Unit Root and cointegration Analysis

Using the dataset provided

$($a$)$ Plot a visual graph of :

$($i$)$ Food expenditure

$($ii$)$ Total expenditure

$($b$)$ What impression about the stationarity of the data can you make from the visual plot.

c$)$ Examine the autocorrelation function $($ACF$)$ and correlogram of the two dataset

$($d$)$ From the correlogram in c$)$ what can you say about the stationarity of the two series.

e$)$ Conduct a unit root test on Foodexpenditure and Total expenditure data using

i$)$ Dickey Fuller Method

ii$)$ Augmented Dickey$-$Fuller method

f$)$ Test for cointegration between Food expenditure and Total expenditure

g$)$ Given the results in $($f$),$ What inference can you draw about the relationship between food expenditure and total expenditure

h$)$ Following the inference observed in $($g$),$ Fit an error correction model and interprete the result.

Obs Food Expenditure Total Expenditure

Obs FdExp TotExp

$1217380$

$2196388$

$3303391$

$4274415$

$5325456$

$6260460$

$7300472$

$8325478$

$9331494$

$10345510$

$11325525$

$12362554$

$13315575$

$14355579$

$15325584$

$16370586$

$17390590$

$18422608$

$19410610$

$20383616$

$21315611$

$22267623$

$23420627$

$24300630$

$25411635$

$26220640$

$27403649$

$28350650$

$29390655$

$30380662$

$31470663$

$32322677$

$33540686$

$34433690$

$35291695$

$36340695$

$37500695$

$38450722$

$39415721$

$40545730$

$41360731$

$42450733$

$43395745$

$44430751$

$45332752$

$46399754$

$47446769$

$48480773$

$49352773$

$50410775$

$51380789$

$52619788$

$53530790$

$54360795$

$55305801$

$56341817$