Core concepts and metrics
The visualization of the time series data has conveyed a similar story in all the examples, from Figure 1 to Figure 7. The trend and seasonality of the observations imply that the future values of the time series are dependent on the current values, and thus we can't assume that the observations are independent of each other. But what does this mean? To reiterate the point, consider the simpler uspop
(US population) dataset, the third-right panel display of Figure 7. Here, we don't have a seasonal influence. Now, consider the census year 1900. The population at the next census is certainly not less than in the year 1890, and it is not well beyond the same number of the same year. A similar narrative holds for most time series; for example, if we are recording the maximum temperature of the day. Here, if today's maximum temperature is 42°C, the next day's maximum temperature is highly influenced by this number and it is almost completely ruled out that the next day...