Forecast with external regressors

[larry77]

First of all thanks for the great work.
It is not really an issue, but I see no possibility to open a discussion for this repo.
I deal with tabular data, in which one column is the variable I want to forecast, one is time, and several others are regressors which can be used to forecast my target variable.
See the reprex

library(tidyverse)


df <- structure(list(close = c(98.7105966925097, 96.2313346349953, 
98.6915690132989, 99.3951329324309, 98.5859745284845, 97.8071009923145, 
91.565816396672, 92.6475989269169, 94.735932953575, 106.983251925824, 
108.331852833761, 104.615419129126, 100.47561734456, 99.1315346651836, 
101.292054275768, 100.01154733467, 101.627999220702, 100.151479501293, 
99.47760478488, 99.8658179766848, 102.965624040528, 102.896699482559, 
112.113906703026, 118.968287428173, 112.426801775758, 111.361039489823, 
109.055895087784, 116.047494171261, 110.285743012413, 102.590279428283, 
104.047233895186, 102.772634452626, 99.3637851897572, 94.8988263559279, 
98.9528066613749, 96.5929146730194, 106.842683676146, 109.765531325619, 
102.936178255801, 105.992990037411, 99.3925649165122, 101.864474841856, 
103.500622756726, 101.173924064775, 96.8108390013624, 96.8582450247056, 
97.2289229372089, 96.5329475478178, 91.5005984071088, 89.4957050864705, 
89.9167852138967, 88.7731705433919, 91.3745411637118, 91.5933893767575, 
91.1491292394452, 93.6712899141147, 93.0073013569139, 85.9607458940066, 
83.8172894709377, 85.8137179385217, 85.6388367460616, 83.2797820104441, 
84.0156182402559, 84.505546045446, 84.0764774803294, 85.2275037567696, 
87.6027909062803, 88.4192473141954, 87.245588696847, 90.9265375176967, 
89.6315058239105, 91.0971770411269, 92.4200794025985, 94.7119257533165, 
93.7882580768199, 94.5551728167723, 96.5369483987356, 93.8815811566226, 
91.756159067423, 91.8551842969357, 94.8487091619709, 101.333185608745, 
100.340869525256, 102.750139860581, 104.874300780072, 104.497152342614, 
105.769481998912, 110.529852059369, 116.479797090716, 112.579313133667, 
114.273868837842), timestamp = structure(c(19696, 19697, 19698, 
19699, 19700, 19701, 19702, 19703, 19704, 19705, 19706, 19707, 
19708, 19709, 19710, 19711, 19712, 19713, 19714, 19715, 19716, 
19717, 19718, 19719, 19720, 19721, 19722, 19723, 19724, 19725, 
19726, 19727, 19728, 19729, 19730, 19731, 19732, 19733, 19734, 
19735, 19736, 19737, 19738, 19739, 19740, 19741, 19742, 19743, 
19744, 19745, 19746, 19747, 19748, 19749, 19750, 19751, 19752, 
19753, 19754, 19755, 19756, 19757, 19758, 19759, 19760, 19761, 
19762, 19763, 19764, 19765, 19766, 19767, 19768, 19769, 19770, 
19771, 19772, 19773, 19774, 19775, 19776, 19777, 19778, 19779, 
19780, 19781, 19782, 19783, 19784, 19785, 19786), class = "Date"), 
    high = c(0.352306070435904, 0.343960286860067, 0.330338595619463, 
    0.355199211944317, 0.440711428595164, 0.335627155803961, 
    0.300230447818673, 0.192545203456709, 0.231956718992288, 
    0.502508802060596, 0.740313121891548, 0.54224143242119, 0.455508365822704, 
    0.35905507583232, 0.505329582760521, 0.463287140384535, 0.383706922927321, 
    0.39541770943297, 0.381831587686781, 0.408271400787283, 0.451965765849236, 
    0.538263007436815, 0.631055972282448, 1, 0.804399694507166, 
    0.724983817219173, 0.749153185607335, 0.702785653127371, 
    0.781352347438019, 0.631929453514064, 0.462800122880898, 
    0.4915971828621, 0.411625182158456, 0.34886210335265, 0.331908220992048, 
    0.322541343747161, 0.558194561975725, 0.737959474287956, 
    0.64483930459665, 0.510297627578978, 0.477241750857009, 0.411741292430683, 
    0.578244590868104, 0.431546578674618, 0.374720907601149, 
    0.288374310582173, 0.304494062853583, 0.307449574451309, 
    0.272360357883913, 0.190787354296709, 0.127859454375021, 
    0.113105725374509, 0.151458082354723, 0.162230095857774, 
    0.19189961316316, 0.202264501831234, 0.235805508804232, 0.187241529166515, 
