The Identification of Seasonal Autoregressive Models

Abstract: In this article we present a new approach for identifying seasonal autoregressive models and the degree of differencing required to induce stationarity in the data. The identification method is iterative and consists in systematically fitting increasing order models to the data and then verifying that the resulting residuals behave like white noise using a two stage autoregressive order determination criterion. Once the order of the process is determined the identified structure is tested to see if it can be simplified. Simulation experiments based on different model structures with varying number of observations and parameter values as well as some macroeconomic data are used to evaluate the performance of the procedure.

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    A Comparison Between Different Order-Determination Criteria for Identification of ARIMA Models

    Abstract: The small sample performance of several order determination criteria for identification of ARIMA models is compared using simulated and economic data. We also demonstrate how the residual white noise autoregressive order determination criterion can be used to identify unit roots in non-stationary data.

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    Using the Residual White Noise Autoregressive Order Determination Criterion to Identify Unit Roots in ARIMA Models

    Abstract: We present a simplified form of a univariate identification approach for time series models based on the residual white noise autoregressive order determination criterion and linear estimation methods. We also show how the procedure can be used to identify the degree of differencing necessary to induce stationarity in data. The performance of this approach is also contrasted with Portmanteau tests for detection of white noise residuals and with Dickey-Fuller procedures for detection of unit roots. Simulated and economic data are used to demonstrate the capabilities of the modified approach.

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