How can I calculate time-varying Value at Risk (VaR) and Conditional VaR for return series in R?

Question

In this time series data, I calculated the return values and the goal is to estimate a GARCH(1,1) to the return values and obtain the estimated parameters. The return data is as below:

daily_xts <- c(
  NA, -0.362483397298163, 0.971212570135149, -1.42617239823122,
  0.659020656052212, -1.07026409134319, -0.620050212514744, 4.1733766704759,
  -1.11087572552901, 1.04457447287807, 1.31783586708174, -1.45058367712325,
  1.05705454632501, -0.329132489568185, -2.17737995495608, 0.89445589392998,
  0.0222637735424858, 0.643376588186362, 1.90565177684849, 0.691894652066738, 0,
  0.430017858618825, 1.84934379021944, -0.337553063128126, 0.316491451897694,
  -0.147568273404008, 0.442057331529488, -0.50537483851647, -0.317154299041889,
  -0.275688857937073, -0.170036176356447, 0.910543111831297, -2.00134210169014,
  0.707175330980503, -1.41938727023909, 0.281174629319159, 2.03107144458357,
  -0.786148733993697, 2.00619329071503, -1.55924352515018, 0.635055062253542,
  0.105451873221307, 0.0632220018951024, 0, -0.995035191910443,
  -1.00503573450124, -0.0644931771735635, 0.600342718606539, 0.639258509358287,
  -1.60585822758295, -0.954253598162724, 0.521631263209388, 0.367842024632026,
  -0.237863670111027, 0.905182904646695, 0.833246987078562, 0.318644978722249,
  -1.32368071322349, 0.364694172308155, 0.277987981498784, -0.664173825265157,
  -0.582086369202983, 0.818266830721681, 1.04533858552691, 2.5768662413336,
  0.227251421854779, -0.289314112624428, -1.73263489514008, 0.210345045786031,
  -0.88646002366799, -1.6027697134926, 0.579962980356985, 0.661761414507556,
  -0.319663571506235, -0.663878663395767, -0.0859866767727979, 2.27499978508798,
  -0.505792426953766, -0.42346240211053, -0.212408745961445, 3.42771080583533,
  0.082154453649963, 0.266532195371827, 0.347466887095305, 0.264902862955552,
  0.406176435819816, -0.630277583374506, -0.880884551328176, 0.840082835927314,
  0.508803397804103, -1.34888623373142, 0.697154782715792, 0,
  -0.163595128510829, -0.369081817690731, -0.473590914271638,
  -0.0206460935814334, -0.538190085407031, 0.66198007567122, 1.14802612701097,
  -0.798127646126101, -1.24045008464169, 0.849305985518978, 0.185471459659459,
  2.78162084699445, -0.100170299874947, 0.280224368325754, -0.300266465215504,
  -0.76474712853063, -0.344021378571879, 1.28903895791947, -1.93985272546637,
  0.142734247904919, 0.892496778383434, -0.22237955186819, 0.665664572668634,
  0.940471154591771, -1.9304822512165, -0.121903714018456, 1.49316940346047,
  -0.421473775737669, 0.9607759862861, -1.78881261021053, 0.928547235456589,
  0.260864996716981, 0.32012631420244, -0.601089774165953, 2.42219907099721,
  0.430615262874223, -0.293402655467601, -0.707689226553487, 0.491981716387135,
  0.235298147776763, -0.569580243883694, -0.157699620280205, -0.375529647518658,
  0.0197960602526415, -0.0594078650883123, -0.317460584077267,
  -0.418200346445508, 1.09160356457991, -0.534392172622988, -0.597133547777373,
  -0.500351289032741, 0.779458328275551, 0.298183301165711, 0.119020049757257,
  -1.19666167919852, -2.66357316678842, -2.92723806577664, -7.5561637168708,
  -1.84762524308226, 2.48631125725982, 3.7049517956655, 0.829158152395015,
  -1.59898049591685, -3.87174395187007, 1.5260562292684, -0.226302424863301,
  -2.45396791073826, 2.22716354950898, -1.85636358815686, -0.254779526989379,
  0.670292590185539, -0.554406607258606, 1.47163614127295, 0.114064113791379,
  0.862663663247565, -2.07841205128214, -0.0692669995457695, -1.91192349800726,