    0.0237082690238707, 0.0332835042265203, 0.0412381502352202, 
    0.0170491358105322, 0.0196845935762706, 0.00938026307996611, 
    0, 0.0386374998358764, 0.111082382913813, 0.0970959013401806, 
    0.108982640796354, 0.137244675586748, 0.143604183963041, 
    0.167840258991487, 0.191308586707997, 0.226490163521036, 
    0.221533844980917, 0.235325800671845, 0.293893043378147, 
    0.271491837674815, 0.209188639820317, 0.199647796013205, 
    0.362529953709619, 0.426214727255178, 0.376352320951623, 
    0.42386799432496, 0.468383563702033, 0.530646474411194, 0.665576136856392, 
    0.578257709894461, 0.7553181544524, 0.759096486168192, 0.684781579536105
    ), low = c(0.45858396806302, 0.469284848124347, 0.443550087220062, 
    0.483564197228645, 0.539104347011376, 0.472529287223802, 
    0.216925559416082, 0.29210020159954, 0.233783562743155, 0.405555965826375, 
    0.740256634199207, 0.726895997096313, 0.60966827905517, 0.403246852678162, 
    0.564542350366974, 0.590775861280328, 0.566317254163334, 
    0.551287206482594, 0.464820887767494, 0.556031626548357, 
    0.556677819332186, 0.564521246499625, 0.585518166046488, 
    1, 0.910207962439877, 0.97042715655205, 0.893006085085746, 
    0.869388757969728, 0.918707830044984, 0.520380549039816, 
    0.654013145357308, 0.600772715625083, 0.524452512778796, 
    0.409691919018865, 0.241137962641686, 0.361388930561609, 
    0.48100712982143, 0.818767037337344, 0.620498754392236, 0.635221043669664, 
    0.579274395310652, 0.58057383589616, 0.66016110324248, 0.60524654222526, 
    0.466122448927825, 0.340205777030698, 0.475063764895461, 
    0.486561452014005, 0.300815458528376, 0.0873136359363124, 
    0.221609793250299, 0.172832173522275, 0.192586533638999, 
    0.286447149319718, 0.280267461703868, 0.287571612230239, 
    0.34955692929012, 0.114298193373348, 0.0409676225695692, 
    0.0221472347699477, 0.108392747304312, 0.0462507071691563, 
    0, 0.0283024084183465, 0.0238334502605286, 0.0770268148160704, 
    0.114499922914884, 0.151850409209552, 0.166581476139377, 
    0.116356773610944, 0.217816024143794, 0.245011145518355, 
    0.282494063359999, 0.299258201773672, 0.319285333671058, 
    0.361322007937186, 0.416190755688001, 0.28903713737305, 0.21580436737515, 
    0.277105053806835, 0.258277529018039, 0.400878244030552, 
    0.526683749666599, 0.540620506967557, 0.639224149627102, 
    0.569263590212304, 0.709925066618501, 0.789229636936498, 
    0.940556939928069, 0.896262248987389, 0.942891261607773), 
    volume = c(0.159178797708374, 0.136023797700209, 0.115901921738471, 
    0.183756019721396, 0.268328302405094, 0.120714661896529, 
    0.194068543034191, 0.108110528429093, 0.126387373481916, 
    0.275837773468005, 0.716494784785395, 0.24185452060395, 0.144240130669764, 
    0.181660565830457, 0.231759288013477, 0.166326907640566, 
    0.191302384810517, 0.173457689054994, 0.194074622332925, 
    0.263795887689011, 0.283834675630238, 0.433613681435888, 
    0.417431015437204, 1, 0.358425292675841, 0.241929980819696, 
    0.26602599142848, 0.146518094634308, 0.299995687664107, 0.393466765612925, 
    0.210436650801066, 0.24400551108784, 0.165356455267928, 0.0779146091840286, 
    0.195383264726355, 0.143095283953021, 0.333093050844963, 
    0.397065838487603, 0.243307861440161, 0.123478479100369, 
    0.0810471412350938, 0.0983113003728025, 0.245330786986372, 
    0.0994140845324473, 0.0970620865461924, 0.115908527402224, 
    0.0581015797440973, 0.0348237093309171, 0.0747365020426526, 
    0.114491336090179, 0.0482984633087547, 0.0230381150837757, 
    0.0413654393733396, 0, 0.0267544925942717, 0.0286475057535545, 
    0.0547949838515532, 0.219980802439823, 0.187705568819311, 
    0.233928543718589, 0.026478423437715, 0.00266972416926254, 
    0.0405908679631698, 0.0466360132670807, 0.124457536141733, 
    0.0911118884539047, 0.178309013089969, 0.0456188712564735, 
    0.0421981168987437, 0.0861555916595821, 0.11041459374258, 
