In California, solar generation has been increased substantially in recent years due to increased solar panel installation. As the top of the first figure has shown, solar generation was low in 2011 and began to take off since 2013. In general, its time series is characterized by a positive trend and a seasonal cycle. Furthermore, its mean and variance increase over time, leading to an asymmetric distribution with a long tail and a peak at low values. Because of this changeable characteristic, power transform is needed before modeling the data.
I applied the Box-Cox transform, which automatically optimizes the transform, to the time series and obtained the lambda value ~ 0.41, implying a transform close to the square root transform. After the transform, the mean and variance stay relatively constant over time and its distribution is more symmetric.
If I took a further step to remove the linear trend from the transformed time series, its residuals are around the zero value, although they are more negative in the last two years (2017 and 2018). The transformed time series after detrending is better used for downstream analysis.
