* open the data set
use wilcox

* output results
log using wilcox.log, replace

* define the data as time series
tsset time

* generate ln retail sales
* and ln oasi payments
gen retail_sales_ln=ln(retail)
gen oasi_ln=ln(oasi)

* generate lags of both
gen retail_sales_ln_1=retail_sales_ln[_n-1]
gen oasi_ln_1=oasi_ln[_n-1]

* test for whether retail sales is a random walk
reg retail_sales_ln retail_sales_ln_1
test retail_sales_ln_1=1

* generate 1st differences in ln(retail sales)
* and ln(oasi)

gen d_retail_sales_ln=retail_sales_ln-retail_sales_ln_1
gen d_oasi_ln=oasi_ln-oasi_ln_1

* generate a lag of d_oasi_ln
gen d_oasi_ln_1=d_oasi_ln[_n-1]

* regress 1st diff in ln(retail) on 1st diff in
* oasi and lag
reg d_retail_sales_ln d_oasi_ln d_oasi_ln_1
test d_oasi_ln d_oasi_ln_1
estat dwatson