ADEC 7460 Final

Install Packages

# Clear the workspace
rm(list = ls()) # Clear environment
gc()            # Clear unused memory
cat("\f")       # Clear the console

library("feasts")
library("seasonal")
library("tsibble")
library("tsibbledata")
library("dplyr")
library("ggplot2")
library("forecast")
library("fable")
library("weathermetrics")
library("seasonalview")
library("tibbletime")
library("fpp3")
library("fma")
library("fpp")
library("fpp2")
library("grid")
library("gridExtra")
library("lubridate")
library("seasonal")
library("zoo")
library("psych")
library("wesanderson")
library("leaflet")

setwd("/Users/spoll/OneDrive/Documents/Boston College/Predictive Analytics_Forecasting/Week 8 Final")

Load Data

raw_reserve <- read.csv("air_reserve.csv"
                           , check.names = FALSE
                           , stringsAsFactors = FALSE
                           , na.strings = ""
)

raw_visit <- read.csv("air_visit_data.csv"
                           , check.names = FALSE
                           , stringsAsFactors = FALSE
                           , na.strings = ""
)

raw_store <- read.csv("air_store_info.csv"
                           , check.names = FALSE
                           , stringsAsFactors = FALSE
                           , na.strings = ""
)

raw_date <- read.csv("date_info.csv"
                           , check.names = FALSE
                           , stringsAsFactors = FALSE
                           , na.strings = ""
)

raw_hpg_reserve <- read.csv("hpg_reserve.csv"
                           , check.names = FALSE
                           , stringsAsFactors = FALSE
                           , na.strings = ""
)

raw_hpg_store <- read.csv("hpg_store_info.csv"
                           , check.names = FALSE
                           , stringsAsFactors = FALSE
                           , na.strings = ""
)

store_id_relation <- read.csv("store_id_relation.csv"
                           , check.names = FALSE
                           , stringsAsFactors = FALSE
                           , na.strings = ""
)

sample <- read.csv("sample_submission.csv"
                           , check.names = FALSE
                           , stringsAsFactors = FALSE
                           , na.strings = ""
)

# sample$id <- gsub("[_]", " ", sample$id)
# sample <- sample %>% separate(id, c('system', 'id', 'date'), pattern )
# sample1 <- separate(sample, id, c('system', 'id', 'date'), sep = " ")
# sample <- sample1 %>% 
#   dplyr::select("date", "visitors")
# sample$date <- as.Date(sample$date)
# sample <- sample %>% distinct(.keep_all = TRUE)
# sample_ts <- ts(sample, frequency = 12)

Summary of Data

summary(raw_reserve)

##  air_store_id       visit_datetime     reserve_datetime   reserve_visitors 
##  Length:92378       Length:92378       Length:92378       Min.   :  1.000  
##  Class :character   Class :character   Class :character   1st Qu.:  2.000  
##  Mode  :character   Mode  :character   Mode  :character   Median :  3.000  
##                                                           Mean   :  4.482  
##                                                           3rd Qu.:  5.000  
##                                                           Max.   :100.000

summary(raw_visit)

##  air_store_id        visit_date           visitors     
##  Length:252108      Length:252108      Min.   :  1.00  
##  Class :character   Class :character   1st Qu.:  9.00  
##  Mode  :character   Mode  :character   Median : 17.00  
##                                        Mean   : 20.97  
##                                        3rd Qu.: 29.00  
##                                        Max.   :877.00

summary(raw_store)

##  air_store_id       air_genre_name     air_area_name         latitude    
##  Length:829         Length:829         Length:829         Min.   :33.21  
##  Class :character   Class :character   Class :character   1st Qu.:34.70  
##  Mode  :character   Mode  :character   Mode  :character   Median :35.66  
##                                                           Mean   :35.65  
##                                                           3rd Qu.:35.69  
##                                                           Max.   :44.02  
##    longitude    
##  Min.   :130.2  
##  1st Qu.:135.3  
##  Median :139.7  
##  Mean   :137.4  
##  3rd Qu.:139.8  
##  Max.   :144.3

summary(raw_date)

##  calendar_date      day_of_week         holiday_flg    
##  Length:517         Length:517         Min.   :0.0000  
##  Class :character   Class :character   1st Qu.:0.0000  
##  Mode  :character   Mode  :character   Median :0.0000  
##                                        Mean   :0.0677  
##                                        3rd Qu.:0.0000  
##                                        Max.   :1.0000

summary(raw_hpg_reserve)

##  hpg_store_id       visit_datetime     reserve_datetime   reserve_visitors 
##  Length:1048575     Length:1048575     Length:1048575     Min.   :  1.000  
##  Class :character   Class :character   Class :character   1st Qu.:  2.000  
##  Mode  :character   Mode  :character   Mode  :character   Median :  3.000  
##                                                           Mean   :  4.889  
##                                                           3rd Qu.:  6.000  
##                                                           Max.   :100.000

summary(raw_hpg_store)

##  hpg_store_id       hpg_genre_name     hpg_area_name         latitude    
##  Length:4690        Length:4690        Length:4690        Min.   :33.31  
##  Class :character   Class :character   Class :character   1st Qu.:34.69  
##  Mode  :character   Mode  :character   Mode  :character   Median :35.66  
##                                                           Mean   :35.81  
##                                                           3rd Qu.:35.70  
##                                                           Max.   :43.77  
##    longitude    
##  Min.   :130.3  
##  1st Qu.:135.5  
##  Median :139.5  
##  Mean   :137.7  
##  3rd Qu.:139.7  
##  Max.   :143.7

summary(store_id_relation)

##  air_store_id       hpg_store_id      
##  Length:150         Length:150        
##  Class :character   Class :character  
##  Mode  :character   Mode  :character

Descriptive Statistics About the Data

describe(raw_reserve)

##                   vars     n    mean      sd median trimmed     mad min  max
## air_store_id*        1 92378  151.34   92.55    147  150.44  121.57   1  314
## visit_datetime*      2 92378 2958.96 1188.51   3079 3054.18 1214.25   1 4975
## reserve_datetime*    3 92378 4806.34 1942.51   5075 5004.60 1752.43   1 7513
## reserve_visitors     4 92378    4.48    4.92      3    3.39    1.48   1  100
##                   range  skew kurtosis   se
## air_store_id*       313  0.10    -1.30 0.30
## visit_datetime*    4974 -0.60    -0.39 3.91
## reserve_datetime*  7512 -0.80    -0.19 6.39
## reserve_visitors     99  4.65    33.52 0.02

describe(raw_visit)

##               vars      n   mean     sd median trimmed    mad min max range
## air_store_id*    1 252108 413.70 239.70    407  413.21 309.86   1 829   828
## visit_date*      2 252108 239.75 142.68    227  238.40 186.81   1 478   477
## visitors         3 252108  20.97  16.76     17   18.82  13.34   1 877   876
##               skew kurtosis   se
## air_store_id* 0.02    -1.21 0.48
## visit_date*   0.13    -1.30 0.28
## visitors      3.31    74.26 0.03

describe(raw_store)

##                 vars   n   mean     sd median trimmed    mad    min    max
## air_store_id*      1 829 415.00 239.46 415.00  415.00 306.90   1.00 829.00
## air_genre_name*    2 829   6.26   3.13   7.00    6.02   2.97   1.00  14.00
## air_area_name*     3 829  54.10  31.14  58.00   54.90  43.00   1.00 103.00
## latitude           4 829  35.65   2.08  35.66   35.26   0.10  33.21  44.02
## longitude          5 829 137.42   3.65 139.69  137.82   0.20 130.20 144.27
##                  range  skew kurtosis   se
## air_store_id*   828.00  0.00    -1.20 8.32
## air_genre_name*  13.00  0.45    -0.41 0.11
## air_area_name*  102.00 -0.17    -1.34 1.08
## latitude         10.81  2.65     7.44 0.07
## longitude        14.08 -0.93    -0.55 0.13

describe(raw_date)

