Forecasting using ARDL model in R

[TalhaAsif]

Hey, I am working on this data where I have used the ARDL model but, when I try to forecast the next future intervals it gives me an error. Though the model output is good I want to see the forecasting plots. Plus, I have used the ardlDlm function to obtain model output. Can someone please help me? Below is the data attached.

Data:

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"2021-07-16", "2021-07-17", "2021-07-18", "2021-07-19", "2021-07-20", 
"2021-07-21", "2021-07-22", "2021-07-23", "2021-07-24", "2021-07-25", 
"2021-07-26", "2021-07-27", "2021-07-28", "2021-07-29", "2021-07-30", 
"2021-07-31", "2021-08-01", "2021-08-02", "2021-08-03", "2021-08-04", 
"2021-08-05", "2021-08-06", "2021-08-07", "2021-08-08", "2021-08-09", 
"2021-08-10", "2021-08-11", "2021-08-12", "2021-08-13", "2021-08-14", 
"2021-08-15", "2021-08-16", "2021-08-17", "2021-08-18", "2021-08-19", 
"2021-08-20", "2021-08-21", "2021-08-22", "2021-08-23", "2021-08-24", 
"2021-08-25", "2021-08-26", "2021-08-27", "2021-08-28", "2021-08-29", 
"2021-08-30", "2021-08-31", "2021-09-01", "2021-09-02", "2021-09-03", 
"2021-09-04", "2021-09-05", "2021-09-06", "2021-09-07", "2021-09-08", 
"2021-09-09", "2021-09-10", "2021-09-11", "2021-09-12", "2021-09-13", 
"2021-09-14", "2021-09-15", "2021-09-16", "2021-09-17", "2021-09-18", 
"2021-09-19", "2021-09-20", "2021-09-21", "2021-09-22", "2021-09-23", 
"2021-09-24", "2021-09-25", "2021-09-26", "2021-09-27", "2021-09-28", 
"2021-09-29", "2021-09-30", "2021-10-01", "2021-10-02", "2021-10-03", 
"2021-10-04", "2021-10-05", "2021-10-06", "2021-10-07", "2021-10-08", 
"2021-10-09", "2021-10-10", "2021-10-11", "2021-10-12", "2021-10-13", 
"2021-10-14", "2021-10-15", "2021-10-16", "2021-10-17", "2021-10-18", 
"2021-10-19", "2021-10-20", "2021-10-21", "2021-10-22", "2021-10-23", 
"2021-10-24", "2021-10-25", "2021-10-26", "2021-10-27", "2021-10-28", 
"2021-10-29", "2021-10-30", "2021-10-31", "2021-11-01", "2021-11-02", 
"2021-11-03", "2021-11-04", "2021-11-05", "2021-11-06", "2021-11-07", 
"2021-11-08", "2021-11-09", "2021-11-10", "2021-11-11", "2021-11-12", 
"2021-11-13", "2021-11-14", "2021-11-15", "2021-11-16", "2021-11-17", 
"2021-11-18", "2021-11-19", "2021-11-20", "2021-11-21", "2021-11-22", 
"2021-11-23", "2021-11-24", "2021-11-25", "2021-11-26", "2021-11-27", 
"2021-11-28", "2021-11-29", "2021-11-30", "2021-12-01", "2021-12-02", 
"2021-12-03", "2021-12-04", "2021-12-05", "2021-12-06", "2021-12-07", 
"2021-12-08", "2021-12-09", "2021-12-10", "2021-12-11", "2021-12-12", 
"2021-12-13", "2021-12-14", "2021-12-15", "2021-12-16", "2021-12-17", 
"2021-12-18", "2021-12-19", "2021-12-20", "2021-12-21", "2021-12-22", 
"2021-12-23", "2021-12-24", "2021-12-25", "2021-12-26", "2021-12-27", 
"2021-12-28", "2021-12-29", "2021-12-30", "2021-12-31", "2022-01-01", 
"2022-01-02", "2022-01-03", "2022-01-04", "2022-01-05", "2022-01-06", 
"2022-01-07", "2022-01-08", "2022-01-09", "2022-01-10", "2022-01-11", 
"2022-01-12", "2022-01-13", "2022-01-14", "2022-01-15", "2022-01-16", 
"2022-01-17", "2022-01-18", "2022-01-19", "2022-01-20", "2022-01-21", 
"2022-01-22", "2022-01-23", "2022-01-24", "2022-01-25", "2022-01-26", 
"2022-01-27", "2022-01-28", "2022-01-29", "2022-01-30", "2022-01-31", 
"2022-02-01", "2022-02-02", "2022-02-03", "2022-02-04", "2022-02-05", 
"2022-02-06", "2022-02-07", "2022-02-08", "2022-02-09", "2022-02-10", 
"2022-02-11", "2022-02-12", "2022-02-13", "2022-02-14", "2022-02-15", 
"2022-02-16", "2022-02-17", "2022-02-18", "2022-02-19", "2022-02-20", 
"2022-02-21", "2022-02-22", "2022-02-23", "2022-02-24", "2022-02-25", 
"2022-02-26", "2022-02-27", "2022-02-28", "2022-03-01", "2022-03-02", 
"2022-03-03", "2022-03-04", "2022-03-05", "2022-03-06", "2022-03-07", 
"2022-03-08", "2022-03-09", "2022-03-10", "2022-03-11", "2022-03-12", 
"2022-03-13", "2022-03-14", "2022-03-15", "2022-03-16", "2022-03-17", 
"2022-03-18", "2022-03-19", "2022-03-20", "2022-03-21", "2022-03-22", 
"2022-03-23", "2022-03-24", "2022-03-25", "2022-03-26", "2022-03-27", 
"2022-03-28", "2022-03-29", "2022-03-30", "2022-03-31", "2022-04-01", 
"2022-04-02", "2022-04-03", "2022-04-04", "2022-04-05", "2022-04-06", 
"2022-04-07", "2022-04-08", "2022-04-09", "2022-04-10", "2022-04-11", 
"2022-04-12", "2022-04-13", "2022-04-14", "2022-04-15", "2022-04-16", 
"2022-04-17", "2022-04-18", "2022-04-19", "2022-04-20", "2022-04-21", 
"2022-04-22", "2022-04-23", "2022-04-24", "2022-04-25", "2022-04-26", 
"2022-04-27", "2022-04-28", "2022-04-29", "2022-04-30", "2022-05-01", 
"2022-05-02", "2022-05-03", "2022-05-04", "2022-05-05", "2022-05-06", 
"2022-05-07", "2022-05-08", "2022-05-09", "2022-05-10", "2022-05-11", 
"2022-05-12", "2022-05-13", "2022-05-14", "2022-05-15", "2022-05-16", 
"2022-05-17", "2022-05-18", "2022-05-19", "2022-05-20"))

