author: “James Lunga” date: “10/31/2021” output: html_document —

library(fpp)

## Warning: package 'fpp' was built under R version 4.0.5

## Loading required package: forecast

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## Registered S3 method overwritten by 'quantmod':
##   method            from
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library('csv')

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library(psych)

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library(MASS)

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library(fitdistrplus)

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library(pscl)

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## Classes and Methods for R developed in the
## Political Science Computational Laboratory
## Department of Political Science
## Stanford University
## Simon Jackman
## hurdle and zeroinfl functions by Achim Zeileis

library(boot)

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library(ggplot2)

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library(fGarch)

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library(pROC)

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library(censReg)

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## 
## Please cite the 'maxLik' package as:
## Henningsen, Arne and Toomet, Ott (2011). maxLik: A package for maximum likelihood estimation in R. Computational Statistics 26(3), 443-458. DOI 10.1007/s00180-010-0217-1.
## 
## If you have questions, suggestions, or comments regarding the 'maxLik' package, please use a forum or 'tracker' at maxLik's R-Forge site:
## https://r-forge.r-project.org/projects/maxlik/

## 
## Please cite the 'censReg' package as:
## Henningsen, Arne (2017). censReg: Censored Regression (Tobit) Models. R package version 0.5. http://CRAN.R-Project.org/package=censReg.
## 
## If you have questions, suggestions, or comments regarding the 'censReg' package, please use a forum or 'tracker' at the R-Forge site of the 'sampleSelection' project:
## https://r-forge.r-project.org/projects/sampleselection/

library(tscount)

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library(randomForest)

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## randomForest 4.6-14

## Type rfNews() to see new features/changes/bug fixes.

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library(mice)

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library(caret)

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library(tensorflow)

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library(keras)

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library(Amelia)

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## ## 
## ## Amelia II: Multiple Imputation
## ## (Version 1.7.6, built: 2019-11-24)
## ## Copyright (C) 2005-2021 James Honaker, Gary King and Matthew Blackwell
## ## Refer to http://gking.harvard.edu/amelia/ for more information
## ##

library(e1071)

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library(xgboost)

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library(AnalyzeFMRI)

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library(psych)
library(ResourceSelection)

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library(MASS)
library(car)

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library(ggplot2)

library(adabag)

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library(neuralnet)

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library(class)

library(simmer)

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library(simmer.plot)

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library(parallel)
library(fpp)
library(xfun)

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library(tidyverse)

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library(ggcorrplot)

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library(dbplyr)

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library(tidyr)
library(ggplot2)
library(readxl)
library(readr)
library(purrr)
library(psych)
library(caret)
library(MASS)
library(pscl)
library(AER)

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library(naniar)

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library(reshape)

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library(kableExtra)

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library(knitr)

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library(cowplot)

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library(reshape2)

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library(corrgram)

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library(gridExtra)

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library(usdm)

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library(mice)
library(pROC)
library(reshape2)
library(caTools)

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library(caret)
library(ROCR)

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library(MASS)

mydata <- read_csv("~/College Documents/Boston College/LAD.csv")

## 
## -- Column specification --------------------------------------------------------
## cols(
##   Date = col_character(),
##   Day = col_double(),
##   `Adj Close` = col_double()
## )

lapply(mydata, as.numeric)

