CointegrationOfTwoTS: Investigate the Cointegration between two time series

In Mthrun/TSAT: Time Series Analysis Tools (TSAT)

Investigate the Cointegration between two time series

Description

If TS1 and TS2 are cointegrated then a linear combination must be stationary.

Usage

CointegrationOfTwoTS(TS1, TS2, alpha = 1, type='c',PlotIt = TRUE)

Arguments

TS1	[1:n] vector of data
TS2	[1:n] vector of data
alpha	linear factor, do not search for right alpha with PLS statistics.
type	a character string describing the type of UnitrootTests (the unit root regression). Valid choices are "nc" for a regression with no intercept (constant) nor time trend, and "c" for a regression with an intercept (constant) but no time trend, "ct" for a regression with an intercept (constant) and a time trend. The default is "c".
PlotIt	TRUE: plot distribution analysis of CointegrationOrder1 (which seems to be the residuals?)

Details

"In the econometric literature, a time series zt is said to be an integrated process of order 1, that is, an I(1) process, if (1−B)zt is stationary and invertible. In general, a univariate time series zt is an I(d) process if (1−B)dzt is stationary and invertible, where d > 0. The order d is referred to as the order of integration or the multiplicity of a unit root. A stationary and invertible time series is said to be an I(0) process." [Tsay, 2013, p.295]

In short, A cointegration relationship exists between two (or more) time series when there is a long-term balance between two (or more) transient (integrated) variables. Cointegration is applied to detrend time series (non-stationary time series). It represents an alternative to a detrending through the computation of differences (DiffFilter). Trend correction is often proposed in order to avoid false regressions.

Value

List of

CointegrationOrder1	CointegrationOrder1=TS1-alpha*TS2
adf_fUnitRoots	Check cointegration with UnitrootTests
adg_tseries	Check cointegration with adf.test

Note

regression analysis fails if ts are non stationary

the simplest unit-root nonstationary time series is the univariate random walk

linear combination of several unit-root nonstationary time series can become a stationary series [Box and Tiao, 1977].

Author(s)

Michael Thrun

References

[Tsay, 2013] Tsay, Ruey S: Multivariate time series analysis: with R and financial applications, John Wiley & Sons, 2013.

[Box and Tiao, 1977] Box, G. E. P. and Tiao, G. C. (1977): A canonical analysis of multiple time serie, Biometrika, 64, pp. 355–366, 1977.

See Also

po.test

Mthrun/TSAT documentation built on Feb. 5, 2024, 11:15 p.m.