Code:

ardl_model1 <- ardlDlm(ATOM_12 ~ Inflation, data = data_1, p = 1, q = 2)
summary(ardl_model1)
checkresiduals(ardl_model1)

fcst1 <- forecast(ardl_model1, h = 3)

Error:

Error in is.constant(y) : 
  'list' object cannot be coerced to type 'double'

[FactOREO]

Hello,

your error is straightforward after looking on the documentation of dLagM::forecast() (as a side note, I told you a few weeks ago to include all packages you use in your code. There are several forecast functions in R so try to avoid confusion and make it clear from the beginning ).

According to the documentation, you have to specify a model, a vector x of new independent values and the forecasting horizon h. Adjusting for this, there is a result given without error:

library('dLagM')

# badly chosen name
Data$ATOM <- Data$`ATOM-USD.Close`
# changed the independent variable name and dataset name
# ardl_model1 <- ardlDlm(ATOM_12 ~ Inflation, data = data_1, p = 1, q = 2)
ardl_model <- dLagM::ardlDlm(ATOM ~ Inflation, data = Data, p = 1, q = 2)
summary(ardl_model)
#> 
#> Time series regression with "ts" data:
#> Start = 3, End = 415
#> 
#> Call:
#> dynlm(formula = as.formula(model.text), data = data)
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -9.1318 -0.9143 -0.0080  0.9420  7.8857 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)   
#> (Intercept)  0.05529    0.38923   0.142  0.88712   
#> Inflation.t -0.19904    0.24727  -0.805  0.42133   
#> Inflation.1  0.18539    0.24668   0.752  0.45276   
#> ATOM.1      -0.14353    0.04888  -2.937  0.00351 **
#> ATOM.2      -0.15705    0.04888  -3.213  0.00142 **
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 1.972 on 408 degrees of freedom
#> Multiple R-squared:  0.04077,    Adjusted R-squared:  0.03137 
#> F-statistic: 4.335 on 4 and 408 DF,  p-value: 0.001912
forecast::checkresiduals(ardl_model)
#> Time Series:
#> Start = 3 
#> End = 415 
#> Frequency = 1 
#>            3            4            5            6            7            8 
#> -0.041997673  1.562036621 -0.093186217  0.496183609 -2.194212709  0.666075791 
#>            9           10           11           12           13           14 
#>  0.667125042 -0.073425352  2.376810747 -1.026651317  1.991790044  3.292363334 
#>           15           16           17           18           19           20 
#>  1.623512377 -1.762457388 -1.134606047 -3.777281113 -2.704125135  1.154764488 
#>           21           22           23           24           25           26 
#> -1.656932860 -0.780773251  1.333995452 -1.967401348  0.232666462  3.141482627 
#>           27           28           29           30           31           32 
#>  1.514624269  0.595563221 -0.681612506  0.479869655  1.049247186 -0.458797599 
#>           33           34           35           36           37           38 
#> -0.054601513 -2.049335316  3.432017856  1.010874396  3.917713883  1.279616149 
#>           39           40           41           42           43           44 
#> -0.042337962 -3.419194256  0.983007739 -4.532568186  0.520742770  1.692696320 
#>           45           46           47           48           49           50 
#> -0.721296978 -0.065737261 -3.425428762  1.226164698 -9.131757342  2.068506880 
#>           51           52           53           54           55           56 
#> -4.378498784 -1.322180665 -1.214237215  2.439712920 -0.206705602  1.717485312 
#>           57           58           59           60           61           62 
#> -0.717387937 -1.593407812 -1.009704450  0.177469916  1.395746908  0.059537079 
#>           63           64           65           66           67           68 
#>  1.300073063  1.920281156 -1.108495000 -0.137417102 -0.032954713 -1.668822068 
#>           69           70           71           72           73           74 
#>  0.026609471  0.091571595 -1.035776267 -0.967785852 -0.603803168  0.716471051 
#>           75           76           77           78           79           80 
#>  0.205105956  0.921426526  0.163930349  0.357820510 -1.117721752 -0.603095761 
#>           81           82           83           84           85           86 
#> -0.163343960 -2.512559895 -0.898431425  0.673764694  0.332777072 -0.967729676 
#>           87           88           89           90           91           92 
#>  0.288104244  0.395534381  0.955077030  0.945409155  0.674697848 -0.696843364 