## Warning in lapply(mydata, as.numeric): NAs introduced by coercion

## $Date
##   [1] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
##  [26] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
##  [51] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
##  [76] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [101] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [126] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [151] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [176] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [201] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [226] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [251] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [276] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [301] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [326] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [351] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [376] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [401] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [426] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [451] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [476] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
## [501] NA NA NA NA NA
## 
## $Day
##   [1]   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18
##  [19]  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36
##  [37]  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54
##  [55]  55  56  57  58  59  60  61  62  63  64  65  66  67  68  69  70  71  72
##  [73]  73  74  75  76  77  78  79  80  81  82  83  84  85  86  87  88  89  90
##  [91]  91  92  93  94  95  96  97  98  99 100 101 102 103 104 105 106 107 108
## [109] 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126
## [127] 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144
## [145] 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162
## [163] 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180
## [181] 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198
## [199] 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216
## [217] 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234
## [235] 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252
## [253] 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270
## [271] 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288
## [289] 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306
## [307] 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324
## [325] 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342
## [343] 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360
## [361] 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378
## [379] 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396
## [397] 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414
## [415] 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432
## [433] 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450
## [451] 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468
## [469] 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486
## [487] 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504
## [505] 505
## 
## $`Adj Close`
##   [1] 155.60879 155.49028 157.75137 158.15619 158.12656 155.44092 155.03536
##   [8] 157.86461 159.65514 160.43663 159.83322 159.44739 159.13086 160.77301
##  [15] 161.06978 159.59580 158.55708 158.80438 161.72267 160.56526 161.92052
##  [22] 158.85387 157.58762 155.45084 155.38159 154.86717 158.23062 156.35104
##  [29] 157.20180 159.87279 161.82159 155.59921 152.50285 153.83835 157.19191
##  [36] 159.42761 156.58846 146.89380 147.25983 146.63658 146.89380 145.71660
##  [43] 145.41985 145.78584 144.54929 140.15701 141.19572 137.91142 137.40689
##  [50] 137.73335 141.83874 140.18669 139.55357 139.78110 141.84863 143.07530
##  [57] 140.24605 142.02670 136.40776 137.91142 139.81078 141.21553 141.38368
##  [64] 134.18195 138.29723 137.03098 140.38454 138.83141 132.01550 134.90407
##  [71] 138.60388 127.36601 129.46323 129.59183 128.40474 129.80946 129.63139
##  [78] 127.99913 126.76256 125.53590 123.17158 119.22446 117.87909 119.05630
##  [85] 115.18833 115.37629 113.74403 110.56854 102.73366 102.62484 100.68591
##  [92]  89.59340  94.65350  75.46482  74.81000  62.88405  67.96398  65.18589
##  [99]  69.96818  83.00536  87.37093  89.93074  82.81685  78.32230  81.14999
## [106]  72.47839  69.72013  66.57494  71.93268  73.82774  77.26067  83.25341
## [113]  83.91816  87.66858  85.97195  87.63882  95.18927  89.92082  87.26179
## [120]  94.66342  96.90572 103.55331 106.05357 111.65937 117.57273 109.69486
## [127] 107.28387 108.08753 106.14289 104.28751 106.09844 112.99389 109.62080
## [134] 103.47160  96.18810 103.36215 103.35221 115.62073 115.42173 115.11327
## [141] 118.13813 118.34708 121.12317 129.10318 121.63062 119.98885 122.14803
## [148] 127.98875 134.31705 135.44142 145.77965 142.90402 140.74486 137.02350
## [155] 124.04851 127.02361 