Multivariate Time Series

See also: Time series in ModelRisk, Vose Time Series window

One often wants to forecast randomly varying values from different quantities in time, where those quantities are somehow related to each other.

Quantities that move together in time are typically modeled using multivariate time series ("MultiTS") models. MultiTS models allow one to easily account for the relations and correlation that exist between the "marginal" components.

A typical example of a situation where one can use multivariate time series is yield curve modeling for example: here we model the interest rates for different times-to-maturity. At any point in time an interest rate for some time to maturity (say, 5 years) is typically related to:

  • the (immediate) past,

  • the interest rates at for other times-to-maturity (e.g. 1 month, 1 year, 10 years...)

A good way to model this is provided by multivariate time series. These are a generalization of their univariate time series counterpart. Use the ModelRisk Multivariate Time Series window to simulate from the following multivariate time series models:

Each of these takes a certain set of parameters, which can be inserted manually by typing in the appropriate field, or dynamically link to a value in a spreadsheet cell.

The output of the multivariate time series window will always span multiple cells, in other words it will be an array function.

To see the output functions of this window, click here.

Window elements

Options

In the Time series parameters area, the type of multivariate time series to model can be selected. Also the multivariate time series' parameters can be entered: you can enter them manually as an array or link them to the spreadsheet.

The Initial Values parameter is the array with starting values to begin your forecast from. Select the Log Return checkbox to whether to model log returns instead of the actual series.

The other parameter fields shown depend on the specific Time Series model selected from the drop-down menu.

A preview of the simulated time series is shown on the right. In the Graphing options area, select the series you wish to display.

When appropriate for the selected Time Series model, Historical data to be taken into account can be selected. This can be either a single cell or array.

For explanations about other fields, buttons, graphs and summary statistics tables in this window, see Common elements of ModelRisk windows.

Useful tips and tricks

See also: Graphics, workflow and error handling in ModelRisk

Using View Function to return to a window

The output of ModelRisk windows always corresponds to VoseFunctions (the functions ModelRisk adds to Excel) being entered into one or more spreadsheet cells.

You can always re-open the window for a ModelRisk function that is in a spreadsheet cell by using View Function. Select the spreadsheet cell and then select View Function from the ModelRisk menu/toolbar/ribbon.

 

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