    0.111068146673966, 0.139587500420286, 0.125386855890125, 
    0.061080814748532, 0.0526366086431032, 0.115364034404825, 
    0.161101220903838, 0.128911898470234, 0.0604366238013439, 
    0.363221983806348, 0.34755265359959, 0.0853452430644858, 
    0.152186925162602, 0.164486130348524, 0.292604470334872, 
    0.350756670925037, 0.1459173662821, 0.246560485257055, 0.280861699731552, 
    0.323490119492833), ad = c(0.895040161811205, 0.808116873897327, 
    0.863043928431609, 0.908877666783657, 0.788088594493494, 
    0.781263190968751, 0.740952491477405, 0.779618753550039, 
    0.86050730920099, 1, 0.886245890517143, 0.794097764641266, 
    0.702224845117892, 0.759108902890472, 0.703460559640697, 
    0.607603275078501, 0.70124494876511, 0.683723240418769, 0.708341926457601, 
    0.646992568814872, 0.701422372047143, 0.664307339358374, 
    0.833182336848473, 0.75633883870587, 0.677868567390032, 0.550689106029081, 
    0.415275526128068, 0.516197406291169, 0.383399882114882, 
    0.320492553611869, 0.354494998884351, 0.331577585505293, 
    0.290296860359611, 0.229886438247118, 0.332265952281195, 
    0.351684587816436, 0.445739809342017, 0.366879042331775, 
    0.28208767894155, 0.331359022955926, 0.253035294752158, 0.279832760974238, 
    0.198014024140746, 0.157983600030951, 0.100574321762122, 
    0.164562421479303, 0.160509277118534, 0.096505026369051, 
    0.0349126171604172, 0.0473692443272689, 0.0729518879542451, 
    0.085959148647158, 0.144087664632392, 0.164546639862129, 
    0.137820224958695, 0.192508221835802, 0.152147001454404, 
    0.0503567222109793, 0, 0.0926036886344493, 0.0749027410413921, 
    0.0272594370444708, 0.0356201198661257, 0.0627480257727215, 
    0.0926893908912134, 0.0847076951285152, 0.0884737382785661, 
    0.118598418923307, 0.0721877717286707, 0.151381031756681, 
    0.14008804118258, 0.158775593229123, 0.19515614526279, 0.278494208330467, 
    0.309674163375252, 0.33780136665974, 0.357034000934539, 0.361962225166731, 
    0.378715434717008, 0.374518833775061, 0.361396646354054, 
    0.44530118915098, 0.473637494798486, 0.54141401057307, 0.610775918104219, 
    0.635074985282618, 0.541012871042244, 0.641736196312681, 
    0.712533533646443, 0.676406111324519, 0.771552251406591), 
    obv = c(0.215769365452672, 0.138564635683114, 0.210500483925132, 
    0.30020382085011, 0.188355364910318, 0.115159308238239, 0.022755653326587, 
    0.0926513375024093, 0.167332784768295, 0.281147583878087, 
    0.510347727342747, 0.405431389469949, 0.326075225853482, 
    0.236920580229393, 0.339193497348912, 0.254053945970507, 
    0.345733286708138, 0.258726551447731, 0.166321304681281, 
    0.276982954966464, 0.392891730311884, 0.237763558206278, 
    0.388654324708701, 0.69208986224128, 0.556649651306719, 0.451713554295282, 
    0.340467954858453, 0.42042059975112, 0.300280088859098, 0.155664323428174, 
    0.252353941577929, 0.14687437023485, 0.0619889302817057, 
    0, 0.0927479127159874, 0.013691525409104, 0.142498528719898, 
    0.288056705714323, 0.182759812832653, 0.256679570686397, 
    0.193870391821027, 0.261200163564623, 0.367026756314351, 
    0.299408222275496, 0.232405555204819, 0.304343133129486, 
    0.361144052858937, 0.310438406833274, 0.249281658900848, 
    0.177715170289087, 0.231949159420381, 0.184329552685385, 
    0.236748140419078, 0.278335253005663, 0.229742518673039, 
    0.278830935519823, 0.222895842716768, 0.123707103492959, 
    0.0329695833574453, 0.135810516666653, 0.0872900706078492, 
    0.0450038949525023, 0.0972196623824343, 0.151018341588765, 
    0.0768422191908081, 0.142286836262903, 0.230563883080772, 
    0.284096225253678, 0.23145960222147, 0.295606420784407, 0.225107420735276, 
    0.295777552590109, 0.373915432303895, 0.448334895614239, 
    0.390753867891333, 0.446123793545614, 0.517918796836518, 
    0.434147583299386, 0.358805093141572, 0.416217440479593, 
    0.552913657431629, 0.685506884949068, 0.621572254889414, 
