Database Reference
In-Depth Information
Change Detection
Outlier detection as discussed in the previous section assumes that the
observed outlier is a true anomaly and does not represent a fundamental
change in the process generating the time series. These changes are much
longer lived and are usually fit in a retrospective manner using fairly
sophisticated approaches, such as clustering or Hidden Markov Models.
There are fewer online approaches to change detection, and those that exist
generally depend on the maintenance of at least two forecasts over the data.
These various forecasts' errors are compared to determine if the underlying
process has undergone a shift.
An example of this approach can be found in the finance community in the
form of the Moving Average Convergence Divergence (MACD) indicator.
Introduced in the 1970s, this indicator uses three different exponential
moving averages to indicate changes in trends. Originally this approach was
applied to detecting changes in the trend of a stock's price, but the approach
is very similar to more modern approaches to change detection.
In the standard formulation, the closing prices for a stock are used to
compute an exponential moving average (EMA) with a period of 12 days,
a period of 26 days, and a period of 9 days. The difference between the
12-day EMA and the 26-day EMA is known as the MACD. The 9-day EMA
is known as the signal line. When the MACD crosses from below the signal
line to above the signal line, the stock is interpreted to have shifted to a
positive trend. When the opposite happens, the stock is interpreted to have
shifted from a positive trend to a negative trend. Similarly, the MACD line
moving from negative to positive and from positive to negative has the same
interpretation, but it is generally considered to be weaker evidence than the
crossing of the signal line.
There are many variations on this approach that use shorter and longer
EMAs depending on the application, but it allows for an easily implemented
method of detecting changes in trend. The primary problem is that it is
prone to false signaling of changes in the trend. An extension would do
the same thing, but it would track trends in the error between a forecaster
and the actual value. This can be useful when there is known seasonality
in the data that should be removed before tracking the trend. Using the
Holt-Winters forecaster, one approach would track changes in the trend
component of the model.
