Engle-Grainger cointegration models in R

This package provides a simplified implementation of the Engle-Granger cointegration model that is geared towards the analysis of securities prices. Summary and plot functions are provided, and a convenient interface to the TTR package is given. A variety of standard unit root tests are supported, and an improved unit root test is included.

This package implements a test for a simplified form of cointegration. Namely, it checks whether or not a linear combination of two time series follows an autoregressive model of order one. In other words, given two series X and Y, it searches for parameters alpha, beta and rho such that:

Y[i] = alpha + beta * X[i] + R[i] R[i] = rho * R[i-1] + epsilon

If |rho| < 1, then X and Y are cointegrated.

Cointegration is a useful tool in many areas of economics, but this implementation is especially geared towards the analysis of securities prices. Testing for cointegration has been proposed as means for assessing whether or not two securities are suitable candidates for pairs trading.

In addition, this package implements two previously unavailable unit root tests. A test based upon the weighted symmetric estimator rho_ws of Pantula, Gonzales-Farias and Fuller is implemented as pgff.test. This test seems to provide superior performance to the standard Dickey-Fuller test adf.test and also improves upon the performance of a number of other tests previously available in R.

The variance ratio test proposed by J. Breitung is implemented as bvr.test. It has the advantage that it is a non-parametric test, and it seems to provide superior performance to other variance ratio tests available in R, although it does not perform as well as pgff.test.

Users who wish to explore more general models for cointegration are referred to the urca package of Bernard Pfaff.

DISCLAIMER: The software in this package is for general information purposes only. It is hoped that it will be useful, but it is provided WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. It is not intended to form the basis of any investment decision. USE AT YOUR OWN RISK!

Breitung, J. (2002). Nonparametric tests for unit roots and cointegration. Journal of econometrics, 108(2), 343-363.

Chan, E. (2013). Algorithmic trading: winning strategies and their rationale. (Vol. 625). John Wiley & Sons.

Clegg, M. (2014). On the Persistence of Cointegration in Pairs Trading, Proceedings of R/Finance, May 2014.

Ehrman, D.S. (2006). The handbook of pairs trading: strategies using equities, options, and futures. (Vol. 240). John Wiley & Sons.

Engle, R. F. and C. W. Granger. (1987) Co-integration and error correction: representation, estimation, and testing. Econometrica, 251-276.

Pantula, S. G., Gonzalez-Farias, G., and Fuller, W. A. (1994). A comparison of unit-root test criteria. Journal of Business & Economic Statistics, 12(4), 449-459.

Pfaff, B. (2008) Analysis of Integrated and Cointegrated Time Series with R. Second Edition. Springer, New York. ISBN 0-387-27960-1

Vidyamurthy, G. (2004). Pairs trading: quantitative methods and analysis. (Vol 217). Wiley.com.

```
library(ttr)
prices.spy <- getYahooData("SPY", 20130101, 20140101)$Close
prices.voo <- getYahooData("VOO", 20130101, 20140101)$Close
egcm(prices.spy, prices.voo)
plot(egcm(prices.spy, prices.voo))
summary(egcm(prices.spy, prices.voo))
# The yegcm method provides a convenient interface to the TTR
# package, which can fetch closing prices from Yahoo. Thus,
# the above can be simplified as follows:
e <- yegcm("SPY", "VOO", 20130101, 20140101)
print(e)
plot(e)
summary(e)
```