1. How to use everything we learned so far?
So far we presented the tools to visually analyze a time series, but what information can you extract from those tools? Each of them is a special representation of a time series and is designed to capture a specific feature.
2. Histograms
Let's go back to our Amazon example. If you look at the histogram two things are instantly striking.
3. Histograms
First the returns are centered around zero,
4. Histograms
second there are a few but very distinct outliers. Outliers are extreme returns positive or negative.
5. Box and whisker
With a Box & Whisker plot you summarize your distribution with 5 numbers:
6. Box and whisker
the median plus the four quantiles. The R implementation of Box & Whisker plot also has the
7. Box and whisker
outliers represented as points outside the quantiles. In the case of Amazon stock price, the Box & Whisker plot confirms the diagnostic made with the histogram. Returns are centered on zero with some very distinct outliers. The dots outside the first and fourth quantiles indicate that some days returns are really extreme in the +/- 10% region. In more layman term, this is an indication of the riskiness of Amazon as an investment. All else being equal you would prefer a series with the same average return but less outliers.
8. Autocorrelation
With the autocorrelogram you are trying to understand the dynamic of the time series. Knowing today's value what is your best bet for tomorrow's value? If the correlation is positive the series trends: good performance is followed by good performance and the same goes for bad performance. On the opposite, if you estimated that the autocorrelation is negative then if the stock went up lately your best bet is to forecast a negative performance for the future. In the case of Amazon there seems to be a positive autocorrelation which translates into an upward trend in the price chart.
9. QQ-plot
As already mentioned the q-q plot is a visual diagnostic of normality. By comparing Amazon returns to a standard normal distribution
10. QQ-plot
you can almost instantly determine if Amazon returns are normally distributed and if not, where the non-normality is coming from. Here, it's difficult to conclude without a robust statistical test but the likelihood of extreme returns probably makes the series non normal.
What is the conclusion of all this?
11. Let's practice!
In simple terms Amazon seems to be a profitable but risky investment. In the following exercises we will use all those concepts to establish a comprehensive time series diagnostic.