#>           93           94           95           96           97           98 
#>  0.610957238  0.024717278  0.574049346  1.375420619 -0.116682485 -0.069034593 
#>           99          100          101          102          103          104 
#> -1.074070486  1.074208858  1.275129640  0.051175322 -0.853389283 -1.113142987 
#>          105          106          107          108          109          110 
#> -0.639617184 -0.498900213 -0.336835333 -0.247217722 -0.064484051 -1.036586736 
#>          111          112          113          114          115          116 
#> -0.605021992  0.720584182  1.037393706  0.384652722  0.172921393  0.029378206 
#>          117          118          119          120          121          122 
#> -0.027113301  0.317205378 -0.100258317  0.246100444  0.411942424  0.561799571 
#>          123          124          125          126          127          128 
#> -0.100019202  0.177632338 -0.401569425  0.678085005  0.291696096  0.717086759 
#>          129          130          131          132          133          134 
#>  0.560560483 -0.709400385  0.508034069  0.370433118  0.667169286 -0.406464234 
#>          135          136          137          138          139          140 
#>  1.184044804  0.440598771  0.602526825  0.069469609  0.205151456  2.031560701 
#>          141          142          143          144          145          146 
#>  1.010705044  0.669045106  3.331037182  0.271917606  0.453982878 -2.231671305 
#>          147          148          149          150          151          152 
#>  0.044052320 -2.283682457  2.272435161  0.934829773  0.397423397  1.033067847 
#>          153          154          155          156          157          158 
#>  0.895312817  2.742272841 -0.712462658  0.224255682  0.125529163  1.379829464 
#>          159          160          161          162          163          164 
#> -0.384659079 -4.077330067 -1.063840426  5.777002627  3.326247572 -0.771554382 
#>          165          166          167          168          169          170 
#>  7.804985544  1.415571681 -0.204134224 -0.074646632  2.556747198 -3.071926732 
#>          171          172          173          174          175          176 
#>  7.393863477  4.226443096 -9.034241224 -4.294949820  7.391114790  2.393410176 
#>          177          178          179          180          181          182 
#>  3.015618397 -2.835558807 -0.146423790 -2.759305804 -3.964250989 -0.583600431 
#>          183          184          185          186          187          188 
#>  1.744632304  2.012339823  1.537150921  0.445100423 -1.899227345 -0.254290425 
#>          189          190          191          192          193          194 
#> -1.817618543  1.326118548 -1.738810243  0.248671289 -2.916558573 -0.769115135 
#>          195          196          197          198          199          200 
#>  0.942045767  1.336062238 -0.455316830 -0.677686080 -0.088832563 -0.797421630 
#>          201          202          203          204          205          206 
#> -0.582491732  3.083907692  1.164303521 -0.902878200 -0.361376146  1.479019946 
#>          207          208          209          210          211          212 
#> -1.243205507  1.068191631  7.885655682 -5.127249610  1.658426872  0.558497747 
#>          213          214          215          216          217          218 
#> -1.713463533 -0.068912338 -0.213877903 -0.242016953  1.359809855 -0.719594695 
#>          219          220          221          222          223          224 
#> -0.496667126 -0.797690004 -0.730973181  0.837377944 -0.773995753 -3.659571565 
#>          225          226          227          228          229          230 
#>  0.332009456 -1.450531502  0.550443653 -0.721011351 -0.427043358 -3.152153954 
#>          231          232          233          234          235          236 
#>  0.493611034 -3.026401348  1.295190582  1.102543941  2.078710261  1.501084836 
#>          237          238          239          240          241          242 
#>  0.503067640 -1.505292124 -0.824608682 -3.172882753 -0.614872705  0.190188417 
#>          243          244          245          246          247          248 
#>  0.827686133 -0.334172594 -0.774031945  1.495040238  4.446867281 -3.631422874 
#>          249          250          251          252          253          254 
#> -3.438777090 -1.385470568 -0.580603590  0.867850578 -2.589432673 -0.137946370 