##                vars   n   mean     sd median trimmed    mad min max range skew
## calendar_date*    1 517 259.00 149.39    259     259 191.26   1 517   516 0.00
## day_of_week*      2 517   4.00   2.00      4       4   2.97   1   7     6 0.00
## holiday_flg       3 517   0.07   0.25      0       0   0.00   0   1     1 3.43
##                kurtosis   se
## calendar_date*    -1.21 6.57
## day_of_week*      -1.26 0.09
## holiday_flg        9.79 0.01

describe(raw_hpg_reserve)

##                   vars       n    mean      sd median trimmed     mad min   max
## hpg_store_id*        1 1048575 6382.07 3674.70   6387 6385.96 4722.08   1 12721
## visit_datetime*      2 1048575 3210.05 1954.17   3043 3176.60 2612.34   1  6582
## reserve_datetime*    3 1048575 4044.90 2325.80   4032 4041.95 3089.74   1  7998
## reserve_visitors     4 1048575    4.89    5.09      3    3.81    1.48   1   100
##                   range  skew kurtosis   se
## hpg_store_id*     12720 -0.01    -1.21 3.59
## visit_datetime*    6581  0.13    -1.30 1.91
## reserve_datetime*  7997  0.01    -1.25 2.27
## reserve_visitors     99  4.72    38.61 0.00

describe(raw_hpg_store)

##                 vars    n    mean      sd  median trimmed     mad    min
## hpg_store_id*      1 4690 2345.50 1354.03 2345.50 2345.50 1738.35   1.00
## hpg_genre_name*    2 4690   14.85    5.08   16.00   14.65    5.93   1.00
## hpg_area_name*     3 4690   66.05   35.10   70.00   67.16   45.96   1.00
## latitude           4 4690   35.81    2.14   35.66   35.38    1.01  33.31
## longitude          5 4690  137.68    3.20  139.50  138.09    0.78 130.34
##                     max   range  skew kurtosis    se
## hpg_store_id*   4690.00 4689.00  0.00    -1.20 19.77
## hpg_genre_name*   34.00   33.00  0.41     0.47  0.07
## hpg_area_name*   119.00  118.00 -0.19    -1.21  0.51
## latitude          43.77   10.46  2.50     6.04  0.03
## longitude        143.71   13.38 -0.98    -0.14  0.05

describe(store_id_relation)

##               vars   n mean    sd median trimmed  mad min max range skew
## air_store_id*    1 150 75.5 43.45   75.5    75.5 55.6   1 150   149    0
## hpg_store_id*    2 150 75.5 43.45   75.5    75.5 55.6   1 150   149    0
##               kurtosis   se
## air_store_id*    -1.22 3.55
## hpg_store_id*    -1.22 3.55

Reformat Dates

raw_visit <- as.data.frame(raw_visit)
raw_visit$visit_date <- mdy(raw_visit$visit_date)
class(raw_visit$visit_date)

## [1] "Date"

visit <- raw_visit %>%
  mutate(month = month(visit_date, label = TRUE)) %>%
  mutate(wday = wday(visit_date, label = TRUE))
unique(raw_reserve$air_store_id)

