Q$1.$ Copy and paste the code as follows.

set.seed$(200)$

install.packages$("$tseries$")$ #Only if you have not already installed

require$($tseries$)$

rwalk$1=$ c$($cumsum$($rnorm$(203)))$

rwalk$1.$ts $=$ ts$($rwalk$1)$

rwalk$2=$ c$($cumsum$($rnorm$(203)))$

rwalk$2.$ts $=$ ts$($rwalk$2)$

#use the seqplot from tseries package

seqplot.ts$($rwalk$1.$ts$,$ rwalk$2.$ts$)$

data.frame$($day$=$rep$(1$:$7,29),$rwalk$1.$ts$=$rwalk$1.$ts$,$ rwalk$2.$ts$=$rwalk$2.$ts$)$

$$

a$.$ Save the results into data.frame object and store it in your PC$.(1)$

b$.$ Comment on the stationarity of the two series using plots. Also, explain the possible models that can be applied on the series. $(1)$

c$.$ Run a regression and test the relationship between the dependent variable rwalk$1.$ts and the independent variable rwalk$2.$ts$.(3)$

d$.$ To check for stationarity, apply the unit root tests, only Ljung$-$Box, Box$-$Pierce, and Augmented Dickey$-$Fuller. $(5)$

e$.$ What is the order of integration in this series. $(1)$

Q$2.$ Suppose the data generated above is of growth in sales. Use the time series generated above and generate $1-$day ahead forecast using the Time Series Additive Model. Explain each step in details. $(7)$

Q$3.$ Describe the assumptions of the Linear Regression Model. $(2)$