@Article{Jonasson:2008:AEV,
  author =       "Kristjan Jonasson",
  title =        "Algorithm 878: Exact {VARMA} Likelihood and its Gradient for Complete and Incomplete Data with {Matlab}",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       "35",
  number =       "1",
  month =        jul,
  year =         "2008",
  pages =        "6:1--6:11",
  URL =          "http://doi.acm.org/10.1145/1377603.1377609",
  abstract =     "Matlab functions for the evaluation of the exact log-likelihood of VAR and VARMA time series models 
                 are presented (vector autoregressive moving average). The functions accept incomplete data, and calculate 
                 analytical gradients, which may be used in parameter estimation with numerical likelihood maximization. 
                 Allowance is made for possible savings when estimating seasonal, structured or distributed lag models. 
                 Also provided is a function for creating simulated VARMA time series that have an accurate distribution 
                 from term one (they are spin-up free). The functions are accompanied by a a simple example driver, a 
                 program demonstrating their use for real parameter fitting, as well as a test suite for verifying their 
                 correctness and aid further development. The paper concludes with description of numerical results obtained 
                 with the algorithm.",
}