I want to know whether there is a time linear trend in a time series. What are some good approaches? One approach seems to test that the model belongs to ARMA(p,q) family however I am not sure if a test exists for this purpose. If necessary I am willing to specify p and q and I am open to other approaches.
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$\begingroup$ Do you know the distinction between a model being a linear model and a model being a line? $\endgroup$– GalenCommented Aug 16, 2023 at 3:13
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$\begingroup$ I am asking for existence of a term proportional to time. $\endgroup$– BronsteinxCommented Aug 16, 2023 at 5:00
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$\begingroup$ The correlation between time as a degenerate stochastic process and some stochastic process that is indexed by time will itself be a random variable. If you want to perform a null hypothesis test you will need some distributional assumptions for this random correlation $R$. $\endgroup$– GalenCommented Aug 16, 2023 at 14:13
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$\begingroup$ @Galen I can assume $y_{t+1} = \beta y_t + \sigma \epsilon_t + a + b t$. I want to test that $b=0$ and $a=0$. $\endgroup$– BronsteinxCommented Aug 16, 2023 at 18:11
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$\begingroup$ Okay, assuming that recurrence relation is a good step. What can we assume about the distributions of $Y_t$ and $\epsilon_t$? $\endgroup$– GalenCommented Aug 16, 2023 at 18:16
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