0.1.1 Data Preparation

Load the required libraries

library(tidyverse)
library(kableExtra)
library(lubridate)
library(forecast)

Load required Datasets

Creating a character object called months.abb

head(data_pro,10)

months.abb <- c("Jan","Feb","Mar",
              "Apr","May","Jun",
              "Jul","Aug","Sep",
              "Oct","Nov","Dec")

0.1.2 Data Exploration

Now, Let’s use the mutate() funtion in the dplyr package to calculate average price for the stocks

head(data_indus)

mutate(data_indus,avg_price = mean(data_pro[]))

## Warning in mean.default(data_pro[]): argument is not numeric or logical:
## returning NA

# Avg Price of the Index
data_price <- data_pro %>% select(open_price,sname) %>% 
  group_by(sname) %>% 
  summarise(Avg_price = mean(open_price)) 

Yearly average price for the stocks

# yearly Price 
data_price_year <- data_pro %>% select(begins_at,open_price,sname) %>% 
  group_by(Year=year(begins_at),sname) %>% 
  summarise(Avg_price = mean(open_price)) 
head(data_price)

Monthly average price for the stocks

# Monthly Price
data_price_month <- data_pro %>% select(begins_at,open_price,sname) %>% 
  group_by(Year=year(begins_at),Month=months.abb[month(begins_at)],sname) %>% 
  summarise(Avg_price = mean(open_price)) 
head(data_price)

data_price_year[which(data_price_year$sname=='AA'),]

Let’s look at our data structure

glimpse(data_pro)

## Observations: 370,440
## Variables: 10
## $ X1           <dbl> 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
## $ begins_at    <dttm> 2015-04-28, 2015-04-29, 2015-04-30, 2015-05-01, 2015-...
## $ open_price   <dbl> 24.8871, 24.8871, 24.8871, 24.8871, 24.8871, 24.8871, ...
## $ close_price  <dbl> 24.8871, 24.8871, 24.8871, 24.8871, 24.8871, 24.8871, ...
## $ high_price   <dbl> 24.8871, 24.8871, 24.8871, 24.8871, 24.8871, 24.8871, ...
## $ low_price    <dbl> 24.8871, 24.8871, 24.8871, 24.8871, 24.8871, 24.8871, ...
## $ volume       <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
## $ session      <chr> "reg", "reg", "reg", "reg", "reg", "reg", "reg", "reg"...
## $ interpolated <lgl> TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, ...
## $ sname        <chr> "AA", "AA", "AA", "AA", "AA", "AA", "AA", "AA", "AA", ...

summary(data_pro)

##        X1           begins_at                     open_price     
##  Min.   :   0.0   Min.   :2015-04-28 00:00:00   Min.   :   0.00  
##  1st Qu.: 314.8   1st Qu.:2016-07-26 18:00:00   1st Qu.:  13.61  
##  Median : 629.5   Median :2017-10-24 12:00:00   Median :  26.33  
##  Mean   : 629.5   Mean   :2017-10-25 14:51:25   Mean   :  48.92  
##  3rd Qu.: 944.2   3rd Qu.:2019-01-25 18:00:00   3rd Qu.:  56.09  
##  Max.   :1259.0   Max.   :2020-04-27 00:00:00   Max.   :1266.56  
##   close_price          high_price        low_price          volume         
##  Min.   :   0.0052   Min.   :   0.00   Min.   :   0.0   Min.   :        0  
##  1st Qu.:  13.6100   1st Qu.:  13.72   1st Qu.:  13.5   1st Qu.:   103282  
##  Median :  26.3300   Median :  26.67   Median :  26.0   Median :   421838  
##  Mean   :  48.9221   Mean   :  49.43   Mean   :  48.4   Mean   :  1650980  
##  3rd Qu.:  56.1200   3rd Qu.:  56.68   3rd Qu.:  55.5   3rd Qu.:  1332573  
##  Max.   :1250.0000   Max.   :1274.41   Max.   :1232.0   Max.   :375088650  
##    session          interpolated       sname          
##  Length:370440      Mode :logical   Length:370440     
##  Class :character   FALSE:362193    Class :character  
##  Mode  :character   TRUE :8247      Mode  :character  
##                                                       
##                                                       
## 

data_pro %>%
  summary() %>%
  kable() %>%
  kable_styling()

Calculate number of ZERO’s in each variable in the dataset

data_pro %>% 
  gather(variable, value) %>%
  filter(value == 0) %>%
  group_by(variable) %>%
  tally() %>%
  mutate(percent = n / nrow(data_pro) * 100) %>%
  mutate(percent = paste0(round(percent, ifelse(percent < 10, 1, 0)), "%")) %>%
  arrange(desc(n)) %>%
#  rename("Variable With Zeros"=variable,"Number of Records"=n,"Share of Total"=percent) %>%
  kable() %>%
  kable_styling()

## Warning: attributes are not identical across measure variables;
## they will be dropped

 # we will not drop these now but we will review it latter. We will not use volume in our anlysis at this time so we will drop those data points latter. 

Now, let’s only target shares whose open prices are between 100 and 200

unique(data_pro$sname)