    0.7030092741272, 0.787666820871008, 0.66946168859508, 0.802893883002686, 
    0.882689228122507, 0.988837815427572, 0.873707509138625, 
    1), rrt = c(0.244483227870048, 0.189098728634769, 0.20583184667526, 
    0.192602018802919, 0.345850453082302, 0.152168402428559, 
    0.687402731453068, 0.0984467023391477, 0.397824796688999, 
    0.877866702587609, 0.808107643413715, 0.233352706657427, 
    0.225641901386414, 0.406439594424975, 0.495879988934145, 
    0.296184525815072, 0.088669827076353, 0.164622379398119, 
    0.330122682698301, 0.196550425459554, 0.340634712671581, 
    0.601442503132466, 0.840761705603838, 0.965782744177498, 
    0.616586563885219, 0.255359352908757, 0.493777937718145, 
    0.408343084830308, 0.531719857974706, 1, 0.145164629522486, 
    0.364857365278548, 0.284335768223526, 0.355059020924508, 
    0.73336671230915, 0.386544974906583, 0.867462994353026, 0.624526018900245, 
    0.799965480876465, 0.343878516142751, 0.369379096320409, 
    0.149260354957915, 0.501290952456054, 0.156704693655608, 
    0.302663225914925, 0.320806704236885, 0.0369680939919164, 
    0.0189833605925878, 0.366173685538038, 0.648414799663179, 
    0.0419736961339596, 0.117574632852137, 0.210209730919573, 
    0, 0.127177959521737, 0.14632143465726, 0.107918375373831, 
    0.559711861664629, 0.134284829538902, 0.226936168971189, 
    0.0137044165333979, 0.0922502659291392, 0.236364089793484, 
    0.112679672021194, 0.0873555728522064, 0.091562950930339, 
    0.270913963285573, 0.11319752443867, 0.118775290620553, 0.365995942282873, 
    0.112219842944522, 0.130857697151719, 0.119117632398378, 
    0.204606700130828, 0.134220308091376, 0.0759281587995698, 
    0.146528029846838, 0.393937625471787, 0.362780303311843, 
    0.164218509220288, 0.793385031014824, 0.639670699703692, 
    0.159478327007823, 0.286097574030625, 0.198196951007282, 
    0.565794146955835, 0.654806703494826, 0.20562446459716, 0.408747047691774, 
    0.515768690822144, 0.194481730601363), sigmat = c(0.244063227439469, 
    0.188761670107159, 0.205468794418444, 0.192259454444581, 
    0.345304646530299, 0.151891327880868, 0.68678356955531, 0.0982626001251242, 
    0.397229794444664, 0.877529598389856, 0.807635021753072, 
    0.232948644508051, 0.225249103338412, 0.405837556048739, 
    0.495225486630751, 0.295695783030243, 0.0885032887361465, 
    0.164324691344712, 0.329593932956677, 0.196201695792759, 
    0.340094455157919, 0.600780144693087, 0.84034762645598, 0.965674822737418, 
    0.615928406842587, 0.254924154997333, 0.493124213362974, 
    0.407739536377961, 0.531055695901891, 1, 0.144899311488554, 
    0.364292261310308, 0.283861977692574, 0.354503682180614, 
    0.732790898493631, 0.385959678640644, 0.867103162746831, 
    0.623870631137925, 0.799479567310211, 0.343334794883511, 
    0.368809619227597, 0.148988147762006, 0.500634553661014, 
    0.156420066954384, 0.302166518560339, 0.320288508595598, 
    0.0368972343197473, 0.0189467511565862, 0.365607299758702, 
    0.647770144355299, 0.0418933853331156, 0.117356715146612, 
    0.209840007193026, 0, 0.126943352051329, 0.146054166839796, 
    0.10771743564636, 0.559045052534974, 0.134038000493114, 0.226541467701333, 
    0.0136779426813554, 0.0920772742369777, 0.235955677683182, 
    0.112470336680133, 0.0871914093615505, 0.0913911961675312, 
    0.270457698312235, 0.112987278780645, 0.118555275480307, 
    0.365429729168183, 0.112011316388394, 0.130616747706965, 
    0.118897019779015, 0.204245524624366, 0.133973589496128, 
    0.0757847782655815, 0.146260414145135, 0.393345905368038, 
    0.362217236508247, 0.163921483657974, 0.792888749381881, 
    0.639021693730726, 0.159189107261666, 0.285621529042608, 
    0.197845663006123, 0.565127350618088, 0.65416554101219, 0.205261729721857, 
    0.408143180858078, 0.515107977570175, 0.194136225809308)), row.names = c(NA, 
-91L), class = c("tbl_df", "tbl", "data.frame"))

