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EstMdl = estimate(Mdl,y)
[EstMdl,EstParamCov,logL,info]
= estimate(Mdl,y)
[EstMdl,EstParamCov,logL,info] = estimate(Mdl,y,Name,Value)
EstMdl = estimate(Mdl,y) uses maximum likelihood to estimate the parameters of the ARIMA(p,D,q) model Mdl given the observed univariate time series y. EstMdl is an arima model that stores the results.
[EstMdl,EstParamCov,logL,info] = estimate(Mdl,y) additionally returns EstParamCov, the variance-covariance matrix associated with estimated parameters, logL, the optimized loglikelihood objective function, and info, a data structure of summary information.
[EstMdl,EstParamCov,logL,info] = estimate(Mdl,y,Name,Value) estimates the model with additional options specified by one or more Name,Value pair arguments.
Suppose EstParamCov is an estimated parameter covariance matrix returned by estimate. The software sets the variances and covariances of parameters fixed during estimation to 0. Enter this command to count the number of free parameters (numParams) in a fitted model.
numParams = sum(any(EstParamCov))
This command counts the number of columns (or equivalently, rows) with any nonzero values.
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[2] Enders, W. Applied Econometric Time Series. Hoboken, NJ: John Wiley & Sons, 1995.
[3] Greene, W. H. Econometric Analysis. 3rd ed. Upper Saddle River, NJ: Prentice Hall, 1997.
[4] Hamilton, J. D. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.