##   [1] "AA"    "AAN"   "AAP"   "AAT"   "AB"    "ABB"   "ABBV"  "ABC"   "ABEV" 
##  [10] "ABG"   "ABM"   "ABR"   "ABT"   "ACC"   "ACCO"  "ACH"   "ACM"   "ACN"  
##  [19] "ACP"   "ACRE"  "ACT"   "ADC"   "ADM"   "ADPT"  "ADS"   "ADT"   "ADX"  
##  [28] "AEB"   "AEE"   "AEG"   "AEL"   "AEM"   "AEO"   "AEP"   "AER"   "AES"  
##  [37] "AFC"   "AFB"   "AFG"   "AFL"   "AFSIA" "AFSIB" "AFSIC" "AFT"   "AG"   
##  [46] "AGCO"  "AGD"   "AGI"   "AGM"   "AGN"   "AGO"   "AGRO"  "AGX"   "AHC"  
##  [55] "AHH"   "AHT"   "AI"    "AIF"   "AIG"   "AIN"   "AIR"   "AIT"   "AIV"  
##  [64] "AIW"   "AIZ"   "AJG"   "AKR"   "AL"    "ALB"   "ALE"   "ALEX"  "ALG"  
##  [73] "ALK"   "ALL"   "ALLE"  "ALLY"  "ALPN"  "ALSN"  "ALV"   "ALX"   "AM"   
##  [82] "AMC"   "AME"   "AMG"   "AMH"   "AMHC"  "AMP"   "AMRC"  "AMT"   "AMTD" 
##  [91] "AMX"   "AN"    "ANET"  "ANF"   "ANH"   "ANTM"  "AOD"   "AON"   "AOS"  
## [100] "AP"    "APA"   "APAM"  "APD"   "APH"   "APLE"  "APO"   "AR"    "ARC"  
## [109] "ARCO"  "ARDC"  "ARE"   "ARES"  "ARI"   "ARL"   "ARMK"  "ARR"   "ARW"  
## [118] "ASA"   "ASB"   "ASC"   "ASG"   "ASGN"  "ASH"   "ASPN"  "ASR"   "ASX"  
## [127] "AT"    "ATEN"  "ATHM"  "ATI"   "ATLS"  "ATO"   "ATR"   "ATTO"  "ATV"  
## [136] "AU"    "AUY"   "AVA"   "AVAL"  "AVB"   "AVD"   "AVH"   "AVK"   "AVT"  
## [145] "AVY"   "AWF"   "AWI"   "AWK"   "AWP"   "AWR"   "AXE"   "AXL"   "AXP"  
## [154] "AXR"   "AXS"   "AXTA"  "AYI"   "AZN"   "AZO"   "AZZ"   "B"     "BA"   
## [163] "BABA"  "BAC"   "BAF"   "BAH"   "BAK"   "BAM"   "BANC"  "BAP"   "BAX"  
## [172] "BBD"   "BBDO"  "BBF"   "BBK"   "BBL"   "BBN"   "BBVA"  "BBW"   "BBX"  
## [181] "BBY"   "BC"    "BCC"   "BCE"   "BCEI"  "BCH"   "BCO"   "BCS"   "BCX"  
## [190] "BDC"   "BDJ"   "BDN"   "BDX"   "BEN"   "BEP"   "BERY"  "BFAM"  "BFK"  
## [199] "BFO"   "BFS"   "BFZ"   "BG"    "BGB"   "BGG"   "BGH"   "BGR"   "BGS"  
## [208] "BGT"   "BGX"   "BGY"   "BH"    "BHE"   "BHK"   "BHLB"  "BHP"   "BIF"  
## [217] "BIG"   "BIO"   "BIP"   "BIT"   "BITA"  "BK"    "BKD"   "BKE"   "BKH"  
## [226] "BKK"   "BKN"   "BKT"   "BKU"   "BLK"   "BLL"   "BLW"   "BLX"   "BMA"  
## [235] "BME"   "BMI"   "BMO"   "BMY"   "BNS"   "BNY"   "BOE"   "BOH"   "BOOT" 
## [244] "BP"    "BPT"   "BPY"   "BQH"   "BR"    "BRC"   "BRFS"  "BRO"   "BRP"  
## [253] "BRT"   "BRX"   "BSAC"  "BSBR"  "BSD"   "BSE"   "BSL"   "BSMX"  "BST"  
## [262] "BSX"   "BTA"   "BTE"   "BTO"   "BTT"   "BTU"   "BTZ"   "BUD"   "BUI"  
## [271] "BURL"  "BVN"   "BWA"   "BWG"   "BX"    "BXC"   "BXMT"  "BXMX"  "BXP"  
## [280] "BXS"   "BYD"   "BYM"   "BZH"   "C"     "CC"    "CL"    "CN"    "CP"   
## [289] "CB"    "CACI"  "CAE"

data_pro %>% filter(open_price > 100 & open_price < 200  ) %>% select(open_price,sname) %>% group_by(sname) %>% summarise(Avg_price = mean(open_price)) %>% ggplot(mapping = aes(x=sname,y= Avg_price)) + geom_col()

The graph above tells us about average price of stocks for each sector name.

Cheking only with 500 stokcs data and analyze the distribution of data in each sector

left_join(data_price,data_indus,by = c("sname"="CODE"))  %>% filter(!is.na(Sector)) %>% ggplot(mapping = aes(Sector)) + geom_bar() + theme(axis.text.x = element_text(angle = 70, hjust = 1))

First graph tells us about increase in count of sectors, division by sectors

spread(data_price_year,Year,Avg_price) %>% left_join(.,data_indus,by = c("sname"="CODE"))  %>% filter(!is.na(Sector)) %>%  pivot_longer(c('2015','2016','2017','2018','2019','2020'),"Year",values_to = "Avg_price" ) %>% ggplot(mapping = aes(Sector,col=Year)) + geom_bar() + theme(axis.text.x = element_text(angle = 70, hjust = 1)) +facet_wrap('Year')

The graph above tells us about yearly increase in count of sectors

spread(data_price_year,Year,Avg_price) %>% left_join(.,data_indus,by = c("sname"="CODE"))  %>% filter(!is.na(Sector)) %>%  pivot_longer(c('2015','2016','2017','2018','2019','2020'),"Year",values_to = "Avg_price" )  %>% ggplot(mapping = aes(Sector,Avg_price,fill=Year)) + geom_col() + theme(axis.text.x = element_text(angle = 70, hjust = 1)) 

#+facet_wrap('Year')

Third graph tells us about yearly increase in average price of sectors

0.1.3 Build Models

Below is Graph of the sector by Month and year,which shows some pattern

We will do some analysis to see how stocks from few of these industries fit with AR(Auto Regression) and MA(Moving Average) model.

Analyzing average price of stocks yearly for each sector in the dataset

spread(data_price_month,Year,Avg_price) %>% left_join(.,data_indus,by = c("sname"="CODE"))  %>% filter(!is.na(Sector)) %>%  pivot_longer(c('2015','2016','2017','2018','2019','2020'),"Year",values_to = "Avg_price" ) %>% filter(Avg_price > 100 & Avg_price < 200  )%>% ggplot(mapping = aes(Sector,Avg_price,fill=Year)) + geom_col(position = "dodge") + theme(axis.text.x = element_text(angle = 70, hjust = 1))

#+ geom_bar(position = "dodge2")
#+facet_wrap('Month')

Analyzing average price of stocks monthly for each sector in the dataset

# By Month 
spread(data_price_month,Year,Avg_price) %>% left_join(.,data_indus,by = c("sname"="CODE"))  %>% filter(!is.na(Sector)) %>%  pivot_longer(c('2015','2016','2017','2018','2019','2020'),"Year",values_to = "Avg_price" ) %>% ggplot(mapping = aes(Sector,Avg_price,fill=Month)) + geom_col(position = "dodge") + theme(axis.text.x = element_text(angle = 70, hjust = 1))

