Skip to content

acf (Model)

Autocovariance and autocorrelation function for model variables

Syntax

[C, R, list] = acf(model, ...)

Input arguments

model [ Model ]

A solved model object for which the autocorrelation function will be computed.

Output arguments

C [ NamedMat | numeric ]

Covariance matrices for measurement and transition variables.

R [ NamedMat | numeric ]

Correlation matrices for measurement and transition variables.

list [ string ]

List of variables in rows and columns of C and R.

Options

ApplyTo=@all [ string | @all ]

List of variables to which the Filter= will be applied; @all means all variables.

Contributions=false [ true | false ]

If true the contributions of individual shocks to ACFs will be computed and stored in the 5th dimension of the C and R matrices.

Filter="" [ string ]

Linear filter that is applied to variables specified by the option ApplyTo=.

NFreq=256 [ numeric ]

Number of equally spaced frequencies over which the filter in the option filter= is numerically integrated.

Order=0 [ numeric ]

Order up to which ACF will be computed.

MatrixFormat="NamedMatrix" [ "NamedMatrix" | "plain" ]

Return matrices C and R as either NamedMatrix objects (matrices with named rows and columns) or plain numeric arrays.

Select=@all [ @all | string ]

Return ACF for selected variables only; @all means all variables.

Description

The output matrices, C and R, are both n-by-n-by-(p+1)-by-v matrices, where n is the number of measurement and transition variables (including auxiliary lags and leads in the state space vector), p is the order up to which the ACF is computed (controlled by the option Order=), and v is the number of parameter variants in the input model object, M.

If Contributions=true, the size of the two matrices is n-by-n-by-(p+1)-by-k-by-v, where k is the number of all shocks (measurement and transition) in the model.

Linear filters

You can use the option Filter= to get the ACF for variables as though they were filtered through a linear filter. You can specify the filter in both the time domain (such as first-difference filter, or Hodrick-Prescott) and the frequncy domain (such as a band of certain frequncies or periodicities). The filter is a text string in which you can use the following references:

  • 'L' for the lag operator, which will be replaced with 'exp(-1i*freq)'

  • 'per' for the periodicity

  • 'freq' for the frequency

Example

A first-difference filter (i.e. computes the ACF for the first differences of the respective variables):

[C, R] = acf(m, 'Filter', '1-L')

Example

The cyclical component of the Hodrick-Prescott filter with the smoothing parameter, \(\lambda\), set to 1,600. The formula for the filter follows from the classical Wiener-Kolmogorov signal extraction theory,

\[ w(L) = \frac{\lambda}{\lambda + \frac{1}{ | (1-L)(1-L) | ^2}} \]
[C, R] = acf(m, 'filter', '1600/(1600 + 1/abs((1-L)^2)^2)')

Example

A band-pass filter with user-specified lower and upper bands. The band-pass filters can be defined either in frequencies or periodicities; the latter is usually more convenient. The following is a filter which retains periodicities between 4 and 40 periods (this would be between 1 and 10 years in a quarterly model), 

[C, R] = acf(m, 'filter', 'per>=4 & per<=40')