Forecasting and Risk in Nelson Siegel
Overview
Once the four Nelson Siegel parameters have been estimated for different dates, each
series of paramters can be viewed as a
time series
and forecast as a time series.
Typically, the first step is to
difference
the series, either by subtraction, using arithmetic returns, or log differences, depending on how you want
to model the dynamics.
Calculating Moments
The primary method of analysis of the Nelson Siegel parameters is to calculate the basic
moments.
The first moment is the average. It can be calculated easily in Python.
#calculated differences in the level parameter
level_diffs = [0.01, 0.0, 0.01, -0.02, -0.01]
average = sum(series)/len(series)
Calculating Covariance
The covariance is the moment that is primarily used to forecast risk. The way that the covariance is modeled
will be based on the assumptions that you want to bring to the model. For example, do you want to measure and
model correlations among the parameters.
If no correlations are assumed, then you simply need to calculate the variance or standard deviation
of each parameter.
If you want to