# KPSS test thinks that regression is spurious

It should be obvious that there is a relationship between the market price of black pepper and the market price of white pepper.

library(forecast)
library(fpp)
library(AER)

data(PepperPrice)

coint_lm <- tslm(PepperPrice[,'black'] ~ PepperPrice[,'white'])
summary(coint_lm)


The PO Test reveals a co-integrated relationship between the two time series.

tseries::po.test(coint_lm$model) # NOT spurious  However, when I run the KPSS test with drift and trend, the test thinks that there is a unit root in the residuals. tseries::kpss.test(coint_lm$residuals, null="Trend") # SPURIOUS!!!!


Is the null hypothesis of no unit root being rejected due to large sample size? Or there is something going on with the null='Trend' argument?

ADF and PP tests behave fine.

tseries::adf.test(coint_lm$residuals) # NOT spurious tseries::pp.test(coint_lm$residuals) # NOT spurious