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I have problems interpreting the parameters that follow using the TimeseriesModelFit command. The time series exists of twelve months and show a positive linear trend. Using TimeseriesModelFit it gives ARIMA 0,1,0. The process output is as follows:

tsm//Normal

gives

ARIMAProcess[273., {}, 1, {}, 3505.09]

My question: how do I interpret these results? What does 273, {}, 1, and so on mean? How can I use these values to create a model? Ultimately, I would like to produce a function, such as y = ax + b, although probably another function applies as we're speaking about a random walk. I do not know how to interpret these results to create such a function.

Thank you in advance for your help.

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    $\begingroup$ Have you looked at the docs of ARIMAProcess? $\endgroup$ – corey979 Jan 17 at 12:18
  • $\begingroup$ Are you familiar with autoregressive models? Personally, I am not, but it seems to me that understanding these models is a precondition to being able to interpret the result of TimeSeriesModelFit. If the gist of your question boils down to what these models are, then it's not a very good fit here ... $\endgroup$ – Szabolcs Jan 17 at 12:22
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    $\begingroup$ @Szabolcs thanks for your reply! I have some, but basic knowledge about AR models. It is just that I need to build a model, and acquiring these parameters so efficiently is amazing, but so far I have not found an option to translate them into a mathematical model, which is exactly what I need. E.g. communicating these parameters to others is not efficient. It would be better if I can communicate a model that they can use to predict future values. $\endgroup$ – TLP Jan 17 at 12:28
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    $\begingroup$ How to interpret ARIMA(0,1,0)? $\endgroup$ – corey979 Jan 17 at 13:47
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    $\begingroup$ I'm voting to close this question as off-topic because while it is a good question, it would be better asked at stats.stackexchange.com. Because there might be some resistance to answer there because it might look to CrossValidated that this is a Mathematica question, if you could possibly run the model in R (using the arima function) and also give those results, there would be a better chance of getting an answer. $\endgroup$ – JimB Jan 17 at 14:26
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This is a kind of a comment because I see this topic has a bit unfriendly description in the docs. The meaning is as follows:

ARIMAProcess[start, {AR}, D, {MA}, [Sigma]^2]

were AR stands for autoregressive process, D stands for difference and MA for moving average (those AR and MA could be matrices). Sigma^2 stands for variance. Most confusing is start, but it is simply the starting value on vertical axis.

Hope that helps.

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