เปรียบเทียบวิธี

	แบบจำลองค่าเฉลี่ยเคลื่อนที่แบบฟูเรียร์ (Fourier MA)	แบบจำลอง ARIMA (Autoregressive Integrated Moving Average)	แบบจำลองฟูเรียร์ ARIMA
สาขาวิชา	เศรษฐมิติ	เศรษฐมิติ	เศรษฐมิติ
ตระกูล	Regression model	Regression model	Regression model
ปีกำเนิด	1990s–2000s	1970	2004-2012
ผู้ริเริ่ม	Harvey, A. C.; Hyndman, R. J.	George Box and Gwilym Jenkins	Becker, Enders, and Hurn; further extended by Enders and Lee
ประเภท	Time series model	Time series forecasting model	Time series model
แหล่งต้นตำรับ	Hyndman, R. J., & Athanasopoulos, G. (2021). Forecasting: Principles and Practice (3rd ed.). OTexts.	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.	Enders, W., & Lee, J. (2012). The flexible Fourier form and Dickey-Fuller type unit root tests. Economics Letters, 117(1), 196-202.
ชื่อเรียกอื่น	Fourier MA, Fourier-augmented moving average, trigonometric MA model, harmonic moving average model	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	Fourier ARIMA, ARIMA with Fourier terms, trigonometric ARIMA, Fourier-flexible ARIMA
ที่เกี่ยวข้อง	2	6	2
สรุป	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 ARIMA(p,d,q) model is the standard workhorse for univariate time series forecasting. It combines autoregressive terms (past values), differencing to induce stationarity, and moving average terms (past shocks) into a unified linear framework. Developed by Box and Jenkins (1970), it remains one of the most widely applied models in econometrics and applied statistics.	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.