Titlebook: Linear Time Series with MATLAB and OCTAVE; Víctor Gómez Textbook 2019 Springer Nature Switzerland AG 2019 Linear time series.MATLAB.State

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https://doi.org/10.1007/978-3-030-20790-8Linear time series; MATLAB; State space models; Kalman filter; Univariate time series; Multivariate time

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Quick Introduction to SSMMATLAB,In this chapter, we will present some examples on how SSMMATLAB can easily handle some of the more popular univariate and multivariate time series models. In this way, the user can quickly familiarize himself/herself with this software tool.

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Stationarity, VARMA, and ARIMA Models,Statistically speaking, a . is a finite set of values {..…, ..} taken by certain .-dimensional random vectors {..…, ..}. The proper framework in which to study time series is that of stochastic processes.

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Multivariate Structural Models,Multivariate structural models are defined in a way similar to that of univariate structural models, described in Sect. .. For example, let the stochastic vector .. satisfy .. = ..?+?..?+?.., where .. is the trend, .. is the seasonal, and .. is the irregular component.

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The State Space Model,The state space model considered in SSMMATLAB is . where {..} is a multivariate process with ., .., .., .., .., .., and .. are time-varying deterministic matrices, . is a constant bias vector, . is the state vector, and {..} is a sequence of uncorrelated stochastic vectors, ., with zero mean and common covariance matrix ...

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Statistics and Computinghttp://image.papertrans.cn/l/image/586432.jpg