  -0.661313219503512, -0.618024310846055, -2.60883877668987, -4.50526628131178,
  1.12017208569051, 1.80637373006816, 1.3336750079052, 1.50965371968508,
  0.0241585116555143, -3.69136407518402, 1.83810937636153, 1.29601763538583,
  1.75802001210483, -0.766835782235109, -1.57598610569769, -0.489949540734536,
  2.78501593473792, 0.832450995802825, -0.165933420818298, -0.977478233272633,
  1.0960295173926, 3.03406933559902, 0.229616638878971, 0.0229400301767324,
  0.617215341125954, 1.98561805645161, 1.06668566956127, -0.977357835707293,
  1.39645626718012, 0.175935831085239, -0.727752704230733, 0, 0.991090581486054,
  -1.27924549979292, 1.56373415084596, -1.51934666626912, -1.97183401894625,
  -0.52183897256266, 2.07121767086127, -0.24540112432061, 2.27457970332035,
  -0.152953161611391, 0.610418302860127, -1.24659682927115, 0.0220090219834379,
  -0.0880497515828527, 0.022014753408639, -1.10694072973021, 1.19497110803928,
  -0.52933074631043, -2.39465166138508, 2.57140380638514, 0.572315011412661,
  -0.0219558775989004, -1.30374184086279, 0.775459740578732, -2.11895957242323,
  1.00931660895012, 1.72570431108516, 1.00393467604385, -1.73041449695277,
  -3.50754710314218, 0.775020957626982, 0.994131538121756, 1.38425522204071, 0,
  -0.155329005667104, 1.7391764919287, -1.20761155774822, -0.79840743482209,
  -4.50896048631773, -0.0233011072295231, -0.842300263454465, -2.42580260084813,
  -2.11661717783134, 0.147425091748632, 1.77641612276789, -2.88740398638554,
  2.01530298162425, -1.37189071495381, -0.271708203816967, -1.1693154897352,
  -1.20847141900464, 1.38349334579368, -0.928602493156783, 1.25283522918238,
  0.768950821396164, -9.75118133292265, 3.0581756775089, 1.57277949161574,
  -1.49354272424227, 0.368904234325074, -0.0263106676859248, -1.59111820233693,
  0.13356219607461, -1.23557576765765, 0.56596028398106, -2.36584525160097,
  2.15062321533628, 2.28977247235775, 1.20357021144897, -0.364773714405286,
  0.572614786886128, 1.62186849780461, -1.98588346980539, 2.08797893423647,
  1.09096601291321, -0.277955955608533, -1.99341632745926, 1.51149276904095,
  0.0254175665428846, -1.33062352200488, 0.923083477553055, 0,
  -0.0255315898140207, 0.280436140976192, -0.638490245680989, 3.37563545227733,
  0.321506401851357, -1.49256000913636, 0.699298536565873, 0.273396463652187,
  1.23336538219689, -0.0735818558469603, 0.660232279487438, -0.611174145719984,
  -0.0735900937612666, 0.318513067041648, 1.43293280148189, 0.433111825995125,
  0.431241663462245, 0.856936916726747, 0.307658511609565, -0.663821775442397,
  2.37406378493161, -1.02732166644461, -0.564844994362712, 0.259283589682058,
  0.79719062278536, 1.23013739289113, 0.3684093675695, -0.2300921454641,
  1.23628175728121, -0.227797367615734, 0.27329327273411, -0.204894773904307,
  0.454755202025403, -0.158937483792698, -0.295817718232705, -0.114009813489169,
  -8.09938975665445, -3.83303604567375, -0.128627670467729, -0.775195126460293,
  -1.17418444297854, 1.04440116545232, -1.38618407134463, 0.0263304803847397,
  0.315452425507567, -0.236499925579148, -0.0263070657038345, -1.05821625220277,
  1.7139563068187, -1.42182755204443, 0.106019094293286, -1.36019695804759,
  0.962049108980034, -0.613578046639862, 1.61914886461805, 1.82629652009538,
  0.541445186901113, 1.0487370975818, 0.836193900582982, -0.328576052867646,
  0.0759180104275003, -0.889343949495647, -0.0255315898140207,
  -0.614593499589011, -0.0513874625902133, -0.102856785911243,
  -1.21652074603364, -1.41623394827359, -0.529664896527127, -0.612600131266872,
  0.186841106002777, -0.293767073246221, 0.958221345113053, -0.0529941718814264,
  2.64171756288554, 2.2713722830678, -4.43715029075094, -2.56492550704333,