#>          255          256          257          258          259          260 
#>  1.456181647  0.478335118 -2.461699984 -0.885642289  0.602870612 -0.432126004 
#>          261          262          263          264          265          266 
#> -0.403634354  1.841815387 -0.798650705 -0.436449092  1.875596325  3.939404903 
#>          267          268          269          270          271          272 
#>  1.952732074 -0.677255565  2.720549178  2.791381189 -1.728347057 -2.928542159 
#>          273          274          275          276          277          278 
#>  0.544296227  2.053585374  2.794406569  4.421102285  0.356211964  4.240568245 
#>          279          280          281          282          283          284 
#>  3.172714647 -2.183206317  1.385294119 -1.899156258 -2.591863485 -1.525320122 
#>          285          286          287          288          289          290 
#>  2.376839441  1.196172621  2.076275220 -2.165354482  2.737656112 -1.187515195 
#>          291          292          293          294          295          296 
#>  4.695477086 -3.915178551 -0.790787696 -1.970625140  1.677517550 -4.502221834 
#>          297          298          299          300          301          302 
#> -5.580838200  3.809454812  1.483777565  0.982460933 -3.184964441 -2.716955229 
#>          303          304          305          306          307          308 
#> -1.451518057 -0.788477565 -2.012636859  0.692366143  0.686487071 -2.239985953 
#>          309          310          311          312          313          314 
#>  2.913770315  1.645245178  0.526783192  0.712695674  0.501911387 -1.011265347 
#>          315          316          317          318          319          320 
#>  0.368134674 -1.839035276 -2.724971888 -0.102597879 -0.981651020  0.863410718 
#>          321          322          323          324          325          326 
#>  1.820453494  0.031285877 -0.268455266 -1.123089965 -0.451000378 -0.595543542 
#>          327          328          329          330          331          332 
#> -2.454694035  0.659968716  0.248933718 -0.066945578  2.352665475  2.909361851 
#>          333          334          335          336          337          338 
#> -2.272618142  4.695968989 -0.064951046  1.856421524  2.053596304 -3.059622356 
#>          339          340          341          342          343          344 
#>  0.282049117 -3.298337757 -0.001824103 -0.914312806  2.276454712 -1.760766928 
#>          345          346          347          348          349          350 
#> -0.397923575 -0.647189830 -0.987426685  0.422022746  0.062772031  2.247190067 
#>          351          352          353          354          355          356 
#> -0.449337110  0.791315288 -0.046054921 -0.714652760  0.122222748  0.015962931 
#>          357          358          359          360          361          362 
#>  0.266921392  1.079701181 -0.831261584  0.753234984  1.070810197 -0.111415683 
#>          363          364          365          366          367          368 
#>  0.982479291 -0.052103591 -1.037845082  0.353175596  1.832578026  0.932529326 
#>          369          370          371          372          373          374 
#> -0.678877413 -1.639829857 -2.835006354  0.212420270 -1.133962579  0.388715582 
#>          375          376          377          378          379          380 
#> -0.793319755 -2.873426260  0.312165319 -0.300640286 -0.632625168 -0.007984754 
#>          381          382          383          384          385          386 
#> -0.059968748 -0.922142976  0.583044793  0.494232661 -0.217607885 -1.016771617 
#>          387          388          389          390          391          392 
#> -0.488772043 -0.083913170 -1.032382368 -0.390208189 -2.054246277  0.777292899 
#>          393          394          395          396          397          398 
#> -0.964892515 -1.302852747 -0.378793800 -0.226786759 -0.381905456 -0.167689897 
#>          399          400          401          402          403          404 
#>  2.278136031 -1.670186587 -0.050908042 -1.481393872 -0.918172659 -3.131775782 
#>          405          406          407          408          409          410 
#>  0.322308892 -3.155477898 -1.244277716  0.067399136  0.499377107  1.757565833 
#>          411          412          413          414          415 
#> -0.973823505  0.570452204 -1.417966724  0.661371676  0.300510661

