# Trying to fit a model after detrending

I have data for Hydrogen Sulfide Series, see here http://www.wikiupload.com/Y4WAZJ4Z0IMTK7V I applied a Box-Cox Transformation with $\lambda =1/3$ to try to stabilize the data. I plotted a few sample PACF/ACF to show that the series is not stationary and does not demonstrate constant second order properties with time.

I have eliminated a possible trend and seasonal component by assuming a model of the form $y_t = m_t + s_t + x_t$ where $x_t$ is the stochastic process I am trying to model. I removed a possible seasonal component and a fluctuating mean and I get the following ACF/PACF for my series. Does that look like something that is known? How can I fit a stationary model in R to this? Is it even stationary? Maybe the above decomposition is not really applicable in this case, i.e. the time dependence is more complicated. Here are the resulting ACF-PACF after detrending

Here are the resulting ACF-PACF after detrending

To a good first approximation, that could be AR(1). There are a few wiggles outside the limits (you should state what limits you used), but for 95% limits you expect a couple.

Is it even stationary?

I don't know. There's a lot of ways to be nonstationary.

• These are 95% confidence intervals yes.Thank you for the answer. According to Ramsey (1974), if $phi_{p,p} \ne 0$ and $\phi_{j,j} = 0$ for j>p, it is necessary an AR(p). I think there are alot of points outside the CI for it to be an AR(1), but it is viable for the first few lags, as can be seen from the ACF – l3win Mar 21 '13 at 3:22
• The big problem is, you don't know the values of $\phi_{jj}$. You also don't know the impact of the various things you did to the series first; it's possible you has a little seasonal component but if so it's very weak. I'd see how you were placed after an AR(1). – Glen_b -Reinstate Monica Mar 21 '13 at 3:26
• But you can estimate it using YW/Burg/MLE. AR(1) seems to work for the first few lags, up to approximately h=6 – l3win Mar 21 '13 at 5:18
• Yes, thereby estimating something with noise. And when you're detrending and stuff your trend estimates also contain noise, fuzzing the distribution about more. What are its properties now? How many results a little outside the 95% interval should you expect? – Glen_b -Reinstate Monica Mar 21 '13 at 5:21
• 95% of 40 is 38, so no more than 38 should fall outside :) – l3win Mar 21 '13 at 7:16