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time_Series_Kroger.Rmd
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---
title: "Time Series Analysis for kroger Data"
author: "Akshay"
date: "18/04/2020"
output: pdf_document
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = FALSE)
library(ggplot2)
library(forecast)
library(fpp)
library(knitr)
library(quantmod)
library(timeSeries)
library(tseries)
library(xts)
library(zoo)
library(gridExtra)
suppressMessages(library(dplyr))
library(tidyverse)
library(tibbletime)
library(ggfortify)
```
```{r}
#loading the data
kroger <- read_csv("KR.csv")
# check for NA values
sum(is.na(kroger))
```
## Plotting general time series plot and Chartseries plot as well
```{r}
#Getting close prices for the kroger data
summary(kroger)
sd(kroger$Close)
kroger.close <-ts(kroger$Close, start = 2005, frequency = 12)
#view(kroger.close)
kroger.close
#plotting the general time series plot for kroger
plot(kroger.close,main="kroger", sub="Stock Price Variation with respect to Time",
xlab="Time (in years)", ylab=" Stock Prices (in USD)",col.lab="green", cex.lab=3, type ="l")
?plot
#converting list object to time series object
kroger <- ts(kroger)
dates <- as.Date("2005-01","%Y/%m") + 0:180
kroger <- as.xts(kroger, reclass=FALSE, order_by =dates)
#data to train my models upon :
kroger.Close <- ts(kroger$Close, start =c(2005,01), end= c(2017,12), frequency = 12)
```
```{r}
summary(kroger.close)
sd(kroger.close)
```
## Lets decompose : the time series
```{r}
kroger.Close.de.add = decompose(kroger.Close, type = "additive")
kroger.Close.de.mul = decompose(kroger.Close, type = "multiplicative")
kroger.close.de.add = decompose(kroger.close, type = "additive")
kroger.close.de.mul = decompose(kroger.close, type = "multiplicative")
plot(kroger.Close.de.mul)
plot(kroger.close.de.mul)
```
#lets convert time series into log and sqrt transformed serieses
```{r}
kroger.close.log = log(kroger.close)
kroger.close.sqrt = sqrt(kroger.close)
kroger.Close.log = log(kroger.Close)
kroger.Close.sqrt = sqrt(kroger.Close)
kroger.close
plot(kroger.close)
plot(kroger.close.log)
plot(kroger.close.sqrt)
```
# lets perform ADF tests on these Time series
```{r}
adf.test(kroger.close)
adf.test(kroger.close.log)
adf.test(kroger.close.sqrt)
```
## Lets us make differenced time series
```{r}
dkroger.close = diff(kroger.close, lag=1)
dkroger.close.log = diff(kroger.close.log, lag=1)
dkroger.close.sqrt = diff(kroger.close.sqrt, lag=1)
```
## Lets us make differenced time series
```{r}
adf.test(dkroger.close )
adf.test(dkroger.close.log)
adf.test(dkroger.close.sqrt)
```
## Lets us make differenced 12 time series
```{r}
dkroger.close.sea = diff(kroger.close, lag=12)
dkroger.close.log.sea = diff(kroger.close.log, lag=12)
dkroger.close.sqrt.sea = diff(kroger.close.sqrt, lag=12)
```
```{r}
library(astsa)
acf2(dkroger.close.sea)
(dkroger.close.log.sea)
dkroger.close.sqrt.sea
```
#Lets look at ACF and PACF plots
```{r height = 10, width = 10}
plot(acf(kroger.close), main = "ACF plot for kroger closing stock Prices")
plot(acf(kroger.close.log))
plot(acf(kroger.close.sqrt))
plot(pacf(kroger.close))
plot(pacf(kroger.close.log))
plot(pacf(kroger.close.sqrt))
