Multivariate Time Series

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

The Multivariate Time Series window from ModelRisk

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:

• Multivariate Autoregressive (order 1)

• Multivariate Autoregressive (order 2) (Industrial edition only)

• Multivariate Geometric Brownian Motion

• Multivariate Moving-Average (order 1)

• Multivariate Moving-Average (order 2) (Industrial edition only)

• Multivariate GARCH (Industrial edition only) (in the BEKK parametrization which keeps the number of parameters within reasonable bounds)

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 LastValues parameter is the array with starting values to begin your forecast from. Select the LogReturn 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 Options area, select View all series to display all series (e.g. 3 lines if it is a 3-dimensional model), or deselect it and click any intersection between two series to display only those two components.

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.

Time Series graph

Time Series graphs from the Time Series window

In the middle pane, a graph for the generated Time Series is shown. The lines represent randomly generated Time Series forecasts.

By default, only one forecast line is shown in blue. This number can be increased by changing the Number of lines field mentioned above