Autoregressive Integrated Moving Average (ARIMA (p, d, q)) Model

Background

An Autoregressive Integrated Moving Average (ARIMA) model is a widely-used statistical method for analyzing and forecasting univariate time series data. The model integrates three key components: autoregression (AR), differencing (I for “Integrated”), and moving averages (MA).

Historical Context

The ARIMA model gained prominence through the work of statisticians Box and Jenkins in the 1970s, who formalized the method in their influential book “Time Series Analysis: Forecasting and Control.” The model has since been a cornerstone in both academic research and practical applications for economic forecasting.

Definitions and Concepts

• Autoregressive (AR) part: Refers to the dependency between an observation and some number of lagged observations.
• Integrated (I) part: Refers to differencing the raw observations to make the time series stationary, which has constant mean and variance over time.
• Moving Average (MA) part: Refers to the dependency between an observation and a residual error from a moving average model applied to lagged observations.
• ARIMA(p, d, q): A notation where p is the number of lagged observations in the AR part, d is the number of times the raw observations are differenced, and q is the size of the moving average window.

Major Analytical Frameworks

Classical Economics

While ARIMA is not rooted in classical economics principles, it can be used to assess economic variables grounded in classical theory, such as identifying trends and cycles in economic growth data.

Neoclassical Economics

ARIMA models can be employed to forecast supply and demand fluctuations and potential economic equilibriums through empirical time series data.

Keynesian Economics

Use of ARIMA in Keynesian economics includes analyzing economic indicators that influence aggregate demand, such as consumption, investment, and government expenditure.

Marxian Economics

The ARIMA model assists in examining economic cycles and crisis theories posited by Marxian economics, by identifying recurring patterns in economic data.

Institutional Economics

By capturing long-term institutional changes and their lagged effects, ARIMA models help institutional economists study structural shifts in economic policies and regulatory practices.

Behavioral Economics

Though not typically used to model behavioral nuances, ARIMA models can analyze how past economic behaviors influence present and future trends in consumer and investor behavior.

Post-Keynesian Economics

ARIMA models are useful in assessing Post-Keynesian concepts, such as instability and uncertainty in capitalist economies, by forecast economic volatility.

Austrian Economics

By identifying cycles of booms and busts through time series data, ARIMA can be aligned with Austrian economics theories on credit cycles and economic dynamics.

Development Economics

It helps in forecasting important developmental indicators like GDP growth, inflation rates, and other key economic metrics in developing economies.

Monetarism

ARIMA models prove useful in monetarist analysis by predicting money supply, velocity, and their effects on inflation and nominal output.

Comparative Analysis

ARIMA models can be compared to other time series models like Structural Equation Models (SEM) for their strengths in forecasting. Unlike SEM, ARIMA doesn’t rely on an underlying structural economic theory but rather on the statisitcal properties of the data itself.

Case Studies

1. Inflation Forecasting: Application of ARIMA in forecasting short-term inflation rates using past price index data.
2. Stock Market Analysis: Usage of ARIMA to predict stock prices and identify trends in financial markets.

Suggested Books for Further Studies

• “Time Series Analysis: Forecasting and Control” by George E. P. Box, Gwilym Jenkins, Gregory C. Reinsel, and Greta M. Ljung.
• “The Analysis of Time Series: An Introduction” by Chris Chatfield.
• “Applied Time Series Analysis” by Terence C. Mills and Raphael N. Markellos.

Related Terms with Definitions

• Autoregression (AR): A component of ARIMA where regressive modeling predicts the variable of interest using its own previous values.
• Differencing (I): The process of making a time series stationary by eliminating trends and seasonality.
• Moving Average (MA): A component of ARIMA that models the variable by accounting for the lagged forecast errors.