##   [1] "air_877f79706adbfb06" "air_db4b38ebe7a7ceff" "air_db80363d35f10926"
##   [4] "air_3bb99a1fe0583897" "air_2b8b29ddfd35018e" "air_6b15edd1b4fbb96a"
##   [7] "air_789466e488705c93" "air_f690c42545146e0a" "air_326ca454ef3558bc"
##  [10] "air_6c91a28278a16f64" "air_e270aff84ac7e4c8" "air_a083834e7ffe187e"
##  [13] "air_ee3a01f0c71a769f" "air_24b9b2a020826ede" "air_142e78ba7001da9c"
##  [16] "air_1653a6c513865af3" "air_2d3afcb91762fe01" "air_54ed43163b7596c4"
##  [19] "air_6d65542aa43b598b" "air_f911308e19d64236" "air_290e7a57b390f78e"
##  [22] "air_622375b4815cf5cb" "air_de692863bb2dd758" "air_b9e27558fb8bd5c4"
##  [25] "air_614e2f7e76dff854" "air_63e28ee0b0c955a7" "air_2a3743e37aab04b4"
##  [28] "air_670a0c1c4108bcea" "air_2cee51fa6fdf6c0d" "air_c8a657c8c5c93d69"
##  [31] "air_e55abd740f93ecc4" "air_2aab19554f91ff82" "air_3c05c8f26c611eb9"
##  [34] "air_3cad29d1a23209d2" "air_8093d0b565e9dbdf" "air_96743eee94114261"
##  [37] "air_632ba66e1f75aa28" "air_6b9fa44a9cf504a1" "air_7831b00996701c0f"
##  [40] "air_03963426c9312048" "air_4cca5666eaf5c709" "air_9d93d95720f2e831"
##  [43] "air_68c1de82037d87e6" "air_32460819c7600037" "air_346ade7d29230634"
##  [46] "air_c2c8435bdb3516d4" "air_c73d319ffabf287a" "air_5e70fe82f9e4fab6"
##  [49] "air_a563896da3777078" "air_f96765e800907c77" "air_fe22ef5a9cbef123"
##  [52] "air_f068442ebb6c246c" "air_0e1eae99b8723bc1" "air_9d452a881f7f2bb7"
##  [55] "air_81c5dff692063446" "air_87f9e1024b951f01" "air_0b184ec04c741a6a"
##  [58] "air_4ce7b17062a1bf73" "air_2c989829acbd1c6b" "air_61de73b097513f58"
##  [61] "air_673acd9fa5e0dd78" "air_97159fc4e90053fe" "air_63a750d8b4b6a976"
##  [64] "air_2a485b92210c98b5" "air_5c817ef28f236bdf" "air_68301bcb11e2f389"
##  [67] "air_b4f32bcc399da2b9" "air_bfafaed35e213fd7" "air_722297e7f26db91d"
##  [70] "air_082908692355165e" "air_9241121af22ff1d6" "air_c759b6abeb552160"
##  [73] "air_48e9fc98b62495a7" "air_37189c92b6c761ec" "air_9352c401d5adb01b"
##  [76] "air_35512c42db0868da" "air_683371d9baabf410" "air_7cc17a324ae5c7dc"
##  [79] "air_70e9e8cd55879414" "air_fbadf737162a5ce3" "air_234d3dbf7f3d5a50"
##  [82] "air_ef789667e2e6fe96" "air_1033310359ceeac1" "air_483eba479dc9910d"
##  [85] "air_f2c5a1f24279c531" "air_a55d17bd3f3033cb" "air_ab3ae0e410b20069"
##  [88] "air_54d6c25d33f5260e" "air_5f3a3ef4cba110a4" "air_cb7467aed805e7fe"
##  [91] "air_0a74a5408a0b8642" "air_2fc478dc9f0a6b31" "air_0f0cdeee6c9bf3d7"
##  [94] "air_1408dd53f31a8a65" "air_396166d47733d5c9" "air_56cebcbd6906e04c"
##  [97] "air_5f6fa1b897fe80d5" "air_bc991c51d6613745" "air_375a5241615b5e22"
## [100] "air_48f4da6223571da4" "air_7ef9a5ea5c8fe39f" "air_97cf68dc1a9beac0"
## [103] "air_b45b8e456f53942a" "air_e0e69668214ff972" "air_eec5e572b9eb9c23"
## [106] "air_b23d0f519291247d" "air_a510dcfe979f09eb" "air_93b9bb641f8fc982"
## [109] "air_b2d97bd2337c5ba7" "air_8b4a46dc521bfcfe" "air_324f7c39a8410e7c"
## [112] "air_646b93e336f0dded" "air_a24bf50c3e90d583" "air_bebd55ed63ab2422"
## [115] "air_aed3a8b49abe4a48" "air_bb4ff06cd661ee9b" "air_256be208a979e023"
## [118] "air_5485912b44f976de" "air_ab9746a0f83084b7" "air_a546cbf478a8b6e4"
## [121] "air_4b55d8aea1d2b395" "air_965b2e0cf4119003" "air_cf5ab75a0afb8af9"
## [124] "air_42c9aa6d617c5057" "air_45326ebb8dc72cfb" "air_4c727b55acdee495"
## [127] "air_b439391e72899756" "air_9b6af3db40da4ae2" "air_9ca2767761efff4d"
## [130] "air_9efaa7ded03c5a71" "air_af63df35857b16e6" "air_bedd35489e666605"
## [133] "air_c88467d88b2c8ecd" "air_0867f7bebad6a649" "air_1707a3f18bb0da07"
## [136] "air_1eeff462acb24fb7" "air_1f34e9beded2231a" "air_20add8092c9bb51d"
## [139] "air_25c583983246b7b0" "air_397d3f32a7196aa2" "air_3e93f3c81008696d"
## [142] "air_4092cfbd95a3ac1b" "air_43b65e4b05bff2d3" "air_5acc13d655a6e8b2"
## [145] "air_640cf4835f0d9ba3" "air_67f87c159d9e2ee2" "air_6ff5fca957798daa"
## [148] "air_707d4b6328f2c2df" "air_7db266904cb0d72a" "air_84f6876ff7e83ae7"
## [151] "air_a88ac559064dec08" "air_b2395df0e874078d" "air_b8a5ee69e5fdcc5b"
## [154] "air_c0385db498b391e5" "air_c47aa7493b15f297" "air_c6a164dd4060e960"
## [157] "air_c7f78b4f3cba33ff" "air_ccd19a5bc5573ae5" "air_d6b3e67261f07646"
## [160] "air_db1233ad855b34d5" "air_de803f7e324936b8" "air_e053c561f32acc28"
## [163] "air_ee3ba9af184c6c82" "air_f180301886c21375" "air_fa12b40b02fecfd8"
## [166] "air_04cae7c1bc9b2a0b" "air_12c4fb7a423df20d" "air_40f6193ea3ed1b91"
## [169] "air_465bddfed3353b23" "air_710d6537cb7623df" "air_7dacea2f22afccfb"
## [172] "air_90213bcae4afa274" "air_97b2a9f975fc702c" "air_9aa32b3db0fab3a5"
## [175] "air_9d474ec2448c700d" "air_a2b29aa7feb4e36f" "air_a38f25e3399d1b25"
## [178] "air_ca6ae8d49a2f1eaf" "air_e89735e80d614a7e" "air_f8233ad00755c35c"
## [181] "air_fea5dc9594450608" "air_de88770300008624" "air_dea0655f96947922"
## [184] "air_2c6fef1ce0e13a5a" "air_399904bdb7685ca0" "air_4beac252540f865e"
## [187] "air_6b942d5ebbc759c2" "air_b1bb1fae86617d7a" "air_bb09595bab7d5cfb"
## [190] "air_0b1e72d2d4422b20" "air_602ca92c0db34f8f" "air_3c938075889fc059"
## [193] "air_066f0221b8a4d533" "air_08cb3c4ee6cd6a22" "air_26f10355d9b4d82a"
## [196] "air_08ef81d5b7a0d13f" "air_36429b5ca4407b3e" "air_4481a87c1d7c9896"
## [199] "air_4d21676ed11f0bac" "air_5a9a6cbeeb434c08" "air_8f3b563416efc6ad"
## [202] "air_938ef91ecdde6878" "air_bcce1ea4350b7b72" "air_ecf7f141339f1d57"
## [205] "air_edd5e3d696a5811b" "air_138ff410757b845f" "air_28064154614b2e6c"
## [208] "air_3440e0ea1b70a99b" "air_0164b9927d20bcc3" "air_1c0b150f9e696a5f"
## [211] "air_6836438b543ba698" "air_83db5aff8f50478e" "air_89e7328af22efe74"
## [214] "air_90f0efbb702d77b7" "air_af03c277a167b2bd" "air_7514d90009613cd6"
## [217] "air_c225148c0fcc5c72" "air_23e1b11aee2a1407" "air_034a3d5b40d5b1b1"
## [220] "air_a257c9749d8d0ff6" "air_d1418d6fd6d634f2" "air_51281cd059d7b89b"
## [223] "air_e5cf003abcc5febb" "air_33b01025210d6007" "air_42d41eb58cad170e"
## [226] "air_4579cb0669fd411b" "air_6b2268863b14a2af" "air_754ae581ad80cc9f"
## [229] "air_b8925441167c3152" "air_fc477473134e9ae5" "air_627cabe2fe53f33f"
## [232] "air_6cbe54f0aa30b615" "air_dc71c6cc06cd1aa2" "air_bf617aa68d5f1cfa"
## [235] "air_c3585b0fba3998d0" "air_00a91d42b08b08d9" "air_831658500aa7c846"
## [238] "air_2bffb19a24d11729" "air_a9178f19da58fe99" "air_96773a6236d279b1"
## [241] "air_7420042ff75f9aca" "air_04341b588bde96cd" "air_1ba4e87ef7422183"
## [244] "air_3980af67be35afdb" "air_99b01136f451fc0e" "air_6ca1d941c8199a67"
## [247] "air_d500b48a8735fbd3" "air_258ad2619d7bff9a" "air_cfcc94797d2b5d3d"
## [250] "air_df554c4527a1cfe6" "air_91beafbba9382b0a" "air_7c7774c66fb237f7"
## [253] "air_a85f0c0c889f6b7e" "air_8e492076a1179383" "air_859feab8e3c9f98d"
## [256] "air_8f273fb9ad2fed6f" "air_1d1e8860ae04f8e9" "air_a17f0778617c76e2"
## [259] "air_084d98859256acf0" "air_32b02ba5dc2027f4" "air_1dd8f6f47480d1a2"
## [262] "air_df9355c47c5df9d3" "air_48ffd31594bc3263" "air_fdc02ec4a3d21ea4"
## [265] "air_6ced51c24fb54262" "air_645cb18b33f938cf" "air_fcfbdcf7b1f82c6e"
## [268] "air_55c3627912b9c849" "air_fcd4492c83f1c6b9" "air_e524c6a9e06cc3a1"
## [271] "air_638c35eb25e53eea" "air_4433ab8e9999915f" "air_e00fe7853c0100d6"
## [274] "air_876d7a23c47811cb" "air_15ae33469e9ea2dd" "air_c8265ecc116f2284"
## [277] "air_a9133955abccf071" "air_ade6e836ffd1da64" "air_96005f79124e12bf"
## [280] "air_950381108f839348" "air_e7fbee4e3cfe65c5" "air_eca4a5a191e8d993"
## [283] "air_97958e7fce98b6a3" "air_d477b6339b8ce69f" "air_87467487d21891dd"
## [286] "air_5bd22f9cc1426a90" "air_694571ea13fb9e0e" "air_51319e7acf0438cf"
## [289] "air_883ca28ef0ed3d55" "air_900d755ebd2f7bbd" "air_fee8dcf4d619598e"
## [292] "air_06f95ac5c33aca10" "air_8cc350fd70ee0757" "air_d07e57b21109304a"
## [295] "air_629d9935273c82ae" "air_8110d68cc869b85e" "air_28dbe91c4c9656be"
## [298] "air_63b13c56b7201bd9" "air_e01d99390355408d" "air_93ebe490d4abb8e9"
## [301] "air_6b65745d432fd77f" "air_2c6c79d597e48096" "air_1f1390a8be2272b3"
## [304] "air_cbe867adcf44e14f" "air_10bbe8acd943d8f6" "air_e657ca554b0c008c"
## [307] "air_97e0f2feec4d577a" "air_cc35590cd1da8554" "air_4de6d887a7b1c1fc"
## [310] "air_b60cc7d6aee68194" "air_f0fb0975bdc2cdf9" "air_b3a824511477a4ed"
## [313] "air_cf2229e64408d9fe" "air_e700e390226d9985"

