partialAR-package: Partial autoregression

Description

Fits time series models which consist of a sum of a permanent and a transient component. The permanent component is modeled as a random walk, while the transient component is modeled as an autoregressive series of order one.

Arguments

Disclaimer

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!

Details

ll{ Package: partialAR Type: Package Version: 1.0 Date: 2015-01-12 License: GPL-2 | GPL-3 } This package fits time series models which consist of a sum of a permanent and a transient component. In other words, the model fitted is:

$$X_t = M_t + R_t$$ $$M_t = \rho M_{t-1} + \epsilon_{M,t}$$ $$R_t = R_{t-1} + \epsilon_{R,t}$$ $$-1 < \rho < 1$$ $$\epsilon_{M,t} \sim N(0,\sigma_M^2)$$ $$\epsilon_{R,t} \sim N(0,\sigma_R^2)$$

This model may be useful when modeling a time series that is thought to be primarily mean-reverting but which may also contain some random drift.

References

Summers, Lawrence H. Does the stock market rationally reflect fundamental values? Journal of Finance, 41(3), 591-601. Poterba, James M. and Lawrence H. Summers. Mean reversion in stock market prices: Evidence and implications. Journal of Financial Economics, 22(1), 27-59. Clegg, Matthew. Modeling Time Series with Both Permanent and Transient Components using the Partially Autoregressive Model. Available at SSRN: http://ssrn.com/abstract=2556957

Examples

Run this code

set.seed(1)
    x <- rpar(1000, 0.8, 1, 0.5)  # Generate a random PAR sequence
    fit.par(x)                  # Estimate its parameters
    plot(fit.par(x))            # Plot the estimate
    test.par(x)                 # Test the goodness of fit

# An example involving European stock market data
    data(EuStockMarkets)   # European Stock Markets 1991-1998
    
    # Check for cointegration between German DAX and Swiss SMI
    egcm(log(EuStockMarkets[,c("DAX", "SMI")]))
    
    # The series are not found to be cointegrated.
    # Perhaps they are partially cointegrated?  Check the residuals
    # of the cointegration fit for partial autoregression:
    fit.par(egcm(EuStockMarkets[,c("DAX", "SMI")])$residuals)
    
    # A plot of the model looks promising:
    \dontrun{plot(fit.par(egcm(EuStockMarkets[,c("DAX", "SMI")])$residuals))}
    
    # 74    # AR(1) process.  However, it is important to check whether this is
    # a better explanation than a simple random walk:
    test.par(egcm(EuStockMarkets[,c("DAX", "SMI")])$residuals)
    
    # The p-value is found to be 0.36, so the random walk hypothesis
    # cannot be rejected.
    
    # Another example involving a potential pairs trade between
    # Coca-Cola and Pepsi.
    
    # Fetch the price series for Coca-Cola (KO) and Pepsi (PEP) in 2014
    library(TTR)
    KO <- getYahooData("KO", 20140101, 20141231)$Close
    PEP <- getYahooData("PEP", 20140101, 20141231)$Close
    
    # Check whether they were cointegrated
    library(egcm)
    egcm(KO,PEP)
    
    # It turns out that they are not cointegrated.  Perhaps a better
    # fit can be obtained with the partially autoregressive model:
    fit.par(egcm(KO,PEP)$residuals)
    
    # The mean-reverting component of the above fit explains 90    # the variance of the daily returns.  Thus, it appears that the
    # two series are close to being cointegrated.  A plot further
    # confirms this:
    plot(fit.par(egcm(KO,PEP)$residuals))
    
    # Still, it is important to check whether or not the residual
    # series is simply a random walk:
    test.par(egcm(KO,PEP)$residuals)
    
    # In this case, the p-value associated with the hypothesis that
    # the series is partially autoregressive is 0.12.  Thus, the
    # evidence of partial autoregression is marginal. The random walk
    # may be a better explanation.