## Warning: Removed 2904 rows containing missing values (geom_col).

Box plot for year

# Box PLot for year 
spread(data_price_month,Year,Avg_price) %>% left_join(.,data_indus,by = c("sname"="CODE"))  %>% filter(!is.na(Sector)) %>%  pivot_longer(c('2015','2016','2017','2018','2019','2020'),"Year",values_to = "Avg_price" ) %>% ggplot(mapping = aes( stringr::str_remove(Sector,'Sector') ,Avg_price,fill=Year)) + geom_boxplot(position = "dodge") + theme(axis.text.x = element_text(angle = 30, hjust = 1)) + labs(title = "Boxplot of Stocks by Year ")+ ylim(0,200) + xlab( "Sector")

## Warning: Removed 3518 rows containing non-finite values (stat_boxplot).

# ----- TEMP
# spread(data_price_month,Year,Avg_price) %>% left_join(.,data_indus,by = c("sname"="CODE"))  %>% filter(!is.na(Sector)) %>%  pivot_longer(c('2015','2016','2017','2018','2019','2020'),"Year",values_to = "Avg_price" ) %>%   ggplot(mapping = aes(Month,Avg_price,fill=Year)) + geom_col() + theme(axis.text.x = element_text(angle = 70, hjust = 1)) +   geom_bar(position = "dodge2")
#   # ggplot(mapping = aes(Avg_price,fill=Month)) +   geom_histogram(position = "fill")
#   # ggplot( aes(Month, Avg_price)) + geom_area(aes(fill = Month))
#    # ggplot(mapping = aes(Month , Avg_price,group=Sector)) + geom_line(aes(colour = Sector), position = "stack") + geom_point(aes(colour = Sector), position = "stack") +  geom_area(aes(fill = Sector))

From the box plot above we can analyze that mostly all the sectors in our dataset have some outliers throughout 5 years, except two sectors that are: Technology and Utilities.

Analyzing top 3 stocks in each Sector

library(dplyr)


data_price_month %>% group_by(sname)  %>%  summarise(Avg = mean(Avg_price)) %>% left_join(.,data_indus,by = c("sname"="CODE"))  %>% filter(!is.na(Sector)) %>%   arrange(desc(Avg)) %>% top_n(n=16,wt = Avg)

data_stock = data_price_month %>% group_by(sname)  %>%  summarise(Avg = mean(Avg_price)) %>% left_join(.,data_indus,by = c("sname"="CODE"))  %>% filter(!is.na(Sector)) %>%   arrange(desc(Avg)) %>% top_n(n=20,wt = Avg)

head(data_stock)

unique(cbind(data_stock$NAME,data_stock$sname,data_stock$Sector))

##       [,1]                                                [,2]  
##  [1,] "AutoZone, Inc"                                     "AZO" 
##  [2,] "AutoZone, Inc"                                     "AZO" 
##  [3,] "BlackRock, Inc"                                    "BLK" 
##  [4,] "Biglari Holdings Inc"                              "BH"  
##  [5,] "Biglari Holdings Inc"                              "BH"  
##  [6,] "The Boeing Company"                                "BA"  
##  [7,] "Bio-Rad Laboratories, Inc"                         "BIO" 
##  [8,] "Allergan plc"                                      "AGN" 
##  [9,] "Alliance Data Systems Corporation"                 "ADS" 
## [10,] "Anthem, Inc"                                       "ANTM"
## [11,] "Becton, Dickinson and Company"                     "BDX" 
## [12,] "Credicorp Ltd"                                     "BAP" 
## [13,] "Canadian Pacific Railway Limited"                  "CP"  
## [14,] "Acuity Brands, Inc"                                "AYI" 
## [15,] "Arista Networks, Inc"                              "ANET"
## [16,] "Grupo Aeroportuario del Sureste, S. A. B. de C. V" "ASR" 
## [17,] "Air Products and Chemicals, Inc"                   "APD" 
## [18,] "CACI International Inc"                            "CACI"
## [19,] "Advance Auto Parts, Inc"                           "AAP" 
## [20,] "Advance Auto Parts, Inc"                           "AAP" 
##       [,3]                       
##  [1,] "Consumer Cyclical Sector" 
##  [2,] "Consumer Defensive Sector"
##  [3,] "Financial Services Sector"
##  [4,] "Consumer Cyclical Sector" 
##  [5,] "Consumer Defensive Sector"
##  [6,] "Industrials Sector"       
##  [7,] "Healthcare Sector"        
##  [8,] "Healthcare Sector"        
##  [9,] "Financial Services Sector"
## [10,] "Healthcare Sector"        
## [11,] "Healthcare Sector"        
## [12,] "Financial Services Sector"
## [13,] "Industrials Sector"       
## [14,] "Industrials Sector"       
## [15,] "Technology Sector"        
## [16,] "Industrials Sector"       
## [17,] "Basic Materials Sector"   
## [18,] "Technology Sector"        
## [19,] "Consumer Cyclical Sector" 
## [20,] "Consumer Defensive Sector"

  # ggplot(mapping = aes(Month,Avg_price,fill=Year)) + geom_col() + theme(axis.text.x = element_text(angle = 70, hjust = 1)) +   geom_bar(position = "dodge2")

We will study the flow on some of the stocks from Health and Tech Sectors like:

ANTM Anthem, Inc

ANET Arista Networks, Inc

BA The Boeing Company

library(stringr)


spread(data_price_month,Year,Avg_price) %>% left_join(.,data_indus,by = c("sname"="CODE"))%>% filter(!is.na(Sector))

summary(data_pro)

##        X1           begins_at                     open_price     
##  Min.   :   0.0   Min.   :2015-04-28 00:00:00   Min.   :   0.00  
##  1st Qu.: 314.8   1st Qu.:2016-07-26 18:00:00   1st Qu.:  13.61  
##  Median : 629.5   Median :2017-10-24 12:00:00   Median :  26.33  
##  Mean   : 629.5   Mean   :2017-10-25 14:51:25   Mean   :  48.92  
##  3rd Qu.: 944.2   3rd Qu.:2019-01-25 18:00:00   3rd Qu.:  56.09  
##  Max.   :1259.0   Max.   :2020-04-27 00:00:00   Max.   :1266.56  
##   close_price          high_price        low_price          volume         
##  Min.   :   0.0052   Min.   :   0.00   Min.   :   0.0   Min.   :        0  
##  1st Qu.:  13.6100   1st Qu.:  13.72   1st Qu.:  13.5   1st Qu.:   103282  
##  Median :  26.3300   Median :  26.67   Median :  26.0   Median :   421838  
##  Mean   :  48.9221   Mean   :  49.43   Mean   :  48.4   Mean   :  1650980  
##  3rd Qu.:  56.1200   3rd Qu.:  56.68   3rd Qu.:  55.5   3rd Qu.:  1332573  
##  Max.   :1250.0000   Max.   :1274.41   Max.   :1232.0   Max.   :375088650  
##    session          interpolated       sname          
##  Length:370440      Mode :logical   Length:370440     
##  Class :character   FALSE:362193    Class :character  
##  Mode  :character   TRUE :8247      Mode  :character  
##                                                       
##                                                       
## 