Create a Time Series For Air Data

# Air Agg Time Series
air_agg <- aggregate(reserve_visitors ~ visit_datetime
                     , data = raw_reserve
                     , FUN = sum)
air_agg$date <- as.Date(air_agg$visit_datetime)

air_agg <- air_agg %>%  
  dplyr::select("date", "reserve_visitors")
class(air_agg$date)

## [1] "Date"

air_agg <- aggregate(reserve_visitors ~ date
                     , data = air_agg
                     , FUN = sum)
air_agg2 <- head(raw_visit, nrow(raw_visit)-220089) %>% 
  dplyr::select("visit_date", "visitors")
store_id2 <- head(raw_visit, nrow(raw_visit)-220089) %>% 
  dplyr::select("air_store_id")

air_ts <- ts(air_agg)

summary(air_ts[,"reserve_visitors"])

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##     2.0   245.0   587.0   956.2  1303.0  4742.0

air_plot <- autoplot(air_ts[,"reserve_visitors"]) + 
  labs(title="Air visitors Time Series") + 
  ylab("visitors") +
  theme(plot.title = element_text(hjust = 0.5))

air_agg <- head(air_agg, nrow(air_agg)-20) %>% 
  dplyr::select("date", "reserve_visitors")

air_test <- tail(air_agg, 20) %>%  
  dplyr::select("date", "reserve_visitors")
air_test_ts <- ts(air_test$reserve_visitors, frequency = 365)

Create a Time Series For HPG Data

# HPG Agg Time Series
hpg_agg <- aggregate(reserve_visitors ~ visit_datetime
                     , data = raw_hpg_reserve
                     , FUN = sum)
hpg_agg$date <- as.Date(hpg_agg$visit_datetime)

hpg_agg <- hpg_agg %>%  
  dplyr::select("date", "reserve_visitors")
class(hpg_agg$date)

## [1] "Date"

hpg_agg <- aggregate(reserve_visitors ~ date
                     , data = hpg_agg
                     , FUN = sum)
hpg_ts <- ts(hpg_agg)

summary(hpg_ts[,"reserve_visitors"])

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##     493    8094   10270   13153   19673   31062

hpg_plot <- autoplot(hpg_ts[,"reserve_visitors"]) + 
  labs(title="HPG visitors Time Series") + 
  ylab("visitors") +
  theme(plot.title = element_text(hjust = 0.5))

Create a Univariate Time Series For Air Data

# UNIVARIATE TIME SERIES-----------------------------------------
# Air Univariate Time Series
air_ts2 <- ts(subset(air_agg
                          , select = "reserve_visitors")
                   , frequency = 2)
air_uts <- ts(subset(air_agg2
                          , select = "visitors")
                   , frequency = 2)

air_decomp_add <- decompose(air_ts2, type = "additive")
air_decomp_mult <- decompose(air_ts2, type = "multiplicative")
plot(air_decomp_add)

plot(air_decomp_mult)

ggtsdisplay(air_ts2) #confirmed diagnostics

Create a Univariate Time Series For HPG Data

# HPG Univariate Time Series
hpg_ts2 <- ts(subset(hpg_agg
                          , select = "reserve_visitors")
                   , frequency = 2)

hpg_decomp_add <- decompose(hpg_ts2, type = "additive")
hpg_decomp_mult <- decompose(hpg_ts2, type = "multiplicative")
plot(hpg_decomp_add)

plot(hpg_decomp_mult)

ggtsdisplay(hpg_ts2) #confirmed diagnostics

Data Exploration and Visualizations

visitplot <- plot(visitors ~  visit_date
     , data = raw_visit
     , main="Time Series of Air Visitors"
     , xlab="Date"
     , ylab="Number of Visitors"
     , col="red")

wkday_visits <- raw_visit %>%
  mutate(day = wday(visit_date
                     , label = TRUE)) %>%
  group_by(day) %>%
  summarise(visits = mean(visitors)) %>%
  ggplot(aes(day, visits
             , fill = day)) +
  geom_col(colour="black") + 
  labs(main = "Visits per Day"
       , x = "Day"
       , y = "Visits") +
  scale_fill_manual(values=wes_palette(n=12
                                       , name="GrandBudapest1"
                                       , type = "continuous"))

wkday_visits

monthly_visits <- raw_visit %>%
  mutate(month = month(visit_date
                       , label = TRUE)) %>%
  group_by(month) %>%
  summarise(visits = mean(visitors)) %>%
  ggplot(aes(month
             , visits
             , fill = month)) +
  geom_col(colour="black") +
  labs(x = "Month"
       , y = "Visits"
       , main="Visits Per Month") +
  scale_fill_manual(values=wes_palette(n=12
                                       , name="GrandBudapest1"
                                       , type = "continuous"))

monthly_visits

leaflet(raw_store) %>%
  addTiles() %>%
  addProviderTiles("CartoDB.Positron") %>%
  addMarkers(~longitude, ~latitude,
             popup = ~air_store_id, label = ~air_genre_name,
             clusterOptions = markerClusterOptions())

raw_hpg_store %>%
    group_by(hpg_genre_name) %>%
    summarise(total = n()) %>%
    ggplot(aes(reorder(hpg_genre_name
                       , total
                       , FUN = min)
               , total
               , fill = hpg_genre_name))  + 
    geom_col() + 
    coord_flip() + 
    theme(legend.position = "none") +
    scale_fill_manual(values=wes_palette(n=34
                                         , name="GrandBudapest1"
                                         , type = "continuous")) +
    ylab("Restaurant Style")

Time Series Plots

# Combine Time Series Plots
grid.arrange(air_plot, hpg_plot, nrow = 2)

Air Linear Regressions

# LINEAR REGRESSIONS ---------------------
# Air Reservation Linear Regression
air_lm <- tslm(reserve_visitors ~ date
                    , data = air_ts)

air_lm_plot <- autoplot(air_ts[,"reserve_visitors"], 
                             main = "Air visitors Linear Regression") + 
  autolayer(fitted(air_lm)
            , series = "Fitted Linear Regression") +
  ylab("visitors") +
  theme(plot.title = element_text(hjust = 0.5))

checkresiduals(air_lm)

## 
##  Breusch-Godfrey test for serial correlation of order up to 10
## 
## data:  Residuals from Linear regression model
## LM test = 321.56, df = 10, p-value < 2.2e-16

HPG Linear Regression

# Air Linear Regression
hpg_lm <- tslm(reserve_visitors ~ date
                    , data = hpg_ts)

hpg_lm_plot <- autoplot(hpg_ts[,"reserve_visitors"], 
                             main = "HPG visitors Linear Regression") + 
  autolayer(fitted(hpg_lm)
            , series = "Fitted Linear Regression") +
  ylab("visitors") +
  theme(plot.title = element_text(hjust = 0.5))

checkresiduals(hpg_lm)

