*! version 1.0.2 24may2026

Title

asycaus fourier -- Fourier-augmented asymmetric Toda-Yamamoto causality (Nazlioglu, Gormus & Soytas 2016; Pata 2020)

Syntax

asycaus fourier depvar causvar [if] [in] [, options]

Description

Augments the asymmetric Toda-Yamamoto VAR with Fourier trigonometric terms
sin(2*pi*k*t/T) and cos(2*pi*k*t/T) to control for smooth
structural breaks of unknown number, timing and form (Enders and Lee 2012;
Nazlioglu, Gormus and Soytas 2016). The asymmetric variant (Pata 2020)
applies the test to cumulative positive and negative shocks separately.

Both single-frequency and cumulative Fourier bases are supported.
The optimal frequency k* in [1, kmax] is chosen automatically.

Options

maxlag(#) max VAR lag (default 8)

ic(string) IC (default hjc)

intorder(#) TY augmentation lags (default 1)

shock(string) pos | neg | both

kmax(#) max Fourier frequency (default 5)

form(string) single (default) or cumulative

boot(#) bootstrap reps (default 1000)

seed(#) seed (default 12345)

lnform log of inputs

nograph suppress graph

saving(name) save graph

Examples

webuse lutkepohl2, clear

tsset qtr

asycaus fourier dln_inv dln_inc, kmax(3) form(single) shock(both)

asycaus fourier dln_inv dln_inc, kmax(5) form(cumulative) shock(both)

Stored results

r(results) matrix: Wald, lag, k*, asy_p, sample

r(kmax) max Fourier frequency searched

r(form) single or cumulative

References

Enders, W., and Lee, J. (2012). The flexible Fourier form and Dickey-Fuller type unit root tests. Economics Letters, 117(1), 196–199.

Nazlioglu, S., Gormus, N. A., and Soytas, U. (2016). Oil prices and real estate investment trusts (REITs): gradual-shift causality and volatility transmission analysis. Energy Economics, 60, 168–175.

Pata, U. K. (2020). How is COVID-19 affecting environmental pollution in US cities? Evidence from asymmetric Fourier causality test. Air Quality, Atmosphere & Health, 13, 1149–1155.

Author

Dr Merwan Roudane -- merwanroudane920@gmail.com

See asycaus for the package overview.