# R Cointegration

From package tseries:

from po.test help:

`x <- ts(diffinv(matrix(rnorm(2000),1000,2)))`

po.test(x)

Phillips-Ouliaris Cointegration Test

data: x

Phillips-Ouliaris demeaned = -13.5288, Truncation lag parameter = 10,

p-value = 0.15

Warning message:

In po.test(x) : p-value greater than printed p-value: ** Fail to reject null hypothesis that there is no cointegration, i.e., not cointegrated**

x <- diffinv(rnorm(1000))
y <- 2.0-3.0*x+rnorm(x,sd=5)
z <- ts(cbind(x,y)) # cointegrated
po.test(z)
Phillips-Ouliaris Cointegration Test
data: z
Phillips-Ouliaris demeaned = -933.6705, Truncation lag parameter = 10,
p-value = 0.01
Warning message:
In po.test(z) : p-value smaller than printed p-value** Reject null hypothesis that there is no cointegration, i.e., cointegrated**

# R Stationarity Test

From kpss.test help

package:tseries

**Level Stationary Example**

`x <- rnorm(1000) `

**# is level stationary**

kpss.test(x)

KPSS Test for Level Stationarity

data: x

KPSS Level = 0.0319, Truncation lag parameter = 7, p-value = **0.1 ** <- fail to reject null hypothesis that** x is stationary**

Warning message:

In kpss.test(x) : p-value greater than printed p-value

**Not Stationary Example**

`y <- cumsum(x) `

**# has unit root**

kpss.test(y)

KPSS Test for Level Stationarity

data: y

KPSS Level = 9.4899, Truncation lag parameter = 7, p-value = **0.01 **<- Safe to **reject null hypothesis that x is stationary**

Warning message:

In kpss.test(y) : p-value smaller than printed p-value

**Trend Stationary Example**

`x <- 0.3*(1:1000)+rnorm(1000) `

**# is trend stationary**

kpss.test(x, null = "Trend")

KPSS Test for Trend Stationarity

data: x

KPSS Trend = 0.1068, Truncation lag parameter = 7, p-value = **0.1 **<- Fail to reject null hypothesis that **x is trend stationary**

Warning message:

In kpss.test(x, null = "Trend") : p-value greater than printed p-value