Estimation for Non-Negative Lévy-Driven CARMA Processes

Modelling Energy Spot Prices by Volatility Modulated Lévy-Driven Volterra Processes

“…Higher lags were however slightly better fitted by the gamma kernel used in the previous subsection. Figure 5 Note that in addition to estimating the parameters of the g function coming from a CARMA process one can also recover the driving Lévy process of a CARMA process based on recent findings by Brockwell, Davis and Yang [36]. This will make it possible to also address the question of whether stochastic volatility is needed to model electricity spot prices or not.…”

Modelling the Impact of Wind Power Production on Electricity Prices by Regime-Switching Lévy Semistationary Processes

“…In our goodness-of-fit study, we indeed find that such a model choice is suitable here. Note that [6] have discussed in detail how a discretely sampled CARMA process can be represented as a weak ARMA process. Using this representation we have first estimated the corresponding ARMA(2,1) parameters by a quasi-maximum likelihood method.…”

A Multifactor Approach to Modelling the Impact of Wind Energy on Electricity Spot Prices

“…, p, the discrete-time process {Y Proof. For the proof we refer the reader to [Brockwell et al, 2011].…”

“…Having estimated the parameters of CARMA(2,1), we need to recover the background driving Lévy process L(t). We will use results from Section 5 of [Brockwell et al, 2011]. The recommended choice is r such that |λ r | is minimal, which minimizes the contribution of λ r t 0 Y (r) (s)ds compared to Y (r) (t) − Y (r) (0), as discussed by [Brockwell et al, 2011, Example 4].…”