The goal of this project is to fit several possible time series models to a given dataset , select one that is preferable using model diagnostics procedures and then perform a forecasting task.
Remember that the analysis of the dataset starts with a time plot and, possibly, some scatterplots. Based on them, you may want to consider a deterministic trend model with a time series error process or a straightforward time series model with a possibly constant mean.
Your next stage should consist of looking at whether the (possibly detrended) data process seems stationary or not. If not, consider applying appropriate transformations to the data to make it stationary.
Next, you will need to analyze resulting series using sample autocorrelations, sample partial autocorrelations etc. to understand the correlation structure of the model. At this stage, you should be able to pick up a few possible ARIMA (p,d,q) model candidates.
For all resulting candidate models, perform appropriate diagnostics procedures. Remember that you always have to start with the residual analysis. If necessary, you may also consider overfitting as a second diagnostic tool.
The final step of your analysis will be forecasting. Please remember to include a plot of the original series with the addition of forecasted values and prediction limits. Include other plots from the model selection and diagnostic stage on an as-needed basis: enough to illustrate your thought flow but not an overwhelming flood of unnecessary plots.
You will be using the dataset called robot that is also included with the TSA package. It consists of 324 observations. The measurements are expressed as deviations from a target position. The robot is put through this planned set of exercises in the hope that its behavior is repeatable and, therefore, predictable. Forecast five values ahead and obtain 95% forecast limist.