dLagM::forecast(ardl_model, x = Data$Inflation[413:415], h = 3)
#> $forecasts
#> [1] -0.21868414 -0.08475143 -0.01556203
#> 
#> $call
#> forecast.ardlDlm(model = ardl_model, x = Data$Inflation[413:415], 
#>     h = 3)
#> 
#> attr(,"class")
#> [1] "forecast.ardlDlm" "dLagM"

^{Created on 2022-10-09 with reprex v2.0.2}

I hope this resolves your error.

Kind regards

[TalhaAsif]

I got it now, Btw's a nice explanation and once again thanks a lot dear. Will like to disturb you more in the future

[TalhaAsif]

@FactOREO

dLagM::forecast(ardl_model, x = Data$Inflation[413:415], h = 3)

Hey! I have a question.

What if we wanted to plot the values generated by the model for the next intervals, how can we do it?
See this I want to generate a forecast plot with these new entries on it.

fcst_7_days <- dLagM::forecast(ardl_model1, x = data_1$Inflation, h = 7)
fcst_7_days

$forecasts
[1]  0.940897180 -0.190210219 -0.112484621  0.053307044  0.016409215 -0.004843290  0.003306165

[FactOREO]

Since there are no confidence intervals provided in the forecast output, you could simply do ssomething like this:

forcastvals <- dLagM::forecast(ardl_model, x = Data$Inflation[401:415], h = 15)

plot(Data$Date[1:400], Data$ATOM[1:400], type = 'l',
     ylab = 'ATOM value', xlab = 'Date', xaxt = 'n')
lines(Data$Date[401:415],forcastvals$forecasts, col = 'red')
axis.Date(1, at = seq(from = min(Data$Date), to = max(Data$Date), by = "3 mon"), format="%m-%Y")

^{Created on 2022-10-10 by the reprex package (v2.0.1)}

Kind regards

[TalhaAsif]

What if we wanted to see the following 7 entries in this plot from 416-424? This code gives us the next 7 entries and I want these to see in the plot.

fcst_7_days <- dLagM::forecast(ardl_model1, x = data_1$Inflation, h = 7)
fcst_7_days

[FactOREO]

Sure, you can just add your new points as I did above. Here is the code, I added a small tweak to make sure the points are connected.

### Forecast values from your forecast
forecast_7days <- c(0.940897180,-0.190210219,-0.112484621,0.053307044,0.016409215,-0.004843290,0.003306165)

### add the points to the complete Date Range in red
plot(Data$Date, Data$ATOM, type = 'l',
     ylab = 'ATOM value', xlab = 'Date', xaxt = 'n')
lines(seq(from = max(Data$Date), to = max(Data$Date) + 7, by = "1 day"), c(Data[which(Data$Date == max(Data$Date)),]$ATOM,forecast_7days), col = 'red')
axis.Date(1, at = seq(from = min(Data$Date), to = max(Data$Date) + 7, by = "3 mon"), format="%m-%Y")

^{Created on 2022-10-11 with reprex v2.0.2}

Kind regards