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State Space Models

In: New Introduction to Multiple Time Series Analysis

Author

Listed:
  • Helmut Lütkepohl

    (European University Institute)

Abstract

State space models may be regarded as generalizations of the models considered so far. They have been used extensively in system theory, the physical sciences, and engineering. The terminology is therefore largely from these fields. The general idea behind these models is that an observed (multiple) time series y 1 ,…, y T depends upon a possibly unobserved state z t which is driven by a stochastic process. The relation between y t and z t is described by the observation or measurement equation 18.1.1 % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEamaaBa % aaleaacaWG0baabeaakiabg2da9iaadIeadaWgaaWcbaGaamiDaaqa % baGccaWG6bWaaSbaaSqaaiaadshaaeqaaOGaey4kaSIaamODamaaBa % aaleaacaWG0baabeaakiaacYcaaaa!4106! $$ y_t = H_t z_t + v_t , $$ where H t is a matrix that may also depend on the period of time, t, and v t is the observation error which is typically assumed to be a noise process.

Suggested Citation

  • Helmut Lütkepohl, 2005. "State Space Models," Springer Books, in: New Introduction to Multiple Time Series Analysis, chapter 18, pages 611-642, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-27752-1_18
    DOI: 10.1007/978-3-540-27752-1_18
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