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Stationary Stochastic Processes and their Properties in the Time
Estimation and Testing of AutoregressiveMoving Average Models
State Space Models and the Kalman Filter
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algorithm ARIMA ARMA models ARMA(p asymptotic autocorrelation function autoregressive autoregressive process chapter co-integration coefficients computed conditional constructed correlogram corresponding covariance matrix cycle cyclical defined denoted derivatives deterministic differencing disturbance term EWMA example explanatory variables expression figure follows forecast function formulation Fourier frequency domain Gaussian generalised given gives independent information matrix invertible Kalman filter lag operator lagged values least squares likelihood function linear trend logarithm ML estimator MMSE moving average multivariate non-linear non-stationary normally distributed null hypothesis obtained parameters periodogram polynomial portmanteau test power spectrum prediction error predictor procedure properties random walk recursion regression model residuals result sample autocorrelations sample spectral density seasonal pattern serial correlation series models smoothing space form spectral density starting values stationary process stochastic process structural time series sum of squares summation uncorrelated univariate unobserved components variance vector white noise white noise process yields yT+i yT+i\T