df|>glimpse()
#> Rows: 91
#> Columns: 9
#> $ close     <dbl> 98.71060, 96.23133, 98.69157, 99.39513, 98.58597, 97.80710, …
#> $ timestamp <date> 2023-12-05, 2023-12-06, 2023-12-07, 2023-12-08, 2023-12-09,…
#> $ high      <dbl> 0.3523061, 0.3439603, 0.3303386, 0.3551992, 0.4407114, 0.335…
#> $ low       <dbl> 0.4585840, 0.4692848, 0.4435501, 0.4835642, 0.5391043, 0.472…
#> $ volume    <dbl> 0.1591788, 0.1360238, 0.1159019, 0.1837560, 0.2683283, 0.120…
#> $ ad        <dbl> 0.8950402, 0.8081169, 0.8630439, 0.9088777, 0.7880886, 0.781…
#> $ obv       <dbl> 0.21576937, 0.13856464, 0.21050048, 0.30020382, 0.18835536, …
#> $ rrt       <dbl> 0.24448323, 0.18909873, 0.20583185, 0.19260202, 0.34585045, …
#> $ sigmat    <dbl> 0.24406323, 0.18876167, 0.20546879, 0.19225945, 0.34530465, …

## In this example the "close" variable is what I want to predict, timestamp is
## obviously the time variable and the other variables are auxiliary variables
## which may be useful to predict "close"

^{Created on 2024-03-05 with reprex v2.1.0}

I cannot find examples/tutorial of modeltime handling this case. I would like to try a couple of models (arima, lasso for instance, not super complicated stuff) to forecast my data by taking the extra variables into account.
Is there any tutorial where the use of external regressors is discussed?
Thanks a lot.

[joranE]

In basically any time series scenario, if you want to forecast using variables that are not derivable from the date index (day of week, month, etc) that means you have to supply future values of those variables when you pass data frames to generate predictions. That's the only difference, but of course now you have multiple forecasting problems.

[larry77]

I see. Then I was looking for the impossible -- to incorporate extra info and still be able to forecast as if I had a vanilla arima model. Thanks for the answer and I can close this.