Diagnostics for Time Series Analysis

Test statistics are proposed to determine the goodness of fit of a time series model. The test statistics are based on a sequence of random variables that are independent and standard normal if the model is correct. The paper shows how to compute this sequence of random variables efficiently using a combination of Markov chain Monte Carlo and importance sampling. The power of the statistics to detect outliers and level shifts is studied for an autoregressive model. The methodology is illustrated using both simulated and real data.

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