# Only Keeping Date, open_price ,      sname  , interpolated = FALSE
glimpse((data_pro))

## Observations: 370,440
## Variables: 10
## $ X1           <dbl> 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...
## $ begins_at    <dttm> 2015-04-28, 2015-04-29, 2015-04-30, 2015-05-01, 2015-...
## $ open_price   <dbl> 24.8871, 24.8871, 24.8871, 24.8871, 24.8871, 24.8871, ...
## $ close_price  <dbl> 24.8871, 24.8871, 24.8871, 24.8871, 24.8871, 24.8871, ...
## $ high_price   <dbl> 24.8871, 24.8871, 24.8871, 24.8871, 24.8871, 24.8871, ...
## $ low_price    <dbl> 24.8871, 24.8871, 24.8871, 24.8871, 24.8871, 24.8871, ...
## $ volume       <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
## $ session      <chr> "reg", "reg", "reg", "reg", "reg", "reg", "reg", "reg"...
## $ interpolated <lgl> TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, ...
## $ sname        <chr> "AA", "AA", "AA", "AA", "AA", "AA", "AA", "AA", "AA", ...

data_Main <- data_pro %>% filter(!interpolated == TRUE )%>% .[,c(2,3,10)] %>% 
  subset( sname %in% data_stock$sname) 



head(data_Main)

Converting the data of stokcs in wide format

wide_data_Main <- spread(data_Main,sname,open_price)

head(wide_data_Main)

Fit an AR model to the follwing data:

ANTM Anthem, Inc

ANET Arista Networks, Inc

BA The Boeing Company

library(xts)

## Warning: package 'xts' was built under R version 3.5.3

## Loading required package: zoo

## Warning: package 'zoo' was built under R version 3.5.3

## 
## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

## 
## Attaching package: 'xts'

## The following objects are masked from 'package:dplyr':
## 
##     first, last

# wide_data_Main$begins_at  <- as_datetime(wide_data_Main$begins_at)
stocks_ANTM <-xts(wide_data_Main$ANTM,  order.by=as.Date(wide_data_Main$begins_at))
stocks_ANET <- xts(wide_data_Main$ANET, order.by=as.Date(wide_data_Main$begins_at))
stocks_BA <- xts(wide_data_Main$BA,  order.by=as.Date(wide_data_Main$begins_at))

# Data for only 2020 data 
wide_data_Main_20 <- wide_data_Main[which(year(wide_data_Main$begins_at) %in% c("2020")),]
# Data for only Rest than 2020 data 
wide_data_Main_Old <- wide_data_Main[-which(year(wide_data_Main$begins_at) %in% c("2020")),]

stocks_ANTM_MY  <-xts(wide_data_Main_20$ANTM,  order.by=as.Date(wide_data_Main_20$begins_at))
stocks_ANET_MY <- xts(wide_data_Main_20$ANET, order.by=as.Date(wide_data_Main_20$begins_at))
stocks_BA_MY <- xts(wide_data_Main_20$BA,  order.by=as.Date(wide_data_Main_20$begins_at))

stocks_ANTM_old  <-xts(wide_data_Main_Old$ANTM,  order.by=as.Date(wide_data_Main_Old$begins_at))
stocks_ANET_old <- xts(wide_data_Main_Old$ANET, order.by=as.Date(wide_data_Main_Old$begins_at))
stocks_BA_old <- xts(wide_data_Main_Old$BA,  order.by=as.Date(wide_data_Main_Old$begins_at))

index(stocks_ANTM_MY)

##  [1] "2020-01-02" "2020-01-03" "2020-01-06" "2020-01-07" "2020-01-08"
##  [6] "2020-01-09" "2020-01-10" "2020-01-13" "2020-01-14" "2020-01-15"
## [11] "2020-01-16" "2020-01-17" "2020-01-21" "2020-01-22" "2020-01-23"
## [16] "2020-01-24" "2020-01-27" "2020-01-28" "2020-01-29" "2020-01-30"
## [21] "2020-01-31" "2020-02-03" "2020-02-04" "2020-02-05" "2020-02-06"
## [26] "2020-02-07" "2020-02-10" "2020-02-11" "2020-02-12" "2020-02-13"
## [31] "2020-02-14" "2020-02-18" "2020-02-19" "2020-02-20" "2020-02-21"
## [36] "2020-02-24" "2020-02-25" "2020-02-26" "2020-02-27" "2020-02-28"
## [41] "2020-03-02" "2020-03-03" "2020-03-04" "2020-03-05" "2020-03-06"
## [46] "2020-03-09" "2020-03-10" "2020-03-11" "2020-03-12" "2020-03-13"
## [51] "2020-03-16" "2020-03-17" "2020-03-18" "2020-03-19" "2020-03-20"
## [56] "2020-03-23" "2020-03-24" "2020-03-25" "2020-03-26" "2020-03-27"
## [61] "2020-03-30" "2020-03-31" "2020-04-01" "2020-04-02" "2020-04-03"
## [66] "2020-04-06" "2020-04-07" "2020-04-08" "2020-04-09" "2020-04-13"
## [71] "2020-04-14" "2020-04-15" "2020-04-16" "2020-04-17" "2020-04-20"
## [76] "2020-04-21" "2020-04-22" "2020-04-23" "2020-04-24" "2020-04-27"

coredata(stocks_ANTM_MY)