## 
##  Breusch-Godfrey test for serial correlation of order up to 10
## 
## data:  Residuals from Linear regression model
## LM test = 44.971, df = 10, p-value = 2.201e-06

# Combine Linear Reg Plots
grid.arrange(air_lm_plot, hpg_lm_plot, nrow = 2)

Linear Regression Forecasts

newdata <- data.frame(date = c(141:150))
forecast(air_lm, newdata = newdata)

##     Point Forecast     Lo 80     Hi 80     Lo 95     Hi 95
## 434      -49174.97 -54717.91 -43632.03 -57663.01 -40686.94
## 435      -49172.01 -54714.63 -43629.39 -57659.56 -40684.46
## 436      -49169.05 -54711.36 -43626.74 -57656.12 -40681.98
## 437      -49166.08 -54708.08 -43624.09 -57652.67 -40679.50
## 438      -49163.12 -54704.80 -43621.44 -57649.23 -40677.01
## 439      -49160.16 -54701.52 -43618.79 -57645.78 -40674.53
## 440      -49157.20 -54698.24 -43616.15 -57642.34 -40672.05
## 441      -49154.23 -54694.97 -43613.50 -57638.89 -40669.57
## 442      -49151.27 -54691.69 -43610.85 -57635.45 -40667.09
## 443      -49148.31 -54688.41 -43608.20 -57632.00 -40664.61

forecast(hpg_lm, newdata = newdata)

##     Point Forecast    Lo 80   Hi 80    Lo 95   Hi 95
## 133        1479089 993299.1 1964878 732967.9 2225209
## 134        1479091 993300.5 1964881 732968.9 2225212
## 135        1479093 993301.8 1964883 732969.9 2225215
## 136        1479095 993303.2 1964886 732970.9 2225218
## 137        1479097 993304.6 1964889 732971.9 2225222
## 138        1479099 993305.9 1964892 732972.9 2225225
## 139        1479101 993307.3 1964894 732973.9 2225228
## 140        1479103 993308.7 1964897 732974.9 2225231
## 141        1479105 993310.0 1964900 732975.9 2225234
## 142        1479107 993311.4 1964902 732976.9 2225237

air_lm_acc <- accuracy(air_lm)
hpg_lm_acc <- accuracy(hpg_lm)

Air Holt-Winters’

# HOLT-WINTERS' ---------------------------
# HOLT-WINTERS' AIR visitors
air_hw <- hw(air_ts2, seasonal = "additive")
air_hw2 <- hw(air_ts2, seasonal = "multiplicative")

air_hw_plot <- autoplot(air_ts2, 
                              main = "Air visitors Holt-Winters'") + 
  autolayer(fitted(air_hw), series = "Fitted Additive") +
  autolayer(fitted(air_hw2), series = "Fitted Multiplicative") +
  ylab("Air visitors") +
  theme(plot.title = element_text(hjust = 0.5))

HPG Holt-Winters’

# HOLT-WINTERS' HPG visitors
hpg_hw <- hw(hpg_ts2, seasonal = "additive")
hpg_hw2 <- hw(hpg_ts2, seasonal = "multiplicative")

hpg_hw_plot <- autoplot(hpg_ts2, 
                              main = "HPG visitors Holt-Winters'") + 
  autolayer(fitted(hpg_hw), series = "Fitted Additive") +
  autolayer(fitted(hpg_hw2), series = "Fitted Multiplicative") +
  ylab("Air visitors") +
  theme(plot.title = element_text(hjust = 0.5))

grid.arrange(air_hw_plot, hpg_hw_plot, nrow = 2)

Holt-Winters’ Accuracy

air_hw_acc <- accuracy(air_hw)
air_hw2_acc <- accuracy(air_hw2)
hpg_hw_acc<- accuracy(hpg_hw)
hpg_hw2_acc <- accuracy(hpg_hw2)

Air Holt-Winters’ Damped

# HOLT-WINTERS' ---------------------------
# HOLT-WINTERS' DAMPED AIR visitors
air_hwd <- hw(air_ts2, seasonal = "additive")
air_hwd2 <- hw(air_ts2, seasonal = "multiplicative")

air_hwd_plot <- autoplot(air_ts2, 
                              main = "Air visitors Holt-Winters' Damped") + 
  autolayer(fitted(air_hwd), series = "Fitted Additive") +
  autolayer(fitted(air_hwd2), series = "Fitted Multiplicative") +
  ylab("Air visitors") +
  theme(plot.title = element_text(hjust = 0.5))

HPG Holt-Winters’ Damped

hpg_hwd <- hw(hpg_ts2, seasonal = "additive")
hpg_hwd2 <- hw(hpg_ts2, seasonal = "multiplicative")

hpg_hwd_plot <- autoplot(hpg_ts2, 
                              main = "HPG visitors Holt-Winters'Damped") + 
  autolayer(fitted(hpg_hwd), series = "Fitted Additive") +
  autolayer(fitted(hpg_hwd2), series = "Fitted Multiplicative") +
  ylab("Air visitors") +
  theme(plot.title = element_text(hjust = 0.5))

grid.arrange(air_hwd_plot
             , hpg_hwd_plot
             , nrow = 2)

Holt-Winters’ Damped Accuracy

air_hwd_acc <- accuracy(air_hwd)
air_hwd2_acc <- accuracy(air_hwd2)
hpg_hwd_acc <- accuracy(hpg_hwd)
hpg_hwd2_acc <- accuracy(hpg_hwd2)

Air ARIMA

# ARIMA MODELS --------------
# Air ARIMA
air_arima <- auto.arima(air_ts2)

checkresiduals(air_arima)

## 
##  Ljung-Box test
## 
## data:  Residuals from ARIMA(1,1,1)(2,0,0)[2]
## Q* = 105.6, df = 3, p-value < 2.2e-16
## 
## Model df: 4.   Total lags used: 7

air_arima_acc <- accuracy(air_arima)

air_arima_fc <- forecast(air_arima, h = 12)

accuracy(air_arima_fc)

##                    ME     RMSE      MAE       MPE     MAPE      MASE
## Training set 1.866716 543.3904 350.7981 -61.12175 84.65856 0.5926106
##                     ACF1
## Training set 0.004705909

air_arima_fc_plot <- autoplot(air_arima_fc) +
  labs(title = "Air ARIMA Forecast using ARIMA(1,1,1)(2,0,0)[2]") +
  ylab("Air visitors") +
  theme(plot.title = element_text(hjust = 0.5))

HPG ARIMA

# ARIMA MODELS --------------
# HPG ARIMA
hpg_arima <- auto.arima(hpg_ts2)

checkresiduals(hpg_arima)

## 
##  Ljung-Box test
## 
## data:  Residuals from ARIMA(1,1,1)(0,0,1)[2]
## Q* = 13.217, df = 3, p-value = 0.00419
## 
## Model df: 3.   Total lags used: 6

hpg_arima_acc <- accuracy(hpg_arima)

hpg_arima_fc <- forecast(hpg_arima, h = 12)

accuracy(hpg_arima_fc)

##                    ME     RMSE      MAE       MPE   MAPE     MASE         ACF1
## Training set 1139.111 6541.987 4866.718 -6.582705 36.316 0.613335 -0.006800734

hpg_arima_fc_plot <- autoplot(hpg_arima_fc) +
  labs(title = "HPG ARIMA Forecast using ARIMA(1,1,1)(0,0,1)[2]") +
  ylab("Air visitors") +
  theme(plot.title = element_text(hjust = 0.5))

# Combine Plots
grid.arrange(air_arima_fc_plot
             , hpg_arima_fc_plot
             , nrow = 2)

Air ETS

# ETS MODELS -------------------------
# Air ETS
air_ets <- ets(air_ts2)
air_ets_acc <- accuracy(air_ets)

checkresiduals(air_ets)

