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I am using statsmodels.tsa.stattools.acf to calculate the lagged autocorrelation of innovations in Kalman filter with alpha=0.05. Innovation is defined as observation - observed equivalent of model forecast. And I want to calculate the lagged autocorrelation of the time series of innovations, to see whether autocorrelation lags at 1,...,10 time steps are zero. So that I would know whether my Kalman Filter is optimal.

I used statsmodels.tsa.stattools.acf to calculate the autocorrelation. But I don't know what does it mean by the p value it returns? and what is the corresponding null hypothesis? what if the p-value returned is very small? say if I set nlags=10, i.e. to calculate the autocorrelation of 10 time steps lag, the result is acf[10] = 0.219018, and its p-value is 1.544171e-218.

I knew p value is the probability that we accept the null hypothesis. But I don't know what is the hypothesis over here.

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