##         [,1]
##  [1,] 302.67
##  [2,] 293.68
##  [3,] 295.75
##  [4,] 299.20
##  [5,] 300.89
##  [6,] 307.83
##  [7,] 307.94
##  [8,] 306.88
##  [9,] 296.04
## [10,] 297.26
## [11,] 302.92
## [12,] 305.07
## [13,] 303.94
## [14,] 306.68
## [15,] 303.46
## [16,] 304.84
## [17,] 293.63
## [18,] 285.00
## [19,] 279.50
## [20,] 269.26
## [21,] 265.68
## [22,] 266.11
## [23,] 269.90
## [24,] 275.36
## [25,] 288.78
## [26,] 279.70
## [27,] 275.88
## [28,] 277.04
## [29,] 286.27
## [30,] 294.73
## [31,] 299.29
## [32,] 297.45
## [33,] 302.01
## [34,] 301.38
## [35,] 292.03
## [36,] 283.49
## [37,] 279.21
## [38,] 269.84
## [39,] 263.06
## [40,] 249.94
## [41,] 259.60
## [42,] 270.13
## [43,] 286.55
## [44,] 287.65
## [45,] 278.18
## [46,] 264.00
## [47,] 278.33
## [48,] 278.60
## [49,] 262.03
## [50,] 267.50
## [51,] 226.50
## [52,] 229.76
## [53,] 224.45
## [54,] 206.22
## [55,] 204.29
## [56,] 188.54
## [57,] 183.98
## [58,] 190.09
## [59,] 221.28
## [60,] 217.61
## [61,] 224.66
## [62,] 235.28
## [63,] 217.01
## [64,] 210.53
## [65,] 208.89
## [66,] 215.51
## [67,] 235.70
## [68,] 227.15
## [69,] 240.94
## [70,] 240.78
## [71,] 245.76
## [72,] 249.15
## [73,] 254.51
## [74,] 279.01
## [75,] 262.48
## [76,] 255.00
## [77,] 255.09
## [78,] 264.71
## [79,] 265.48
## [80,] 267.56

first(stocks_ANTM_MY)

##              [,1]
## 2020-01-02 302.67

stocks_ANTM_MY[]

##              [,1]
## 2020-01-02 302.67
## 2020-01-03 293.68
## 2020-01-06 295.75
## 2020-01-07 299.20
## 2020-01-08 300.89
## 2020-01-09 307.83
## 2020-01-10 307.94
## 2020-01-13 306.88
## 2020-01-14 296.04
## 2020-01-15 297.26
## 2020-01-16 302.92
## 2020-01-17 305.07
## 2020-01-21 303.94
## 2020-01-22 306.68
## 2020-01-23 303.46
## 2020-01-24 304.84
## 2020-01-27 293.63
## 2020-01-28 285.00
## 2020-01-29 279.50
## 2020-01-30 269.26
## 2020-01-31 265.68
## 2020-02-03 266.11
## 2020-02-04 269.90
## 2020-02-05 275.36
## 2020-02-06 288.78
## 2020-02-07 279.70
## 2020-02-10 275.88
## 2020-02-11 277.04
## 2020-02-12 286.27
## 2020-02-13 294.73
## 2020-02-14 299.29
## 2020-02-18 297.45
## 2020-02-19 302.01
## 2020-02-20 301.38
## 2020-02-21 292.03
## 2020-02-24 283.49
## 2020-02-25 279.21
## 2020-02-26 269.84
## 2020-02-27 263.06
## 2020-02-28 249.94
## 2020-03-02 259.60
## 2020-03-03 270.13
## 2020-03-04 286.55
## 2020-03-05 287.65
## 2020-03-06 278.18
## 2020-03-09 264.00
## 2020-03-10 278.33
## 2020-03-11 278.60
## 2020-03-12 262.03
## 2020-03-13 267.50
## 2020-03-16 226.50
## 2020-03-17 229.76
## 2020-03-18 224.45
## 2020-03-19 206.22
## 2020-03-20 204.29
## 2020-03-23 188.54
## 2020-03-24 183.98
## 2020-03-25 190.09
## 2020-03-26 221.28
## 2020-03-27 217.61
## 2020-03-30 224.66
## 2020-03-31 235.28
## 2020-04-01 217.01
## 2020-04-02 210.53
## 2020-04-03 208.89
## 2020-04-06 215.51
## 2020-04-07 235.70
## 2020-04-08 227.15
## 2020-04-09 240.94
## 2020-04-13 240.78
## 2020-04-14 245.76
## 2020-04-15 249.15
## 2020-04-16 254.51
## 2020-04-17 279.01
## 2020-04-20 262.48
## 2020-04-21 255.00
## 2020-04-22 255.09
## 2020-04-23 264.71
## 2020-04-24 265.48
## 2020-04-27 267.56

tail(stocks_ANTM_MY,n=10)

##              [,1]
## 2020-04-14 245.76
## 2020-04-15 249.15
## 2020-04-16 254.51
## 2020-04-17 279.01
## 2020-04-20 262.48
## 2020-04-21 255.00
## 2020-04-22 255.09
## 2020-04-23 264.71
## 2020-04-24 265.48
## 2020-04-27 267.56

endpoints(stocks_ANTM_MY,on="months")  

## [1]  0 21 40 62 80

stocks_ANTM_MY['2020-04-14']

##              [,1]
## 2020-04-14 245.76

month.abb[month(index(stocks_ANTM_MY))]

##  [1] "Jan" "Jan" "Jan" "Jan" "Jan" "Jan" "Jan" "Jan" "Jan" "Jan" "Jan" "Jan"
## [13] "Jan" "Jan" "Jan" "Jan" "Jan" "Jan" "Jan" "Jan" "Jan" "Feb" "Feb" "Feb"
## [25] "Feb" "Feb" "Feb" "Feb" "Feb" "Feb" "Feb" "Feb" "Feb" "Feb" "Feb" "Feb"
## [37] "Feb" "Feb" "Feb" "Feb" "Mar" "Mar" "Mar" "Mar" "Mar" "Mar" "Mar" "Mar"
## [49] "Mar" "Mar" "Mar" "Mar" "Mar" "Mar" "Mar" "Mar" "Mar" "Mar" "Mar" "Mar"
## [61] "Mar" "Mar" "Apr" "Apr" "Apr" "Apr" "Apr" "Apr" "Apr" "Apr" "Apr" "Apr"
## [73] "Apr" "Apr" "Apr" "Apr" "Apr" "Apr" "Apr" "Apr"

nmonths(stocks_ANTM_MY)

## [1] 4

head(stocks_ANTM_MY,n=10)

