手法を比較

	フーリエ移動平均 (Fourier MA) モデル	フーリエARIMAモデル
分野	計量経済学	計量経済学
系統	Regression model	Regression model
提唱年	1990s–2000s	2004-2012
提唱者	Harvey, A. C.; Hyndman, R. J.	Becker, Enders, and Hurn; further extended by Enders and Lee
種類	Time series model	Time series model
原典	Hyndman, R. J., & Athanasopoulos, G. (2021). Forecasting: Principles and Practice (3rd ed.). OTexts.	Enders, W., & Lee, J. (2012). The flexible Fourier form and Dickey-Fuller type unit root tests. Economics Letters, 117(1), 196-202.
別名	Fourier MA, Fourier-augmented moving average, trigonometric MA model, harmonic moving average model	Fourier ARIMA, ARIMA with Fourier terms, trigonometric ARIMA, Fourier-flexible ARIMA
関連	2	2
概要	The Fourier MA model combines a Moving Average (MA) error structure with Fourier series terms — sine and cosine pairs — to capture complex or high-frequency seasonal patterns in time series data. It is particularly useful when the seasonal period is long or irregular, making classical seasonal ARIMA parameterisation infeasible.	The Fourier ARIMA model augments a standard ARIMA specification with trigonometric sine and cosine terms, allowing it to capture smooth, gradual structural change and flexible nonlinear seasonality without specifying the exact timing or number of breaks in advance. It is widely used in applied macroeconometrics and finance for series exhibiting slowly evolving dynamics.