ACF and Plot

library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(ggplot2)
library(forecast)

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

## Registered S3 methods overwritten by 'forecast':
##   method             from    
##   fitted.fracdiff    fracdiff
##   residuals.fracdiff fracdiff

library(tseries)
library(TSA)

## Registered S3 methods overwritten by 'TSA':
##   method       from    
##   fitted.Arima forecast
##   plot.Arima   forecast

## 
## Attaching package: 'TSA'

## The following objects are masked from 'package:stats':
## 
##     acf, arima

## The following object is masked from 'package:utils':
## 
##     tar

setwd("~/Desktop")
data <- read.csv("data.csv")
summary(data)

##   observation_date     SP500            LR              UR      
##  1/1/2015 : 1      Min.   :1904   Min.   :1.500   Min.   :3.70  
##  1/1/2016 : 1      1st Qu.:2083   1st Qu.:2.047   1st Qu.:4.10  
##  1/1/2017 : 1      Median :2303   Median :2.300   Median :4.70  
##  1/1/2018 : 1      Mean   :2350   Mean   :2.320   Mean   :4.57  
##  1/1/2019 : 1      3rd Qu.:2642   3rd Qu.:2.655   3rd Qu.:5.00  
##  10/1/2015: 1      Max.   :2902   Max.   :3.150   Max.   :5.70  
##  (Other)  :44

UR <- ts(data["UR"], frequency=12, start=c(2015, 1))
plot(UR, type='o')

1. Based on steady decline in the plot it is clear that Unemployment is on a downward Trend with some iregularities with respect to the trend.

library(dplyr)
library(ggplot2)
library(forecast)
library(tseries)
library(TSA)

setwd("~/Desktop")
data <- read.csv("data.csv")

UR <- ts(data["UR"], frequency=12, start=c(2015, 1))

ggAcf(UR)

2. What we see here is a consistent decrease within each lag period. This showing stays consistent with the time series represented above with clear indication trending downwards.

setwd("~/Desktop")
data <- read.csv("data.csv")

UR <- ts(data["UR"], frequency=12, start=c(2015, 1))

summary(UR) #Summary

##        UR      
##  Min.   :3.70  
##  1st Qu.:4.10  
##  Median :4.70  
##  Mean   :4.57  
##  3rd Qu.:5.00  
##  Max.   :5.70

mean(UR)-2*sd(UR) #3.444

## [1] 3.444235

mean(UR)+2*sd(UR) #5.696

## [1] 5.695765

3. There is a 95% chance the next months uemployment will be between (3.444, 5.696) You can say approximately there is less than a 10% chance of next months unemployment being greater than 5.4%