GARCH Toolbox

Technical Conventions

This user's guide uses the following definitions and descriptions:

• The size of an array describes the dimensions of the array. If a matrix has m rows and n columns, its size is m-by-n. If two arrays are the same size, their dimensions are the same.

• If two vectors are of the same size, then they not only have the same length, but they also have the same orientation.

• The length of a vector indicates only the number of elements in the vector. If the length of a vector is n, it could be a 1-by-n (row) vector or an n-by-1 (column) vector. Two vectors of length n, one a row vector and the other a column vector, do not necessarily have the same size.
• The rows of a time series matrix correspond to a time index and the columns correspond to sample paths, independent realizations, or individual time series. In any given column, the first row contains the oldest observation and the last row contains the most recent observation.
• Time series vectors and matrices are time-tagged series of asset returns. If you have a price series, the GARCH Toolbox lets you convert it to a return series using either continuous compounding or periodic compounding.
• Continuous compounding is the default compounding method of the GARCH Toolbox. The results of some GARCH Toolbox functions are approximate for periodic compounding, but exact for continuous compounding. Using continuous compounding when moving between prices and returns, ensures exact results regardless of the function.
• The GARCH Toolbox assumes that return series are stationary processes. The price-to-return transformation generally guarantees a stable data set for GARCH modeling.
• The term conditional implies explicit dependence on a past sequence of observations. The term unconditional is more concerned with long-term behavior of a time series and assumes no explicit knowledge of the past.

See the Glossary for general term definitions.

Expected Background

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