## 
##  Ljung-Box test
## 
## data:  Residuals from ETS(M,A,A)
## Q* = 96.639, df = 3, p-value < 2.2e-16
## 
## Model df: 6.   Total lags used: 9

HPG ETS

# HPG ETS
hpg_ets <- ets(hpg_ts2)
hpg_ets_acc <- accuracy(hpg_ets)
checkresiduals(hpg_ets)

## 
##  Ljung-Box test
## 
## data:  Residuals from ETS(A,Ad,N)
## Q* = 55.749, df = 3, p-value = 4.751e-12
## 
## Model df: 5.   Total lags used: 8

Air ETS Forecast

# ETS FORECASTS ------------------------------
# Air ETS
air_ets_fc <- forecast(air_ets, h = 12)


accuracy(air_ets_fc)

##                     ME     RMSE      MAE       MPE     MAPE      MASE      ACF1
## Training set -147.3028 658.9757 469.1776 -191.0366 205.9678 0.7925916 0.3235844

air_ets_fc_plot <- air_ets_fc %>% autoplot() +
  labs(title="Air visitors Forecast Using ETS(M,A,A)") +
  ylab("visitors") +
  theme(plot.title = element_text(hjust = 0.5))

HPG ETS Forecast and Combined Plots

# ETS FORECASTS ------------------------------
# HPG ETS
hpg_ets_fc <- forecast(hpg_ets, h = 12)

accuracy(hpg_ets_fc)

##                   ME     RMSE      MAE       MPE   MAPE      MASE      ACF1
## Training set 99.5092 6794.227 5854.746 -20.73566 49.281 0.7378525 0.3200496

hpg_ets_fc_plot <- hpg_ets_fc %>% autoplot() +
  labs(title="HPG visitors Forecast Using ETS(A,Ad,N)") +
  ylab("visitors") +
  theme(plot.title = element_text(hjust = 0.5))

grid.arrange(air_ets_fc_plot
             , hpg_ets_fc_plot
             , nrow = 2)

Air Neural Net

air_nnet <- nnetar(air_uts, MaxNWts = 32019)
air_nnet

## Series: air_uts 
## Model:  NNAR(45,1,23)[2] 
## Call:   nnetar(y = air_uts, MaxNWts = 32019)
## 
## Average of 20 networks, each of which is
## a 45-23-1 network with 1082 weights
## options were - linear output units 
## 
## sigma^2 estimated as 188.3

air_nnet_acc <- accuracy(air_nnet)

