• Corpus ID: 248693347

The multivariate ARMA/CARMA transformation relation

@inproceedings{Eggen2022TheMA,
  title={The multivariate ARMA/CARMA transformation relation},
  author={Mari Dahl Eggen},
  year={2022}
}
  • M. Eggen
  • Published 10 May 2022
  • Mathematics
A transformation relation between multivariate ARMA and CARMA processes is derived through a discretization procedure. This gives a direct relationship between the discrete time and continuous time analogues, serving as the basis for an estimation method for multivariate CARMA models. We will see that the autoregressive coefficients, making up the deterministic part of a multivariate CARMA model, are entirely given by the transformation relation. An Euler discretization convergence rate of jump… 
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References

SHOWING 1-10 OF 46 REFERENCES

Multivariate CARMA processes, continuous-time state space models and complete regularity of the innovations of the sampled processes

The class of multivariate Levy-driven autoregressive moving average (MCARMA) processes, the continuous-time analogs of the classical vector ARMA processes, is shown to be equivalent to the class of…

Factorization and discrete-time representation of multivariate CARMA processes

In this paper we show that stationary and non-stationary multivariate continuous-time ARMA (MCARMA) processes have the representation as a sum of multivariate complexvalued Ornstein-Uhlenbeck…

Parametric estimation of the driving Lévy process of multivariate CARMA processes from discrete observations

Some approaches on how to use the delta operator when identifying continuous-time processes

When identifying a continuous-time process from discrete-time data, an obvious approach is to replace the derivative operator in a continuous-time model by an approximation such as the delta…

Whittle estimation for continuous-time stationary state space models with finite second moments

We consider Whittle estimation for the parameters of a stationary solution of a continuous-time linear state space model sampled at low frequencies. In our context, the driving process is a Lévy…

Continuous time ARMA processes: Discrete time representation and likelihood evaluation

Estimation of stable CARMA models with an application to electricity spot prices

The theoretical properties and estimation of continuous-time ARMA (CARMA) processes, which are driven by a stable Lévy process, are discussed and a CARMA(2,1) model is fit to spot prices from the Singapore New Electricity Market.

Recent results in the theory and applications of CARMA processes

Just as ARMA processes play a central role in the representation of stationary time series with discrete time parameter, $$(Y_n)_{n\in \mathbb {Z}}$$(Yn)n∈Z, CARMA processes play an analogous role in…

Levinson-Durbin-type algorithms for continuous-time autoregressive models and applications

Different forms of Levinson-Durbin-type algorithms, which relate the coefficients of a continuous-time autoregressive model to the residual variances of certain regressions or their ratios, are…

Sampling, Embedding and Inference for CARMA Processes

A CARMA(p,q) process Y is a strictly stationary solution Y of the pth‐order formal stochastic differential equation a(D)Yt = b(D)DLt, where L is a two‐sided Lévy process, a(z) and b(z) are…