  1.63740065063198, 2.65350912560067, 1.90041926524516, 0.583387816072722,
  -0.253233865385072, 3.46366499356092, 1.28971000630491, 1.27328567087743,
  0.547555243718678, 0.82753043471282, -1.18428666991703, 0.735903617814992,
  -0.426644416779531, -0.0237510399917262, -0.691386717521381, 2.01310052237393,
  0.910261825672443, 0.301582415118684, 0.554406607258606, 0.436727517192592,
  0.160421721601001, 1.7703662757663, 0.672646026376356, 1.1994834927187,
  -0.486944294549474, -0.266605353798655, -0.311943205007159, 0.999224490176243,
  -0.531676053767471, 0.133189805856038, -0.600738242264809, 0.534161074228967,
  -0.0221955822866882, 0.243931812586062, -0.510723881313835,
  -0.535711114564386, -0.718778917600238, -0.270878260296259, -0.15836220932024,
  -0.61314146896212, -1.67686024002953, -0.767351765936786, 0.326264563481615,
  0.626234216352417, -0.975839505436893, -1.9093142906665, 0.664136699471563,
  -0.497687962909099, 0.16617214506276, -0.618602957231884, -0.119412551502984,
  -2.02758585103844, 0.99479170462109, -1.90110290176575, 0.417439525758478,
  0.756742290633117, 1.807495931976, -0.454815870249181, -0.24020669151974,
  0.814366177294801, 0.713107380276945, -0.0710863671683271, -1.21618049888368,
  1.54747043355346, -0.0945426649996861, -2.03041013106957, 2.03041013106957,
  0.612915638697142, -1.06321383352239, 1.50876035031757, 0.536692437338138, 0,
  1.22587170356847, -5.52940271287894, -0.43827681550952, 0, -0.464716496547446,
  -0.491524699447288, 1.41880563519434, -2.85804143211106, 1.80810870088211,
  -0.590848577796699, -0.222469502211098, -0.545909551108448,
  -0.573925482397053, 0.822439526798302, -1.8790480989995, -0.761615736775489,
  -0.485383498806025, -0.900322480197113, -0.83031092407384, 1.83301631700727,
  1.95066600675924, -0.0752892465497368, 0.600747724109496, 1.33864416746294,
  -1.16410478672959, -2.36965461487664, 1.54413898249217, 0.351053511203014,
  1.09535075731455, -1.37107721003202, -0.201010122983636, -4.26471018473458,
  2.28344644401992, 0.460712358289506, -1.07831080572351, -0.025821607841392,
  -1.71879231322545, -1.24225731900482, 0.794716765447001, 1.38872397179246,
  -0.0260299292563992, 0.15605205133169, 0.518404478758816, 1.33541017215268, 0,
  0.610373207284409, -1.58449266386005, 0.282958388150023, -2.15509319831488,
  0.627950797828314, -0.392006256493937, 0.130846543189511, 0.130665112122808,
  0.338931367850615, 0.46741193731239, -0.989325968087407, 0.235201983896394
) |>
  structure(
    dim = c(492L, 1L),
    index = c(
      1421712000, 1421798400, 1421884800, 1421971200, 1422230400, 1422316800,
      1422403200, 1422489600, 1422576000, 1422835200, 1422921600, 1423008000,
      1423094400, 1423180800, 1423440000, 1423526400, 1423612800, 1423699200,
      1423785600, 1424131200, 1424217600, 1424304000, 1424390400, 1424649600,
      1424736000, 1424822400, 1424908800, 1424995200, 1425254400, 1425340800,
      1425427200, 1425513600, 1425600000, 1425859200, 1425945600, 1426032000,
      1426118400, 1426204800, 1426464000, 1426550400, 1426636800, 1426723200,
      1426809600, 1427068800, 1427155200, 1427241600, 1427328000, 1427414400,
      1427673600, 1427760000, 1427846400, 1427932800, 1428278400, 1428364800,
      1428451200, 1428537600, 1428624000, 1428883200, 1428969600, 1429056000,
      1429142400, 1429228800, 1429488000, 1429574400, 1429660800, 1429747200,
      1429833600, 1430092800, 1430179200, 1430265600, 1430352000, 1430438400,
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      1431388800, 1431475200, 1431561600, 1431648000, 1431907200, 1431993600,
