559, 
3.85578309665615, -0.548618645046983, -5.24202364693075, -8.7712809791652, 
-7.09500250779817, -7.16354480740695, -7.58114653887925, -3.08012101944444, 
2.62113229598139, 1.32855538393817, 1.50117870753859, -2.44460010581697, 
1.645267308057, 0.199188824369545, -0.887628423879772, -5.61830936031906, 
-5.74638631321538, -2.71493060161975, -0.919722903920506, 1.42866366807393, 
-1.43341008537605, 5.43387005503757, 5.20560882134319, 8.33395390226683, 
1.20868743993362, 1.31279661693897, -0.543345372299553, 3.91216412765538, 
2.91417355648912, -0.738587264937851, -1.25145426621802, -1.18610585344509, 
-2.21991097975971, -6.58033155080164, -6.12161627978961, -2.52038211449749, 
-1.54605765735112, -1.20920457650285, -2.11305387385244, -3.45676157376054, 
-4.54493164337924, -2.72383606121054, 0.406820194550239, -0.502671495145146, 
-1.9626141135178, -0.934015342005534, -1.90383524994467, -1.80417785007652, 
-1.84217313145933, -1.60993688383013, -2.00755436123629, -1.97336641569503, 
2.71333305601531, 4.33635366330811, 3.47841824109761, -0.0595474412196761, 
0.242429178426662, 0.35691662254953, -0.256458823876415, 0.206197904016014, 
8.44696514602612, 11.1597494668917, 20.3150607031918, 16.9890510156044, 
19.710190662601, 11.47069570089, 7.23973987166013, 2.20634392649682, 
-2.64193587528628, -12.3953259428904, -14.0201049207465, -12.1636347846417
), x = c(0.671625296333, 1.54362436939559, 1.637706612339, 1.32441994000243, 
1.01604845752641, 0.450073977294263, 0.357727708511124, -0.781802352417116, 
-0.558416681834029, -0.862358355802773, -0.92420724843334, -0.521845842083302, 
-0.987720816524806, -1.20932588988809, -1.18645635624453, -0.901328907176357, 
-0.982231567722991, -0.199355302490889, 0.138448308013261, 0.636346180966418, 
0.450661643970141, -0.0225548044904933, -0.248266428872879, -0.394778618956315, 
-0.271280301737598, -0.226661368767456, -0.63217522993948, -0.251566171958628, 
-0.161596187036706, -0.231086025115745, -0.116487898100992, -0.115777265178085, 
0.302560726368295, 0.503284442198426, 0.581463140124949, 0.271813325626891, 
0.291569892434995, 0.209464285290695, -0.0116547446634696, -0.0929998756175054, 
-0.0929998756175054, 0, -0.0560519563453932, -0.140034180840565, 
-0.114341624579706, -0.0583375164133093, 0.0631601445525209, 
0.0631601445525209, -0.521485682618894, -0.521485682618894, -0.545403690196244, 
0.0275554663206945, -0.25815444231907, -0.115542628336573, 0.132358246166775, 
0.130814931653456, 0.329477413812618, 0.904777891604569, 0.993942080821464, 
0.951306667035867, 0.940052106211731, 1.11748817546984, 1.10377102332677, 
0.685349270194124, 0.845665072233803, 0.785087546250263, 0.831855887220012, 
0.8012052996061, 0.903143527105632, 1.11840475449192, 1.03052017512997, 
0.890829574181562, 0.82475429197657, 0.674638508362269, 0.706102261584585, 
0.810235447979846, 0.975515717467723, 1.20210022067029, 1.26190020594807, 
1.21824510799304, 1.18957861397164, 1.16054980164135, 1.04306257943316, 
0.735010266918112, 0.544047190321395, 0.367747438098243, 0.471147816935136, 
0.558565961090451, 0.673800728969565, 0.42338404560065, 0.397525748402838, 
0.221007642370386, 0.339458602227216, 0.458315469000259, 0.589717489311226, 
0.444232978225023, 0.264646594664608, 0, 0.468940112499605, 0.583172150728983, 
0.884045705200354, 0.813294888597427, 0.829026844033853, 0.893242431394614, 
0.89552066551819, 0.849525978069554, 0.719371374343281, 0.648792850044577, 
0.691508701163168, 1.10714577668785, 1.15019617812904, 1.21912685905337, 
1.1526733298995, 1.25017983296747, 1.52982915177884, 1.56101035102276, 
1.55295688946586, 1.55295688946586, 1.56645097034289, 1.53586612545755, 
1.5063453789421, 1.54620787089574, 1.54007825926861, 1.62967544547703, 
1.61250182740058, 1.52595289543696, 1.27328906087516, 1.16965992135829, 
1.49128327465062, 1.59397543583708, 1.36885523410477, 1.43254359299754, 
1.30584614856402, 1.26137750581869, 1.19756862311013, 1.19163260058091, 
1.21560551347202, 1.09969479309346, 1.24012360054562, 1.3443687144457, 
1.61432482131922, 1.54258425387499, 1.47069283954526, 1.53128436060559, 
1.55778678747667, 1.43270877557657, 1.47022272899227, 1.65057725613533, 
1.69394488590238, 1.38909505925759, 0.976870941516861, 0.810346372709114, 
0.887606913197669, 0.740777796151049, 0.739025614446476, 0.669485168883077, 
0.710041667929695, 0.62096549544437, 0.638497995433318, 0.623627706105023, 
