Database Reference
In-Depth Information
the small examples used in this chapter, using the momentum modification
has relatively little effect. However, if the network being trained is slow
to converge without momentum, adding the momentum term can improve
performance.
Forecasting with Models
Forecasting is widely used in real-time data analysis both on its own to
predict future values (forexample toallowforautomated capacity planning)
and to form the basis of comparison with the observed data used by the
monitoring and optimization application areas discussed later in this
chapter. The most naïve methods of forecasting are essentially trivial,
simply using the historical average or perhaps the moving average as the
forecast for future values. For very simple systems, this is sufficient, but
most of the time these naïve methods will not capture sufficient information
about the underlying system to produce good forecasts.
The topic of forecasting is large, and many topics have been written about
it over the years. This chapter covers a few techniques that have gained
widespread popularity due to their simplicity, their effectiveness, or both.
Exponential Smoothing Methods
Exponential smoothing methods of forecasting are fairly widespread thanks
to their relative ease of implementation, ability to handle the seasonality
present in many time series, and general good performance when the signal
is not too noisy. The simplest form of these forecasts, when the data has
no trend or seasonal components, is to simply use the exponential moving
average of the current time period as the forecast for the next time period.
Of course, most time series have either a trend or seasonality and often
have both. When this is the case, it is possible to build a variety of different
models with different types of trend and seasonality components. Of all
these possibilities, the most well-known models are the Holt-Winters
models. Dating back to the late 1950s, these models assume an additive
trend with either additive or multiplicative seasonal components.
Holt's method is used to compute the portion of the model ascribed to the
additive trend portion of the model. (The seasonal component is discussed
later in this section.) To compute the trend components of the model, the
forecast equation is decomposed into two parts: a level and a trend. In