##              [,1]
## 2020-01-02 302.67
## 2020-01-03 293.68
## 2020-01-06 295.75
## 2020-01-07 299.20
## 2020-01-08 300.89
## 2020-01-09 307.83
## 2020-01-10 307.94
## 2020-01-13 306.88
## 2020-01-14 296.04
## 2020-01-15 297.26

to.weekly(stocks_ANTM_MY)%>% as.data.frame %>% cbind(.,yr=week(index(to.weekly(stocks_ANTM_MY))))%>% pivot_longer(c(stocks_ANTM_MY.Open,stocks_ANTM_MY.High,stocks_ANTM_MY.Low,stocks_ANTM_MY.Close),names_to="Key" , values_to = "Prc")  %>% ggplot(aes(x=yr, y= Prc,fill=Key))+  geom_line(aes(colour=Key)) #+geom_col(position="dodge", alpha=0.5) 

In the above graph, it shows weekly change in Anthem stock data i.e. open price, close price, high price, low price.

to.monthly(stocks_ANTM_MY) %>% as.data.frame %>% cbind(.,yr=index(to.monthly(stocks_ANTM_MY)))%>% pivot_longer(c(stocks_ANTM_MY.Open,stocks_ANTM_MY.High,stocks_ANTM_MY.Low,stocks_ANTM_MY.Close),names_to="Key" , values_to = "Prc")  %>% ggplot(aes(x=yr, y= Prc,fill=Key))+  geom_line(aes(colour=Key)) +geom_col(position="dodge", alpha=0.5) 

## Don't know how to automatically pick scale for object of type yearmon. Defaulting to continuous.

In the above graph, it shows monthly change in Anthem stock data i.e. open price, close price, high price, low price.

Periodicity of Anthem Stocks data

periodicity(stocks_ANTM_MY)

## Daily periodicity from 2020-01-02 to 2020-04-27

str(stocks_ANTM_MY)

## An 'xts' object on 2020-01-02/2020-04-27 containing:
##   Data: num [1:80, 1] 303 294 296 299 301 ...
##   Indexed by objects of class: [Date] TZ: UTC
##   xts Attributes:  
##  NULL

week(index(to.weekly(stocks_ANTM_MY)))

##  [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 17

stocks_ANTM_MY[c("2020-01-02","2020-01-03")]

##              [,1]
## 2020-01-02 302.67
## 2020-01-03 293.68

stocks_ANTM_MY[str_which(index(stocks_ANTM_MY),"\\d+-\\d+-03")]

##              [,1]
## 2020-01-03 293.68
## 2020-02-03 266.11
## 2020-03-03 270.13
## 2020-04-03 208.89

With the commands head() and tail() we can see the first and last 6 lines of the base. There are 6 columns with: opening price, maximum and minimum prices, closing price, volume of transactions and adjusted price. Using the command summary() we verify the descriptive statistics of each price series and volume. The command str() returns the object structure. In this case, it’s a xts object, a time series.

0.1.4 Time Series Forecasting

library(forecast)

head(stocks_ANTM)

##              [,1]
## 2015-04-28 150.15
## 2015-04-29 155.96
## 2015-04-30 151.83
## 2015-05-01 151.92
## 2015-05-04 153.45
## 2015-05-05 154.67

tail(stocks_ANTM)

##              [,1]
## 2020-04-20 262.48
## 2020-04-21 255.00
## 2020-04-22 255.09
## 2020-04-23 264.71
## 2020-04-24 265.48
## 2020-04-27 267.56

summary(stocks_ANTM)

##      Index             stocks_ANTM   
##  Min.   :2015-04-28   Min.   :117.0  
##  1st Qu.:2016-07-26   1st Qu.:145.2  
##  Median :2017-10-24   Median :195.9  
##  Mean   :2017-10-25   Mean   :206.5  
##  3rd Qu.:2019-01-26   3rd Qu.:262.8  
##  Max.   :2020-04-27   Max.   :317.6

str(stocks_ANTM)

## An 'xts' object on 2015-04-28/2020-04-27 containing:
##   Data: num [1:1259, 1] 150 156 152 152 153 ...
##   Indexed by objects of class: [Date] TZ: UTC
##   xts Attributes:  
##  NULL

plot(stocks_BA)

acf(stocks_ANTM)

acf_ANTM = acf(stocks_ANTM,lag.max = 30)

acf_BA = acf(stocks_BA,lag.max = 30)

acf_ANET = acf(stocks_ANET,lag.max = 30)

acf_BA= acf(stocks_BA,lag.max = 30,plot = FALSE)


autoplot(stocks_ANTM)

frequency(stocks_ANTM)

## [1] 1

Plot for 2020 Data only

acf(stocks_ANTM_MY,lag.max = 30)

autoplot(stocks_ANTM_MY)

head(stocks_ANTM_MY)

##              [,1]
## 2020-01-02 302.67
## 2020-01-03 293.68
## 2020-01-06 295.75
## 2020-01-07 299.20
## 2020-01-08 300.89
## 2020-01-09 307.83

frequency(stocks_ANTM_MY)

## [1] 1

For for rest of the data before 2020

Plot for 2020 Data only

acf(stocks_ANTM_old)

plot(stocks_ANTM_old)

head(stocks_ANTM_old)

##              [,1]
## 2015-04-28 150.15
## 2015-04-29 155.96
## 2015-04-30 151.83
## 2015-05-01 151.92
## 2015-05-04 153.45
## 2015-05-05 154.67

frequency(stocks_ANTM_old)

## [1] 1

The ACF plots test if an individual lag autocorrelation is different than zero. An alternative approach is to use the Ljung-Box test, which tests whether any of a group of autocorrelations of a time series are different from zero.

In essence it tests the “overall randomness” based on a number of lags. If the result is a small p-value than it indicates the data are probably not white noise.

For 2020 Data

Box.test(wide_data_Main_20$ANTM, lag = 30, fitdf = 0, type = "Lj")

## 
##  Box-Ljung test
## 
## data:  wide_data_Main_20$ANTM
## X-squared = 480.01, df = 30, p-value < 2.2e-16

Box.test(wide_data_Main$ANTM, lag = 4, fitdf = 0, type = "Lj")

## 
##  Box-Ljung test
## 
## data:  wide_data_Main$ANTM
## X-squared = 4976, df = 4, p-value < 2.2e-16

Here, we perform a Ljung-Box test on the first 24 lag autocorrelations. The resulting p-value is significant at p < .001, so this supports our ACF plot consideration above where we stated it’s likely this is not purely white noise and that some time series information exists in this data.

plot(cbind(stocks_ANTM,stocks_ANET,stocks_BA))

plot(cbind(stocks_ANTM_MY,stocks_ANET_MY,stocks_BA_MY))

plot(cbind(stocks_ANTM_old,stocks_ANET_old,stocks_BA_old))

These plots suggest that these slots the stocks improved from their position from mid of 2016 though 2018, and then it remained constant in progress untill Late 2019 and early 2020.

