lagpol: Lag polynomials

In tfarima: Transfer Function and ARIMA Models

Lag polynomials

Description

lagpol creates a lag polynomial of the form:

(1 - coef_1 B^s - ... - coef_d B^{sd})^p

This class of lag polynomials is defined by:

• the base lag polynomial 1 - coef_1 B^s - ... - coef_d B^{sd},

• the exponent 'p' of the base lag polynomial (default is 'p = 1'),

• the spacing parameter 's' in sparse lag polynomials (default is 's = 1'),

• the vector of 'd' coefficients 'c(coef_1, ..., coef_d)', which can be mathematical expresions dependent on 'k' parameters 'c(param_1, ..., param_k)'.

Usage

lagpol(param = NULL, s = 1, p = 1, lags = NULL, coef = NULL)

Arguments

param	a vector/list of named parameters. These parameters can be used within the coefficient expressions.
s	an integer specifying the lag spacing or seasonal period.
p	an integer specifying the exponent applied to the base lag polynomial.
lags	an optional vector of lags for sparse polynomials. If NULL, lags are determined by s.
coef	an optional vector of mathematical expressions defining the coefficients of the lag polynomial. If NULL, the names in param are used.

Value

lagpol An object of class 'lagpol' with the following components:

coef

vector of coefficients c(coef_1, ..., coef_p) provided to create the lag polynomial.

pol

base lag polynomial vector: 1 - \text{coef}_1 B^s - \dots - \text{coef}_d B^{sd}.

Pol

lag polynomial raised to the power 'p'. If 'p = 1', this equals 'pol'.

Examples

# Simple AR(1) lag polynomial: 1 - 0.8B
lagpol(param = c(phi = 0.8))

# AR(2) lag polynomial with seasonal lag s = 4: 1 - 1.2B^4 + 0.6B^8
lagpol(param = c(phi1 = 1.2, phi2 = -0.6), s = 4)

# Integration operator squared: (1 - B)^2 = 1 - 2B + B^2
lagpol(param = c(delta = 1), p = 2)

# Lag polynomial using explicit coefficients
lagpol(coef = c("1"), p = 2)  # (1 - B)^2 = 1 - 2B + B^2

# Custom coefficients defined by mathematical expressions
lagpol(param = c(theta = 0.8), coef = c("2*cos(pi/6)*sqrt(theta)", "-theta"))

tfarima documentation built on Nov. 5, 2025, 7:43 p.m.