VoseCopulaDataSeries

 

=VoseCopulaDataSeries(Data, Uncertainty)

 

 

 

This array function returns a set of random values from a copula created by analyzing the correlation in a data series between contiguous values.

Data – a set of sequential observations from a time series.

Uncertainty – an optional Boolean parameter determining whether one should incorporate the statistical uncertainty about the estimated copula relationship. Uncertainty is not included if the parameter is set to FALSE (or 0) or omitted, and is included if the parameter is set to TRUE (or 1)

Application

Imagine that you have a set of time series data for a single variable from which you wish to make a forecast. One approach would be to use one of the time series fitting functions in ModelRisk. However, each of ModelRisk’s time series fitting functions involves a number of assumptions that you may not be comfortable in accepting.

The VoseCopulaDataSeries function offers a more flexible alternative. The function analyzes a data series for any autocorrelation between sequential values in a series. For example, consider the following time series of log returns of a stock:

A scatter plot of the returns in each period against the returns in the previous period reveal some correlation relationship:

Fitting a distribution to the log returns shows that the 3-parameter Student is a good fit:

By using the VoseCopulaDataSeries function to simulate a correlation, and a VoseStudent3 distribution to simulate the size of returns one can produce a forecast. This model illustrates the example.

This approach has its own set of assumptions, namely: in terms of the use of the VoseCopulaDataSeries function, that the autocorrelation occurs over just a single lag period; and in terms of the use of the 3-parameter Student distribution, that the distribution of the underlying variable is constant (although this could be relaxed by changing the distribution over the range of the forecast).

 

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