the trend is the long-term increase or decrease in the data. There is an increasing trend in the cement data. the seasonal pattern occurs when a time series is affected by seasonal factors such as the time of the year or the day of the week. The daily data of the stocks_ANTM doens’t show any seasonality in the graph.

the cycle occurs when the data exhibit rises and falls that are not of a fixed period. These fluctuations are usually due to economic conditions and are often related to the “business cycle”. We can see a few cycles in our in stocks_ANTM data from 2015 to 2018 and then in 2020 we have sudden drop due to covid 19. #https://afit-r.github.io/ts_exploration

0.1.5 Autocorrelation of Time Series

Another way to look at time series data is to plot each observation against another observation that occurred some time previously. For example, we could plot yt agaisnt yt-1 . This is called a lag plot because you are plotting the time series against lags of itself.

plot(diff(stocks_ANTM))

plot(diff(stocks_BA))

plot(diff(stocks_ANET))

dif_stocks_ANTM <- diff(stocks_ANTM)
dif_stocks_ANET <- diff(stocks_ANET)
dif_stocks_BA <- diff(stocks_BA)

plot(cbind(dif_stocks_ANTM,dif_stocks_ANET,dif_stocks_BA))

# Correatliton Between the stocks 
cor(stocks_BA,stocks_ANET)

##           [,1]
## [1,] 0.9344986

cor(wide_data_Main$ANET,wide_data_Main$ANTM)

## [1] 0.8950863

cor(wide_data_Main_20$ANET,wide_data_Main_20$ANTM)

## [1] 0.6139195

cor(wide_data_Main_Old$ANET,wide_data_Main_Old$ANTM)

## [1] 0.9075179

cor(stocks_BA,stocks_ANTM)

##           [,1]
## [1,] 0.9196915

cor(wide_data_Main$BA,wide_data_Main$ANTM)

## [1] 0.9196915

cor(wide_data_Main_20$BA,wide_data_Main_20$ANTM)

## [1] 0.8360629

cor(wide_data_Main_Old$BA,wide_data_Main_Old$ANTM)

## [1] 0.9595244

psych::pairs.panels(as.matrix(wide_data_Main[,c('ANTM','BA','ANET')]))

psych::pairs.panels(as.matrix(wide_data_Main_Old[,c('ANTM','BA','ANET')]))

psych::pairs.panels(as.matrix(wide_data_Main_20[,c('ANTM','BA','ANET')]))

class(stocks_ANTM)

## [1] "xts" "zoo"

plot.xts(stocks_ANTM)

acf(stocks_ANTM,lag.max = 30)

acf(stocks_ANET)

acf(stocks_BA)

plot(diff(as.zoo(stocks_ANTM)))

head(as.zoo(stocks_ANTM))

##                  
## 2015-04-28 150.15
## 2015-04-29 155.96
## 2015-04-30 151.83
## 2015-05-01 151.92
## 2015-05-04 153.45
## 2015-05-05 154.67

White Noise : Time series that show no autocorrelation are called “white noise”. Above plots shows that its of type of Random Walk model , and the (MA Model) Moving Average model should give better estimates of this index.

#   For a given time series�x�we can fit the autoregressive (AR) model using the�arima()�command and setting�order�equal to�c(1, 0, 0). Note for reference that an AR model is an�ARIMA(1, 0, 0)�model.

# Fit with Full Data
# plot.ts(stocks_ANTM)
AR_ANTM <- arima(stocks_ANTM, order  = c(1,0,0))
MA_ANTM <- arima(stocks_ANTM, order  = c(0,0,1))
AR_ANTM_fit <- as.ts(stocks_ANTM) - resid(AR_ANTM)
MA_ANTM_fit <- as.ts(stocks_ANTM) - resid(MA_ANTM)
summary(AR_ANTM)

## 
## Call:
## arima(x = stocks_ANTM, order = c(1, 0, 0))
## 
## Coefficients:
##          ar1  intercept
##       0.9978   222.5894
## s.e.  0.0018    45.1308
## 
## sigma^2 estimated as 16.88:  log likelihood = -3568.12,  aic = 7142.25
## 
## Training set error measures:
##                     ME     RMSE      MAE         MPE    MAPE     MASE
## Training set 0.0542719 4.108244 2.529343 -0.01210249 1.19899 1.002039
##                    ACF1
## Training set -0.0209907

summary(MA_ANTM)

## 
## Call:
## arima(x = stocks_ANTM, order = c(0, 0, 1))
## 
## Coefficients:
##          ma1  intercept
##       0.9678   206.4969
## s.e.  0.0058     1.7300
## 
## sigma^2 estimated as 973.9:  log likelihood = -6119.59,  aic = 12245.19
## 
## Training set error measures:
##                      ME     RMSE      MAE       MPE     MAPE     MASE      ACF1
## Training set 0.01566924 31.20706 27.96412 -4.741534 15.01558 11.07842 0.9108069

# points(AR_ANTM_fit, type = "l", col = 4, lty = 2)
# points(MA_ANTM_fit, type = "l", col = 3, lty = 3)


ggplot(stocks_ANTM, aes(x = index(stocks_ANTM))) +
  geom_line(aes(y= coredata(stocks_ANTM) , color="BASE")) +
  geom_line(aes(y = AR_ANTM_fit, color = "AR Fit")) + 
   geom_line(aes(y = MA_ANTM_fit, color = "MA Fit"))+
  ggtitle("Anthem(ANTM) from 2015-20") +
  scale_x_date(date_labels = "%b %y", date_breaks = "3 months")+
  xlab("Date") + ylab("Price") 

  # scale_colour_manual("Series", values=c("AR Fit"="gray40", "MA Fit"="firebrick4", "BASE"="darkcyan"))

Fit with Only data After 2020

# plot.ts(stocks_ANTM_MY)
AR_ANTM_MY <- arima(stocks_ANTM_MY, order  = c(1,0,0))
MA_ANTM_MY <- arima(stocks_ANTM_MY, order  = c(0,0,1))
AR_ANTM_MY_fit <- as.ts(stocks_ANTM_MY) - resid(AR_ANTM_MY)
MA_ANTM_MY_fit <- as.ts(stocks_ANTM_MY) - resid(MA_ANTM_MY)
# points(AR_ANTM_MY_fit, type = "l", col = 4, lty = 2)
# points(MA_ANTM_MY_fit, type = "l", col = 3, lty = 3)


ggplot(stocks_ANTM_MY, aes(x = index(stocks_ANTM_MY))) +
  geom_line(aes(y= coredata(stocks_ANTM_MY) , color="BASE")) +
  geom_line(aes(y = AR_ANTM_MY_fit, color = "AR Fit")) + 
   geom_line(aes(y = MA_ANTM_MY_fit, color = "MA Fit"))+
   ggtitle("Anthem(ANTM) from 2020") +
  scale_x_date(date_labels = "%b %y", date_breaks = "3 months")+
  xlab("Date") + ylab("Price") 