```
# Fitting auto.arima to get the best model
```{r}
kroger.Close.auto.arima= auto.arima(kroger.Close, trace = TRUE)
#best model ARIMA(0,1,0) without drift i.e. include.drift=FALSE,
# seasonal best model : ARIMA(0,1,0)(0,0,1)[12] with drift 552.0378
kroger.Close.log.auto.arima = auto.arima(kroger.Close.log, trace = TRUE)
#best model ARIMA(1,1,1), with drift = -411.2681
#seasonal best model : ARIMA(1,1,1)(0,0,1)[12] with drift = -404.947
kroger.Close.sqrt.auto.arima = auto.arima(kroger.Close.sqrt, trace = TRUE)
#best model ARIMA(1,1,1) = -160.08
#seasonal best model : ARIMA(0,1,0)(0,0,1)[12] with drift = -153.205
```
#making all the above models
```{r}
kroger.Close.arima = Arima(kroger.Close, order = c(0,1,0), include.drift = FALSE )
kroger.Close.arima.s = Arima(kroger.Close, order =c(0,1,0),include.drift = TRUE,seasonal = list(order=c(0,0,1)))
kroger.Close.log.arima = Arima(kroger.Close.log, order = c(1,1,1), include.drift = TRUE )
kroger.Close.log.arima.s = Arima(kroger.Close.log, order = c(1,1,1), include.drift = TRUE, seasonal = list(order=c(0,0,1)))
kroger.Close.sqrt.arima = Arima(kroger.Close.sqrt, order = c(1,1,1), include.drift = FALSE )
kroger.Close.sqrt.arima.s = Arima(kroger.Close.sqrt, order = c(0,1,0), include.drift = TRUE, seasonal = list(order=c(0,0,1)))
```
#lets make interactive Plots for the test data
```{r}
fkroger.Close.arima = forecast(kroger.Close.arima, h=24)
fkroger.Close.arima.s = forecast(kroger.Close.arima.s, h=24)
fkroger.Close.log.arima = forecast(kroger.Close.log.arima, h=24)
fkroger.Close.log.arima.s = forecast(kroger.Close.log.arima.s, h=24)
fkroger.Close.sqrt.arima = forecast(kroger.Close.sqrt.arima, h=24)
fkroger.Close.sqrt.arima.s = forecast(kroger.Close.sqrt.arima.s, h=24)
```
#lets find RMS error on test set
```{r}
#Values to be predicted
original_val <- window(kroger.close, start =2018)
rmserr <- function(x,y){
p =x-y
r=sum(p^2)
r = r /length(x)
r= sqrt(r)
return (r)
}
(Ekroger.Close.arima <- rmserr(fkroger.Close.arima$mean,original_val ))
(Ekroger.Close.arima.s <- rmserr(fkroger.Close.arima.s$mean,original_val))
(Ekroger.Close.log.arima. <- rmserr(exp(fkroger.Close.log.arima$mean),original_val ))
(Ekroger.Close.log.arima.s <- rmserr(exp(fkroger.Close.log.arima.s$mean),original_val))
(Ekroger.Close.sqrt.arima. <- rmserr((fkroger.Close.sqrt.arima$mean)^2,original_val ))
(Ekroger.Close.sqrt.arima.s <- rmserr((fkroger.Close.sqrt.arima.s$mean)^2,original_val))
```
```{r}
```
#lets see the parameters for the best model
```{r}
kroger.Close.arima.s
```
#fitting the best model for time series till 2020 and prediction for 2023
```{r}
kroger.close.arima.s = Arima(kroger.close, order = c(0,1,0), include.drift = TRUE, seasonal = list(order=c(0,0,1)))
Fkroger.close.arima.s = forecast(kroger.close.arima.s,h=36)
```
```{r}
plot_forecast(Fkroger.close.arima.s, title = "Forcasting of Kroger Share Closing price for 2020 to 2023", Xtitle = "Year", Ytitle = "Closing Stock Price")
```
```{r}
# Validation of the model by the ljung test
Box.test(Fkroger.close.arima.s$residuals, lag =12, type = "Ljung")
```
```{r}
# Confedence interval ofthe
confint(kroger.close.arima.s)
Fkroger.close.arima.s$mean
```
#