134.26730 136.80461 137.65034 140.58565 141.70007
## [162] 148.20747 147.69005 142.79459 148.31691 142.50604 152.37660 150.57561
## [169] 154.17755 154.71487 157.17256 159.38148 159.61035 156.89395 163.95856
## [176] 160.06807 168.01822 174.11766 172.56545 172.58534 170.61522 173.91864
## [183] 209.64963 219.49034 227.52013 225.37089 221.91817 240.41550 231.63947
## [190] 228.00768 233.61955 235.39069 241.23143 241.29112 240.02745 238.24638
## [197] 245.29109 257.67899 258.31656 257.47977 265.06091 272.36313 260.51822
## [204] 259.23312 260.52817 261.50443 265.72833 252.87729 248.39435 246.63109
## [211] 248.01582 257.34030 256.80237 245.19655 242.18799 239.95648 246.85023
## [218] 242.60640 238.33266 242.89529 240.33502 236.13104 234.22827 227.94222
## [225] 221.83546 227.62343 224.67465 220.74959 217.36249 227.45407 222.10445
## [232] 227.07552 245.83412 270.48032 281.10980 268.06946 282.71371 279.94428
## [239] 282.54434 269.43426 265.81802 265.30997 275.99927 273.72787 265.96747
## [246] 259.04382 259.10358 249.20128 249.39056 240.38484 235.85211 232.60446
## [253] 231.32933 228.69934 238.47214 248.23497 254.33176 264.09460 261.63394
## [260] 257.84833 266.86408 265.35977 259.47531 265.33984 265.27002 268.75079
## [267] 273.38855 280.70926 280.89877 292.28870 307.81775 301.07553 301.68390
## [274] 288.53857 299.05087 289.56589 292.37845 293.91440 293.05667 290.62311
## [281] 278.52502 271.83267 269.97760 268.85055 280.45993 286.98270 294.78213
## [288] 283.62155 285.53650 278.54498 287.69086 289.24676 294.76218 283.35226
## [295] 292.43832 291.89975 283.49191 294.00418 312.22611 318.97827 316.95361
## [302] 318.34992 323.55621 315.02869 321.40186 308.80514 306.29175 326.30896
## [309] 329.66010 337.14035 338.26740 341.81802 319.17773 318.87854 317.84128
## [316] 335.14563 336.48209 337.55926 357.28720 368.27820 377.05505 389.82135
## [323] 368.03882 372.80624 381.57309 372.39731 370.35269 369.78421 379.68808
## [330] 369.76425 369.51492 386.13104 370.00366 372.96585 378.20200 373.51437
## [337] 373.72382 357.02789 374.47183 376.82565 373.99310 395.12732 397.54288
## [344] 395.18723 399.25967 403.80124 413.35352 399.51920 394.66818 382.29114
## [351] 370.79245 361.21024 372.20981 377.23050 373.61722 398.97021 389.36801
## [358] 397.81232 390.86523 381.97171 387.10223 393.09112 398.68076 402.08441
## [365] 387.20206 391.48407 392.73175 387.31183 386.60315 374.09634 383.43899
## [372] 381.49264 389.97690 386.47339 396.68445 394.84784 386.63309 383.66858
## [379] 389.49777 389.31811 380.49448 379.96497 379.57532 368.73544 365.38858
## [386] 350.39261 359.89374 369.03519 365.74823 355.91742 329.46213 338.42377
## [393] 357.89560 347.26550 348.23462 357.18625 357.77567 351.66141 356.45694
## [400] 348.17465 338.06412 337.20490 334.99698 334.64731 327.98355 327.54395
## [407] 333.67819 330.62106 338.63361 334.68726 323.89737 312.84769 322.00912
## [414] 324.94638 324.26700 329.49210 341.43097 335.04691 336.49557 343.31921
## [421] 352.88025 348.34451 342.33011 343.70883 344.66794 358.64490 361.05264
## [428] 354.77847 356.66672 348.89398 340.60175 335.48651 355.22806 370.78354
## [435] 375.01956 379.38550 372.13229 372.96152 374.70987 381.16382 376.86786
## [442] 374.33023 364.71921 357.66580 369.45477 364.71921 362.74103 369.75452
## [449] 374.57999 375.17001 375.16000 375.64002 339.23001 339.60998 333.78000
## [456] 328.51001 335.87000 341.87000 341.42999 333.51001 334.51001 327.53000
## [463] 331.29999 335.45001 326.44000 325.82001 318.89999 325.62000 332.10998
## [470] 331.76001 325.79001 319.29001 322.51999 339.64999 337.07999 328.53000
## [477] 325.48001 335.82001 340.92999 345.20001 351.88000 343.84000 345.76001
## [484] 317.04001 317.67001 314.57001 312.00000 310.47000 323.48001 326.60001
## [491] 320.23999 330.00000 330.29001 337.23999 337.20999 338.44000 338.70999
## [498] 342.01001 337.38000 338.37000 335.91000 327.20001 317.19000 317.48001
## [505] 319.22000

mdl1 <- auto.arima(mydata$'Adj Close', ic = "aic")
plot(forecast(mdl1))

linearMod <- lm(mydata$Day ~ mydata$`Adj Close`, data=mydata)
print(linearMod)

## 
## Call:
## lm(formula = mydata$Day ~ mydata$`Adj Close`, data = mydata)
## 
## Coefficients:
##        (Intercept)  mydata$`Adj Close`  
##            -64.647               1.265

summary(linearMod)

## 
## Call:
## lm(formula = mydata$Day ~ mydata$`Adj Close`, data = mydata)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -131.858  -51.946   -7.465   51.375  167.136 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        -64.64665    8.19794  -7.886 1.96e-14 ***
## mydata$`Adj Close`   1.26468    0.03026  41.795  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 69.07 on 503 degrees of freedom
## Multiple R-squared:  0.7764, Adjusted R-squared:  0.776 
## F-statistic:  1747 on 1 and 503 DF,  p-value: < 2.2e-16

#The model provides the following regression: Adj Close = 1.26468 * (Days) -64.64665 Adj Close = Close value of stock Days = Number of Days since 10/30/2019