air_nnet_fc <- forecast(air_nnet, h = 10000)
air_nnet_fc

##          Point Forecast
## 16010.50       34.89440
## 16011.00       26.44432
## 16011.50       21.23853
## 16012.00       21.98759
## 16012.50       25.85134
## 16013.00       34.32124
## 16013.50       38.64397
## 16014.00       31.80211
## 16014.50       22.29211
## 16015.00       21.93086
## 16015.50       23.53675
## 16016.00       26.56773
## 16016.50       30.17907
## 16017.00       39.52999
## 16017.50       36.45393
## 16018.00       25.12814
## 16018.50       22.56302
## 16019.00       22.18862
## 16019.50       26.70467
## 16020.00       30.54118
## 16020.50       36.35004
## 16021.00       32.91588
## 16021.50       24.89372
## 16022.00       21.98517
## 16022.50       23.10781
## 16023.00       25.48644
## 16023.50       30.02287
## 16024.00       37.89867
## 16024.50       33.07985
## 16025.00       22.45866
## 16025.50       21.49002
## 16026.00       23.02738
## 16026.50       27.44713
## 16027.00       30.85614
## 16027.50       39.67455
## 16028.00       32.66137
## 16028.50       21.84052
## 16029.00       21.79029
## 16029.50       23.75712
## 16030.00       27.39016
## 16030.50       33.41897
## 16031.00       41.61505
## 16031.50       34.08252
## 16032.00       22.95845
## 16032.50       24.68738
## 16033.00       26.77056
## 16033.50       27.20155
## 16034.00       34.54633
## 16034.50       43.75052
## 16035.00       34.36144
## 16035.50       23.06852
## 16036.00       26.32425
## 16036.50       27.84696
## 16037.00       28.23367
## 16037.50       35.93498
## 16038.00       44.73207
## 16038.50       34.67231
## 16039.00       23.80279
## 16039.50       27.73678
## 16040.00       28.90985
## 16040.50       29.61187
## 16041.00       37.80551
## 16041.50       45.91758
## 16042.00       34.69655
## 16042.50       24.76583
## 16043.00       29.60822
## 16043.50       30.06616
## 16044.00       31.35533
## 16044.50       39.87380
## 16045.00       47.14482
## 16045.50       35.22897
## 16046.00       26.57678
## 16046.50       31.49801
## 16047.00       31.62170
## 16047.50       33.36520
## 16048.00       41.93310
## 16048.50       47.79896
## 16049.00       35.60005
## 16049.50       28.10432
## 16050.00       33.18743
## 16050.50       33.20736
## 16051.00       35.42884
## 16051.50       44.11256
## 16052.00       47.98620
## 16052.50       35.98290
## 16053.00       29.85566
## 16053.50       34.66957
## 16054.00       35.00448
## 16054.50       37.40600
## 16055.00       46.01012
## 16055.50       47.99215
## 16056.00       36.45261
## 16056.50       31.89445
## 16057.00       36.23847
## 16057.50       36.80900
## 16058.00       39.52609
## 16058.50       47.67023
## 16059.00       47.77432
## 16059.50       37.05090
## 16060.00       34.25170
## 16060.50       37.87331
## 16061.00       38.60163
## 16061.50       41.64464
## 16062.00       49.02442
## 16062.50       47.49259
## 16063.00       37.80665
## 16063.50       36.60070
## 16064.00       39.40333
## 16064.50       40.28664
## 16065.00       43.70690
## 16065.50       50.17057
## 16066.00       47.20594
## 16066.50       38.72914
## 16067.00       38.74595
## 16067.50       40.89186
## 16068.00       41.82844
## 16068.50       45.49886
## 16069.00       50.93776
## 16069.50       46.97446
## 16070.00       39.88474
## 16070.50       40.71121
## 16071.00       42.32424
## 16071.50       43.15772
## 16072.00       46.83274
## 16072.50       51.28552
## 16073.00       46.78635
## 16073.50       41.25847
## 16074.00       42.36380
## 16074.50       43.55593
## 16075.00       44.40725
## 16075.50       48.09563
## 16076.00       51.35851
## 16076.50       46.75505
## 16077.00       42.61243
## 16077.50       43.64503
## 16078.00       44.59191
## 16078.50       45.60666
## 16079.00       49.30334
## 16079.50       51.31364
## 16080.00       46.89713
## 16080.50       43.79648
## 16081.00       44.56762
## 16081.50       45.46329
## 16082.00       46.72572
## 16082.50       50.31590
## 16083.00       51.19639
## 16083.50       47.12139
## 16084.00       44.80602
## 16084.50       45.38025
## 16085.00       46.25494
## 16085.50       47.85256
## 16086.00       51.10480
## 16086.50       51.06030
## 16087.00       47.36402
## 16087.50       45.71319
## 16088.00       46.18281
## 16088.50       47.02682
## 16089.00       48.94286
## 16089.50       51.64193
## 16090.00       50.98787
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## 19640.50       51.67354
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## 19700.00       51.67354
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## 19702.50       51.67354
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## 19750.00       51.67354
## 19750.50       51.67354
## 19751.00       51.67354
## 19751.50       51.67354
## 19752.00       51.67354
## 19752.50       51.67354
## 19753.00       51.67354
## 19753.50       51.67354
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## 19755.50       51.67354
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## 19758.50       51.67354
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## 19760.00       51.67354
## 19760.50       51.67354
## 19761.00       51.67354
## 19761.50       51.67354
## 19762.00       51.67354
## 19762.50       51.67354
## 19763.00       51.67354
## 19763.50       51.67354
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## 19764.50       51.67354
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## 19768.50       51.67354
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## 19770.50       51.67354
## 19771.00       51.67354
## 19771.50       51.67354
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## 19772.50       51.67354
## 19773.00       51.67354
## 19773.50       51.67354
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## 19775.50       51.67354
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## 19778.50       51.67354
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## 19780.00       51.67354
## 19780.50       51.67354
## 19781.00       51.67354
## 19781.50       51.67354
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## 19782.50       51.67354
## 19783.00       51.67354
## 19783.50       51.67354
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## 19784.50       51.67354
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## 19786.00       51.67354
## 19786.50       51.67354
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## 19788.00       51.67354
## 19788.50       51.67354
## 19789.00       51.67354
## 19789.50       51.67354
## 19790.00       51.67354
## 19790.50       51.67354
## 19791.00       51.67354
## 19791.50       51.67354
## 19792.00       51.67354
## 19792.50       51.67354
## 19793.00       51.67354
## 19793.50       51.67354
## 19794.00       51.67354
## 19794.50       51.67354
## 19795.00       51.67354
## 19795.50       51.67354
## 19796.00       51.67354
## 19796.50       51.67354
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## 19799.00       51.67354
## 19799.50       51.67354
## 19800.00       51.67354
## 19800.50       51.67354
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## 19801.50       51.67354
## 19802.00       51.67354
## 19802.50       51.67354
## 19803.00       51.67354
## 19803.50       51.67354
## 19804.00       51.67354
## 19804.50       51.67354
## 19805.00       51.67354
## 19805.50       51.67354
## 19806.00       51.67354
## 19806.50       51.67354
## 19807.00       51.67354
## 19807.50       51.67354
## 19808.00       51.67354
## 19808.50       51.67354
## 19809.00       51.67354
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## 19810.00       51.67354
## 19810.50       51.67354
## 19811.00       51.67354
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## 19812.00       51.67354
## 19812.50       51.67354
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## 19814.00       51.67354
## 19814.50       51.67354
## 19815.00       51.67354
## 19815.50       51.67354
## 19816.00       51.67354
## 19816.50       51.67354
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## 19819.50       51.67354
## 19820.00       51.67354
## 19820.50       51.67354
## 19821.00       51.67354
## 19821.50       51.67354
## 19822.00       51.67354
## 19822.50       51.67354
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## 19824.50       51.67354
## 19825.00       51.67354
## 19825.50       51.67354
## 19826.00       51.67354
## 19826.50       51.67354
## 19827.00       51.67354
## 19827.50       51.67354
## 19828.00       51.67354
## 19828.50       51.67354
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## 19841.50       51.67354
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## 19842.50       51.67354
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## 19990.00       51.67354
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## 19992.50       51.67354
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## 19993.50       51.67354
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## 20101.00       51.67354
## 20101.50       51.67354
## 20102.00       51.67354
## 20102.50       51.67354
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## 20106.50       51.67354
## 20107.00       51.67354
## 20107.50       51.67354
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## 20108.50       51.67354
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## 20110.50       51.67354
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## 20112.00       51.67354
## 20112.50       51.67354
## 20113.00       51.67354
## 20113.50       51.67354
## 20114.00       51.67354
## 20114.50       51.67354
## 20115.00       51.67354
## 20115.50       51.67354
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## 20117.50       51.67354
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## 20122.50       51.67354
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## 20124.50       51.67354
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## 20125.50       51.67354
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## 20127.50       51.67354
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## 20129.50       51.67354
## 20130.00       51.67354
## 20130.50       51.67354
## 20131.00       51.67354
## 20131.50       51.67354
## 20132.00       51.67354
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## 20134.50       51.67354
## 20135.00       51.67354
## 20135.50       51.67354
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## 20136.50       51.67354
## 20137.00       51.67354
## 20137.50       51.67354
## 20138.00       51.67354
## 20138.50       51.67354
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## 20139.50       51.67354
## 20140.00       51.67354
## 20140.50       51.67354
## 20141.00       51.67354
## 20141.50       51.67354
## 20142.00       51.67354
## 20142.50       51.67354
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## 20144.00       51.67354
## 20144.50       51.67354
## 20145.00       51.67354
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## 20146.50       51.67354
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## 20147.50       51.67354
## 20148.00       51.67354
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## 20150.00       51.67354
## 20150.50       51.67354
## 20151.00       51.67354
## 20151.50       51.67354
## 20152.00       51.67354
## 20152.50       51.67354
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## 20154.50       51.67354
## 20155.00       51.67354
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## 20156.00       51.67354
## 20156.50       51.67354
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## 20159.50       51.67354
## 20160.00       51.67354
## 20160.50       51.67354
## 20161.00       51.67354
## 20161.50       51.67354
## 20162.00       51.67354
## 20162.50       51.67354
## 20163.00       51.67354
## 20163.50       51.67354
## 20164.00       51.67354
## 20164.50       51.67354
## 20165.00       51.67354
## 20165.50       51.67354
## 20166.00       51.67354
## 20166.50       51.67354
## 20167.00       51.67354
## 20167.50       51.67354
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## 20992.50       51.67354
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## 20994.00       51.67354
## 20994.50       51.67354
## 20995.00       51.67354
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## 20996.00       51.67354
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## 20997.50       51.67354
## 20998.00       51.67354
## 20998.50       51.67354
## 20999.00       51.67354
## 20999.50       51.67354
## 21000.00       51.67354
## 21000.50       51.67354
## 21001.00       51.67354
## 21001.50       51.67354
## 21002.00       51.67354
## 21002.50       51.67354
## 21003.00       51.67354
## 21003.50       51.67354
## 21004.00       51.67354
## 21004.50       51.67354
## 21005.00       51.67354
## 21005.50       51.67354
## 21006.00       51.67354
## 21006.50       51.67354
## 21007.00       51.67354
## 21007.50       51.67354
## 21008.00       51.67354
## 21008.50       51.67354
## 21009.00       51.67354
## 21009.50       51.67354
## 21010.00       51.67354

accuracy(air_nnet_fc)

##                       ME     RMSE      MAE       MPE     MAPE      MASE
## Training set -0.04382958 13.72363 9.888302 -71.06881 94.88617 0.6269395
##                     ACF1
## Training set 0.003057586

air_nnet_fc %>% autoplot() +
  labs(title="Air Visit Forecast using NNAR(21,1,11)[2]") +
  ylab("visitors") +
  theme(plot.title = element_text(hjust = 0.5))

HPG Neural Net

hpg_nnet <- nnetar(hpg_ts2)
hpg_nnet

## Series: hpg_ts2 
## Model:  NNAR(9,1,5)[2] 
## Call:   nnetar(y = hpg_ts2)
## 
## Average of 20 networks, each of which is
## a 9-5-1 network with 56 weights
## options were - linear output units 
## 
## sigma^2 estimated as 5438674

hpg_nnet_acc <- accuracy(hpg_nnet)
hpg_nnet_fc <- forecast(hpg_nnet, h = 36)
hpg_nnet_fc

