As you know, auto-regressive models assume weak stationarity. What happens if this assumption does not hold? To study the effect of non-stationarity, we will add a linear trend to the “Appliances” column of the dataset, which measures the energy consumption of appliances across a period of 4.5 months.
- First, preprocess the dataset to remove any trend (if necessary)
- Perform an autoregressive analysis on the clean time series
- Add a linear trend to the time series
- Perform the autoregressive analysis on the new time series
Show the results of the analysis with and without the linear trend, discussing your design choices and the results. To perform the autoregressive analysis, fit an autoregressive model on the first 3 months of data and estimate performance on the remaining 1.5 months. Remember to update the autoregressive model as you progress through the 1.5 testing months. For instance, if you have trained the model until time T, use it to predict at time T+1. Then to predict at time T+2 retrain the model using data until time T+1. And so on. You might also try and experimenting with less "computationally heavy" retraining schedule (e.g. retrain only "when necessary"). You can use the autoregressive model of your choice (AR, ARMA, ...).