Description Usage Arguments Details Value Author(s) References See Also Examples

Computes the log likelihood of a partially cointegrated model

1 2 3 4 | ```
loglik.pci(Y, X, beta, rho, sigma_M, sigma_R,
M0 = 0, R0 = 0,
calc_method = c("css", "kfas", "ss", "sst", "csst"),
nu = pci.nu.default())
``` |

`Y` |
The time series that is to be modeled. A plain or |

`X` |
A (possibly |

`beta` |
A vector of length |

`rho` |
The coefficient of mean reversion. |

`sigma_M` |
The standard deviation of the innovations of the mean-reverting component of the model. |

`sigma_R` |
The standard deviation of the innovations of the random walk component of the model. |

`M0` |
The initial value of the mean-reverting component. Default = 0. |

`R0` |
The initial value of the random walk component. Default = 0. |

`calc_method` |
Specifies the Kalman filter implementation that will be used for computing the likelihood score: "ss" Steady-state Kalman filter "css" C++ implementation of steady-state Kalman filter "kfas" Kalman filter implementation of the KFAS package "sst" Steady-state Kalman filter using t-distributed innovations "csst" C++ implementation of steady-state Kalman filter using t-distributed innovations
Default: |

`nu` |
The degrees-of-freedom parameter to be used if |

The partial cointegration model is given by the equations:

*
Y[t] = beta[1] * X[t,1] + beta[2] * X[t,2] + ... + beta[k] * X[t,k] + 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] ~ N(0, sigma_M^2)*

*epsilon_R[t] ~ N(0, sigma_R^2)*

Given the input series
`Y`

and `X`

,
and given the parameter values
`beta`

, `rho`

, `M0`

and `R0`

,
the innovations `epsilon_M[t]`

and `epsilon_R[t]`

are calculated
using a Kalman filter. Based upon these values, the log-likelihood score
is then computed and returned.

The log of the likelihood score of the Kalman filter

Matthew Clegg matthewcleggphd@gmail.com

Christopher Krauss christopher.krauss@fau.de

Jonas Rende jonas.rende@fau.de

Clegg, Matthew, 2015.
Modeling Time Series with Both Permanent and Transient Components
using the Partially Autoregressive Model.
*Available at SSRN: http://ssrn.com/abstract=2556957*

`egcm`

Engle-Granger cointegration model

`partialAR`

Partially autoregressive models

1 2 3 4 5 6 7 | ```
##---- Should be DIRECTLY executable !! ----
##-- ==> Define data, use random,
##-- or do help(data=index) for the standard data sets.
set.seed(1)
YX <- rpci(n=500, beta=c(2,3,4), sigma_C=c(1,1,1), rho=0.9, sigma_M=0.1, sigma_R=0.2)
loglik.pci(YX[,1], YX[,2:ncol(YX)], beta=c(2,3,4), rho=0.9, sigma_M=0.1, sigma_R=0.2)
``` |

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