0.664603323635804, 0.647244150299664, 0.558380676276671, 0.469360170559008, 
0.484189932218393, 0.544736150894121, 0.34838810403941, 0.347913634790253, 
0.226913836275888, 0.149495022303858, 0.0771035141940102, 0.175635744956804, 
0.13952121706069, 0.10795317317871, 0.103016335194894, 0.0167262532817958, 
0.0428968334643898, 0.126320826825155, 0.119233510482086, 0.104903298747394, 
0.192948089362899, 0.147985149522478, 0.228896842826098, 0.252954267257532, 
0.217227450852708, 0.210043833971008, 0.19576397793204, 0.238787463084811, 
0.265400849305641, 0.218089271127875, 0.215838045453509, 0.150834884448692, 
0.134222718096022, 0.172523311939221, 0.115064314284763, 0.0791038642537156, 
0.0623574112023517, 0.100659834166139, 0.1916112050101, 0.217826804639332, 
0.267801340100138, 0.217795974670176, 0.232107002492743, 0.172133058527346, 
0.179248313581892, 0.203090870136968, 0.265007642680559, 0.336442734461029, 
0.381524614784312, 0.395748560076736, 0.383841631360671, 0.423612405429896, 
0.440627797675197, 0.453254293742722, 0.453094680381705, 0.448230401731076, 
0.424507166836263, 0.426907146120148, 0.476640585958932, 0.498037727701095, 
0.476942665732749, 0.482528092387091, 0.470999503657854, 0.352075731595369, 
0.240161173961995, 0.197282573396995, 0.0722845401141869, 0.0699075006406646, 
0.0674800219235383, 0.0698575963594017, -0.0698077751235759, 
-0.0240553435044699, -0.0528991544161528, -0.0527265468221794, 
-0.0742517747654103, -0.0430788313489305, 0.00718209121175484, 
0.0191339606234964, 0.0239140697626761, -0.0262859693310968, 
-0.0549383068898512, -0.143120606208269, -0.147932999582934, 
-0.131263214215194, -0.128917504150228, -0.174271424539474, -0.159981530407038, 
-0.152899053872435, -0.100503120432105, 0.0672639523241925, 0.144352879855036, 
0.120439932284011, 0.23663759150141, 0.292626349553182, 0.336254846059214, 
0.343919713218455, 0.351754949649985, 0.460556759198494, 0.484015847681718, 
0.462435125264249, 0.528712214420035, 0.54582737300608, 0.516378803893391, 
0.523130015801399, 0.523663764846205, 0.555213723499692, 0.550562369001661, 
0.536310019680952, 0.53125692529401, 0.516906458536215, 0.54885555461972, 
0.625160455330387, 0.647439423732399, 0.642722185908751, 0.572099989362984, 
0.572309532363779, 0.577433865176014, 0.574829104329644, 0.61201578539376, 
0.578027092344491, 0.607055170248993, 0.631309993890783, 0.682374746574221, 
0.694572432932494, 0.711623963488339, 0.743391358088519, 0.760372451745628, 
0.791828203288558, 0.808665511872642, 0.824887421286946, 0.789119657006543, 
0.800666819103091, 0.761329340072603, 0.702301400571259, 0.65565627540678, 
0.587022205406029, 0.554933314094663, 0.496193509312626, 0.493244032977458, 
0.459027073945895, 0.400649464751801, 0.364081464600519, 0.276620807224148, 
0.213485125927249, 0.155228070943125, 0.12600474375335, 0.0774744403384764, 
0.0411331593390019, 0.00241838186072485, -0.038676077753963, 
-0.0749214961585754, -0.0941818394463834, -0.120655288927085, 
-0.139890142367616, -0.18792686902207, -0.161441523742845, -0.101140632222996, 
-0.0698276936663467, -0.0481312703893844, -0.0288746419627062, 
-0.0192456456412193, 0.0504748803139776, 0.0432749603021199, 
0.0600848726248548, 0.0913127989197404, 0.103257880472096, 0.139184199696207, 
0.155965744721209, 0.232057753060966, 0.222945705805788, 0.319472349384209, 
0.325856390275758, 0.30325094021737, 0.603365168302283, 0.66373349138964, 
0.733382376322766, 0.653902164789777, 0.70224234139129, 0.70922716638433, 
0.675627721409811, 0.668626716233645, 0.105881327426416, 0.67189531493923, 
0.0632207499327464, 0.22422131555937, 0.158071829703332, 0.0815086649976315, 
0.0817077392039289, -0.0272661869347379, 0.0870207950156132, 
0.0223601164017095, -0.0049798452207872)), .Names = c("y", "x"
), row.names = 4:355, class = "data.frame", na.action = structure(c(1L, 
2L, 3L, 356L, 357L, 358L), .Names = c("1", "2", "3", "356", "357", 
"358"), class = "omit"))

Now roll the VAR:

p1ct.y<- VAR(data, p = 1, type = "both") 
plot(irf(p1ct.y, impulse = "x", ci = 0.95, n.ahead = 30, response = c("y"), boot = FALSE))

My second doubt is if this result of the impulse response function already considers the decomposition of Cholesky? Otherwise, how do I have an impulse response function that takes into account cholesky decomposition?

    
asked by anonymous 12.06.2017 / 15:34

0 answers