      1432080000, 1432166400, 1432252800, 1432598400, 1432684800, 1432771200,
      1432857600, 1433116800, 1433203200, 1433289600, 1433376000, 1433462400,
      1433721600, 1433808000, 1433894400, 1433980800, 1434067200, 1434326400,
      1434412800, 1434499200, 1434585600, 1434672000, 1434931200, 1435017600,
      1435104000, 1435190400, 1435276800, 1435536000, 1435622400, 1435708800,
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      1436745600, 1436832000, 1436918400, 1437004800, 1437091200, 1437350400,
      1437436800, 1437523200, 1437609600, 1437696000, 1437955200, 1438041600,
      1438128000, 1438214400, 1438300800, 1438560000, 1438646400, 1438732800,
      1438819200, 1438905600, 1439164800, 1439251200, 1439337600, 1439424000,
      1439510400, 1439769600, 1439856000, 1439942400, 1440028800, 1440115200,
      1440374400, 1440460800, 1440547200, 1440633600, 1440720000, 1440979200,
      1441065600, 1441152000, 1441238400, 1441324800, 1441670400, 1441756800,
      1441843200, 1441929600, 1442188800, 1442275200, 1442361600, 1442448000,
      1442534400, 1442793600, 1442880000, 1442966400, 1443052800, 1443139200,
      1443398400, 1443484800, 1443571200, 1443657600, 1443744000, 1444003200,
      1444089600, 1444176000, 1444262400, 1444348800, 1444608000, 1444694400,
      1444780800, 1444867200, 1444953600, 1445212800, 1445299200, 1445385600,
      1445472000, 1445558400, 1445817600, 1445904000, 1445990400, 1446076800,
      1446163200, 1446422400, 1446508800, 1446595200, 1446681600, 1446768000,
      1447027200, 1447113600, 1447200000, 1447286400, 1447372800, 1447632000,
      1447718400, 1447804800, 1447891200, 1447977600, 1448236800, 1448323200,
      1448409600, 1448582400, 1448841600, 1448928000, 1449014400, 1449100800,
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      1475625600, 1475712000, 1475798400, 1476057600, 1476144000, 1476230400,
      1476316800, 1476403200, 1476662400, 1476748800, 1476835200, 1476921600,
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      1477872000, 1477958400, 1478044800, 1478131200, 1478217600, 1478476800,
      1478563200, 1478649600, 1478736000, 1478822400, 1479081600, 1479168000,
      1479254400, 1479340800, 1479427200, 1479686400, 1479772800, 1479859200,
      1480032000, 1480291200, 1480377600, 1480464000, 1480550400, 1480636800,
      1480896000, 1480982400, 1481068800, 1481155200, 1481241600, 1481500800,
      1481587200, 1481673600, 1481760000, 1481846400, 1482105600, 1482192000,
      1482278400, 1482364800, 1482451200, 1482796800, 1482883200, 1482969600
    ) |>
      structure(tzone = "UTC", tclass = "Date"),
    class = c("xts", "zoo")
  )

First Problem

I used the following codes for the estimation:

# Fit a GARCH(1,1) model
garch_spec <- ugarchspec(variance.model = list(model = "sGARCH", garchOrder = c(1, 1)),
                         mean.model = list(armaOrder = c(0, 0), include.mean = F),
                         distribution.model = "norm")
garch_fit <- ugarchfit(spec = garch_spec, data = na.omit(daily_xts))

The output of the series is as follows:

> garch_fit@fit$matcoef
           Estimate  Std. Error      t value     Pr(>|t|)
omega  1.839909e+00  0.47477279 3.875347e+00 0.0001064727
alpha1 1.633124e-01  0.07551724 2.162584e+00 0.0305731569
beta1  8.861043e-10  0.22817177 3.883497e-09 0.9999999969

But the correct output is in the following image:

Second Problem

used many approaches and as far as I know, the VaR and CVaR are one value per series. I do not understand the time-varying VaR/CVaR. The output should be like the following image: https://i.stack.imgur.com/i3JKL.png Any help would be appreciated.