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# What does the correlation coefficient tell you

you hypothesize that your data is generated by the following process: $y_t=\phi_0+\sum_^P\phi_ky_+\varepsilon_t$, where $\phi_k$ are your autocorrelation coefficients, and $\varepsilon_T$ - random errors. Next, you estimate your $\phi_t$ using one of the methods of estimation of autoregressive processes AR(P) of order P, e.g. see AR(P). there's no point in doing manually, use statistical packages like Stata.

you have to choose order P, there are ways of doing it, such as trying many different Ps and comparing their AIC

next, you test your model for the unit root. in case of P=1, i.e. $y_t=\phi_0+\phi_1y_+\varepsilon_t$, this is testing whether $\phi_1=1$. there are ways of testing this hypothesis too. if it's very close to 1 then you have a unit root.

what does this mean? it

means that your $y_t$ will drift away over time, it's non-stationary. it is not a deterministic trend like $y_t=\beta t$, where you know where and how fast it's going. on the other hand you know that $|E[y_\infty]|=\infty$. if you have no unit root then the process is stationary and in the long run your $y_\infty$ will not deviate too much from where it is now.

examples. interest rates are stationary, they don't have stochastic trends. in ancient Egypt some 4-5 thousands years ago the interest rate on the unsecured personal loans were around 20% annual.

asset prices are not stationary, they have drifts, possible both stochastic and deterministic. look at house prices 50 years ago and now, they grew maybe 10-folds if not more.

Source: quant.stackexchange.com
Category: Forex