Trends
Overview
A trend in a time series is a pattern in the data, such as a general upward slope or wavelike behaviour that persists over time.
Deterministic vs Stochastic Trends
The difference between determistic versus stochastic trends is subtle.
Deterministic vs Stochastic Trends
Determistic Trend
A determistic trend is a trend that is not random. That is, the time series can be modeled as a determistic
function of time plus a random component.
{% Y_t = f(t) + X_t %}
where {% X_t %} is a stationary process.
A determistic trend shows a great degree of stability to the trend.
The random walk often displays the presence of stochastic trends. Trends within a random walk tend not to
be stable, and can reverse course or vary length.
Click run to re-run.
Determining the Type of Trend
One way to understand the type of trend present in the data is to difference the data first. Note what happens when
we first difference both examples of trends from above.