# Fit with Data before 2020
AR_ANTM_old <- arima(stocks_ANTM_old, order  = c(1,0,0))
MA_ANTM_old <- arima(stocks_ANTM_old, order  = c(0,0,1))
AR_ANTM_old_fit <- as.ts(stocks_ANTM_old) - resid(AR_ANTM_old)
MA_ANTM_old_fit <- as.ts(stocks_ANTM_old) - resid(MA_ANTM_old)

ggplot(stocks_ANTM_old, aes(x = index(stocks_ANTM_old))) +
  geom_line(aes(y= coredata(stocks_ANTM_old) , color="BASE")) +
  geom_line(aes(y = AR_ANTM_old_fit, color = "AR Fit")) + 
   geom_line(aes(y = MA_ANTM_old_fit, color = "MA Fit"))+
  ggtitle("Anthem(ANTM) Before 2020") +
  scale_x_date(date_labels = "%b %y", date_breaks = "3 months")+
  xlab("Date") + ylab("Price") 

0.1.6 Predicting Time Series data

We will evalute all the data models and see its predction using both the models with Currnt Years data.

# Make a 1-step through 10-step forecast based on MA
predict(AR_ANTM,n.ahead = 10)

## $pred
## Time Series:
## Start = 1260 
## End = 1269 
## Frequency = 1 
##  [1] 267.4619 267.3640 267.2663 267.1688 267.0716 266.9745 266.8777 266.7811
##  [9] 266.6846 266.5884
## 
## $se
## Time Series:
## Start = 1260 
## End = 1269 
## Frequency = 1 
##  [1]  4.108244  5.803600  7.100186  8.189663  9.146360 10.008444 10.798612
##  [8] 11.531670 12.217916 12.864855

# Plot the  series plus the forecast and 95% prediction intervals

AR_forecasts <- predict(AR_ANTM, n.ahead = 300)$pred
AR_forecast_se <- predict(AR_ANTM, n.ahead = 300)$se
plot.ts(stocks_ANTM)
points(AR_forecasts, type = "l", col = 4,lty=2)
# points(AR_forecasts - AR_forecast_se, type = "l", col = 2, lty = 1)
points(AR_forecasts - 2*AR_forecast_se, type = "l", col = 2, lty = 1)
points(AR_forecasts + 2*AR_forecast_se, type = "l", col = 2, lty = 1)

#--------------------
library(forecast)
# We can then use the ARIMA model to make forecasts for future values of the time series, using the "forecast.
AR_ANTM_forcast <- forecast(AR_ANTM, h=30,level=c(99.5))
# We can plot the observed value of stock for the , as well as the predicted that would be predicted for these and for the next 5 days using our ARIMA(0,0,1) model, 
plot(AR_ANTM_forcast)

#--------------------

# Plot of orignal data set and predicaitn  of 2020 based on old data

AR_old_forecasts <- predict(AR_ANTM_old, n.ahead = 300)$pred
AR_old_forecast_se <- predict(AR_ANTM_old, n.ahead = 300)$se
plot.ts(stocks_ANTM)
points(AR_old_forecasts, type = "l", col = 4,lty=2)
points(AR_old_forecasts - 2*AR_old_forecast_se, type = "l", col = 2, lty = 1)
points(AR_old_forecasts + 2*AR_old_forecast_se, type = "l", col = 2, lty = 1)

# MA Moving Average Modege
MA_old_forecasts <- predict(MA_ANTM_old, n.ahead = 300)$pred
MA_old_forecast_se <- predict(MA_ANTM_old, n.ahead = 300)$se
plot.ts(stocks_ANTM)
points(MA_old_forecasts, type = "l", col = 4,lty=2)
points(MA_old_forecasts - 2*MA_old_forecast_se, type = "l", col = 2, lty = 1)
points(MA_old_forecasts + 2*MA_old_forecast_se, type = "l", col = 2, lty = 1)

# @----------------------
AR_MY_forecasts <- predict(AR_ANTM_MY, n.ahead = 5)$pred
AR_MY_forecast_se <- predict(AR_ANTM_MY, n.ahead = 3)$se
plot.ts(stocks_ANTM_MY)
points(AR_MY_forecasts, type = "l", col = 4,lty=2)
points(AR_MY_forecasts - 2*AR_MY_forecast_se, type = "l", col = 2, lty = 1)
points(AR_MY_forecasts + 2*AR_MY_forecast_se, type = "l", col = 2, lty = 1)

dim(coredata(stocks_ANTM_MY))

## [1] 80  1

length(AR_MY_forecasts)

## [1] 5

# REDUCE DATE TO SEE HWO IT GOES FOR MONT OG MARCH
# PLOT COR PLOT WITH OTHER SHARS ON TOP
# ggplot(stocks_ANTM_MY, aes(x = index(stocks_ANTM_MY))) 

  # autoplot(AR_ANTM_forcast) + geom_smooth()
  # geom_line(aes(y= coredata(stocks_ANTM_MY) , color="BASE")) +
  #   ggtitle("Anthem(ANTM): Predicted next 30") +
  # scale_x_date(date_labels = "%b %y", date_breaks = "3 months")+
  # xlab("Date") + ylab("Price") 
  # 
  # geom_line(aes(y = AR_forecasts, color = "EXACT")) + 
  # geom_line(aes(y = AR_forecasts - 2*AR_forecast_se, color = "-Range"))+
  # geom_line(aes(y = AR_forecasts + 2*AR_forecast_se, color = "+Range"))+
  # ggtitle("Anthem(ANTM): Predicted next 30") +
  # scale_x_date(date_labels = "%b %y", date_breaks = "3 months")+
  # xlab("Date") + ylab("Price") 


AIC(AR_ANTM,MA_ANTM)

BIC(AR_ANTM,MA_ANTM)

AIC(AR_ANTM_MY,MA_ANTM_MY)

BIC(AR_ANTM_MY,MA_ANTM_MY)

AIC(AR_ANTM_old,MA_ANTM_old)

BIC(AR_ANTM_old,MA_ANTM_old)

0.1.7 References