##       Point Forecast
## 67.00      18495.988
## 67.50      14080.285
## 68.00      10121.804
## 68.50      13816.296
## 69.00      11018.805
## 69.50      18662.006
## 70.00      13161.586
## 70.50      20364.816
## 71.00      22012.903
## 71.50      12958.627
## 72.00      10269.430
## 72.50      10318.196
## 73.00      11692.753
## 73.50      12692.553
## 74.00      22113.578
## 74.50      23952.251
## 75.00      15018.864
## 75.50      13048.064
## 76.00      12491.463
## 76.50      12510.987
## 77.00      10974.219
## 77.50      12387.818
## 78.00      10053.742
## 78.50      16414.032
## 79.00      21528.931
## 79.50      10964.463
## 80.00       9348.359
## 80.50      11224.611
## 81.00      12203.111
## 81.50      12133.840
## 82.00      17911.282
## 82.50      14875.209
## 83.00      13775.055
## 83.50      15821.684
## 84.00      11428.509
## 84.50       8437.460

accuracy(hpg_nnet_fc)

##                     ME     RMSE      MAE       MPE     MAPE      MASE
## Training set -1.319432 2332.097 1526.517 -5.191934 12.39389 0.1923814
##                    ACF1
## Training set 0.01622013

hpg_nnet_fc %>% autoplot() +
  labs(title="HPG Visit Forecast using NNAR(9,1,5)[2]") +
  ylab("visitors") +
  theme(plot.title = element_text(hjust = 0.5))

Compare All Model Accuracies

rbind(air_lm_acc
      , hpg_lm_acc
      , air_hw_acc
      , air_hw2_acc
      , hpg_hw_acc
      , hpg_hw2_acc
      , air_hwd_acc
      , air_hwd2_acc
      , hpg_hwd_acc
      , hpg_hwd2_acc
      , air_arima_acc
      , hpg_arima_acc
      , air_ets_acc
      , hpg_ets_acc
      , air_nnet_acc
      , hpg_nnet_acc
      )

##                         ME       RMSE         MAE         MPE       MAPE
## Training set  5.455015e-14  845.10296  585.935702 -982.791825 1011.48091
## Training set  2.711636e-14 6951.25188 6000.016441  -40.641889   66.29348
## Training set -4.379600e+01  642.78592  430.717205  -66.440063   88.80221
## Training set -2.742310e+01  659.46225  415.587427  -35.135517   63.92213
## Training set -3.065214e+02 7259.44865 6122.807752  -23.173570   54.48020
## Training set -4.055501e+02 7314.79362 6208.431791  -28.895602   55.42954
## Training set -4.379600e+01  642.78592  430.717205  -66.440063   88.80221
## Training set -2.742310e+01  659.46225  415.587427  -35.135517   63.92213
## Training set -3.065214e+02 7259.44865 6122.807752  -23.173570   54.48020
## Training set -4.055501e+02 7314.79362 6208.431791  -28.895602   55.42954
## Training set  1.866716e+00  543.39036  350.798102  -61.121754   84.65856
## Training set  1.139111e+03 6541.98664 4866.718491   -6.582705   36.31600
## Training set -1.473028e+02  658.97571  469.177558 -191.036575  205.96783
## Training set  9.950920e+01 6794.22741 5854.745807  -20.735662   49.28100
## Training set -4.382958e-02   13.72363    9.888302  -71.068814   94.88617
## Training set -1.319432e+00 2332.09659 1526.516501   -5.191934   12.39389
##                   MASE         ACF1
## Training set 1.6070665  0.711057938
## Training set 1.1066447  0.350669971
## Training set 0.7276197  0.371255950
## Training set 0.7020606  0.218831401
## Training set 0.7716353  0.329198293
## Training set 0.7824262  0.360976759
## Training set 0.7276197  0.371255950
## Training set 0.7020606  0.218831401
## Training set 0.7716353  0.329198293
## Training set 0.7824262  0.360976759
## Training set 0.5926106  0.004705909
## Training set 0.6133350 -0.006800734
## Training set 0.7925916  0.323584441
## Training set 0.7378525  0.320049566
## Training set 0.6269395  0.003057586
## Training set 0.1923814  0.016220134

Final Prediction

# Predictions
air_predict <- forecast(air_nnet, h = 100)
air_predict

##          Point Forecast
## 16010.50       34.89440
## 16011.00       26.44432
## 16011.50       21.23853
## 16012.00       21.98759
## 16012.50       25.85134
## 16013.00       34.32124
## 16013.50       38.64397
## 16014.00       31.80211
## 16014.50       22.29211
## 16015.00       21.93086
## 16015.50       23.53675
## 16016.00       26.56773
## 16016.50       30.17907
## 16017.00       39.52999
## 16017.50       36.45393
## 16018.00       25.12814
## 16018.50       22.56302
## 16019.00       22.18862
## 16019.50       26.70467
## 16020.00       30.54118
## 16020.50       36.35004
## 16021.00       32.91588
## 16021.50       24.89372
## 16022.00       21.98517
## 16022.50       23.10781
## 16023.00       25.48644
## 16023.50       30.02287
## 16024.00       37.89867
## 16024.50       33.07985
## 16025.00       22.45866
## 16025.50       21.49002
## 16026.00       23.02738
## 16026.50       27.44713
## 16027.00       30.85614
## 16027.50       39.67455
## 16028.00       32.66137
## 16028.50       21.84052
## 16029.00       21.79029
## 16029.50       23.75712
## 16030.00       27.39016
## 16030.50       33.41897
## 16031.00       41.61505
## 16031.50       34.08252
## 16032.00       22.95845
## 16032.50       24.68738
## 16033.00       26.77056
## 16033.50       27.20155
## 16034.00       34.54633
## 16034.50       43.75052
## 16035.00       34.36144
## 16035.50       23.06852
## 16036.00       26.32425
## 16036.50       27.84696
## 16037.00       28.23367
## 16037.50       35.93498
## 16038.00       44.73207
## 16038.50       34.67231
## 16039.00       23.80279
## 16039.50       27.73678
## 16040.00       28.90985
## 16040.50       29.61187
## 16041.00       37.80551
## 16041.50       45.91758
## 16042.00       34.69655
## 16042.50       24.76583
## 16043.00       29.60822
## 16043.50       30.06616
## 16044.00       31.35533
## 16044.50       39.87380
## 16045.00       47.14482
## 16045.50       35.22897
## 16046.00       26.57678
## 16046.50       31.49801
## 16047.00       31.62170
## 16047.50       33.36520
## 16048.00       41.93310
## 16048.50       47.79896
## 16049.00       35.60005
## 16049.50       28.10432
## 16050.00       33.18743
## 16050.50       33.20736
## 16051.00       35.42884
## 16051.50       44.11256
## 16052.00       47.98620
## 16052.50       35.98290
## 16053.00       29.85566
## 16053.50       34.66957
## 16054.00       35.00448
## 16054.50       37.40600
## 16055.00       46.01012
## 16055.50       47.99215
## 16056.00       36.45261
## 16056.50       31.89445
## 16057.00       36.23847
## 16057.50       36.80900
## 16058.00       39.52609
## 16058.50       47.67023
## 16059.00       47.77432
## 16059.50       37.05090
## 16060.00       34.25170

air_nnet_fc %>% autoplot(main = "Air visitors Predictions using NNAR(45,1,23)[2]") +
  ylab("Visit") +
  theme(plot.title = element_text(hjust = 0.5))

unique_date <- as.Date(unique(air_agg$date))
final_prediction_output <- as.data.frame(cbind(store_id2, air_predict$x))
sample$visitors <- air_predict$x
final_prediction_output2 <- as.data.frame(sample)
# colnames(final_prediction_output2) <- c("id", "visitors")
# final_prediction_output$date <- as.Date(final_prediction_output$date)

write.csv(final_prediction_output2, file = "Forecasting_Final_Kaggle_Pollastro.csv", row.names = FALSE)