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Vector Autoregressive Moving Average Processes

In: New Introduction to Multiple Time Series Analysis

Author

Listed:
  • Helmut Lütkepohl

    (European University Institute)

Abstract

In this chapter, we extend our standard finite order VAR model, % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEamaaBa % aaleaacaWG0baabeaakiabg2da9iabe27aUjabgUcaRiaadgeadaWg % aaWcbaGaaGymaaqabaGccaWG5bWaaSbaaSqaaiaadshacqGHsislca % aIXaaabeaakiabgUcaRiablAciljabgUcaRiaadgeadaWgaaWcbaGa % amiCaaqabaGccaWG5bWaaSbaaSqaaiaadshacqGHsislcaWGWbaabe % aakiabgUcaRiabew7aLnaaBaaaleaacaWG0baabeaakiaacYcaaaa!4E94! $$y_t = \nu + A_1 y_{t - 1} + \ldots + A_p y_{t - p} + \varepsilon _t , $$ by allowing the error terms, here εt, to be autocorrelated rather than white noise. The autocorrelation structure is assumed to be of a relatively simple type so that εt has a finite order moving average (MA) representation, % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aaS % baaSqaaiaadshaaeqaaOGaeyypa0JaamyDamaaBaaaleaacaWG0baa % beaakiabgUcaRiaad2eadaWgaaWcbaGaaGymaaqabaGccaWG1bWaaS % baaSqaaiaadshacqGHsislcaaIXaaabeaakiabgUcaRiablAciljab % gUcaRiaad2eadaWgaaWcbaGaamyCaaqabaGccaWG1bWaaSbaaSqaai % aadshacqGHsislcaWGXbaabeaakiaacYcaaaa!4C08! $$\varepsilon _t = u_t + M_1 u_{t - 1} + \ldots + M_q u_{t - q} ,$$ where, as usual, u t is zero mean white noise with nonsingular covariance matrix Σu. A finite order VAR process with finite order MA error term is called a VARMA (vector autoregressive moving average) process.

Suggested Citation

  • Helmut Lütkepohl, 2005. "Vector Autoregressive Moving Average Processes," Springer Books, in: New Introduction to Multiple Time Series Analysis, chapter 11, pages 419-446, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-27752-1_11
    DOI: 10.1007/978-3-540-27752-1_11
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