Autoregressive Models in Economics
Economic time series often display patterns of persistence, cycles, and responses to unexpected shocks, which are crucial for economists to understand. Persistence refers to the tendency of economic variables, such as inflation or GDP, to remain influenced by their past values. Cycles capture the regular up-and-down movements, while shocks represent sudden, unpredictable changes. Autoregressive (AR) models are designed to capture these features by expressing the current value of a variable as a function of its own past values. This approach helps you model the inertia commonly observed in macroeconomic variables and analyze how economies respond over time to policy changes or external events.
1234567891011121314151617set.seed(42) # Synthetic monthly inflation data (5 years) inflation <- 2 + arima.sim( model = list(ar = 0.6), n = 60, sd = 0.15 ) ar1_model <- arima(inflation, order = c(1, 0, 0)) summary(ar1_model) resids <- residuals(ar1_model) # Ljung-Box test (valid now) Box.test(resids, lag = 12, type = "Ljung-Box")
When you estimate an AR(1) model, the key parameter is the autoregressive coefficient, often denoted as φ (phi). This coefficient measures how much of the current value of the series is explained by its immediately preceding value. In an economic context, a high AR coefficient (close to 1) indicates strong inertia or persistence; for example, if inflation was high last month, it is likely to remain high this month. Conversely, a low AR coefficient suggests that shocks dissipate quickly and the series reverts rapidly to its mean. Understanding the magnitude and sign of AR coefficients helps you interpret the underlying economic dynamics, such as the tendency of inflation to persist or the speed at which economies recover from disturbances.
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Economic time series often display patterns of persistence, cycles, and responses to unexpected shocks, which are crucial for economists to understand. Persistence refers to the tendency of economic variables, such as inflation or GDP, to remain influenced by their past values. Cycles capture the regular up-and-down movements, while shocks represent sudden, unpredictable changes. Autoregressive (AR) models are designed to capture these features by expressing the current value of a variable as a function of its own past values. This approach helps you model the inertia commonly observed in macroeconomic variables and analyze how economies respond over time to policy changes or external events.
1234567891011121314151617set.seed(42) # Synthetic monthly inflation data (5 years) inflation <- 2 + arima.sim( model = list(ar = 0.6), n = 60, sd = 0.15 ) ar1_model <- arima(inflation, order = c(1, 0, 0)) summary(ar1_model) resids <- residuals(ar1_model) # Ljung-Box test (valid now) Box.test(resids, lag = 12, type = "Ljung-Box")
When you estimate an AR(1) model, the key parameter is the autoregressive coefficient, often denoted as φ (phi). This coefficient measures how much of the current value of the series is explained by its immediately preceding value. In an economic context, a high AR coefficient (close to 1) indicates strong inertia or persistence; for example, if inflation was high last month, it is likely to remain high this month. Conversely, a low AR coefficient suggests that shocks dissipate quickly and the series reverts rapidly to its mean. Understanding the magnitude and sign of AR coefficients helps you interpret the underlying economic dynamics, such as the tendency of inflation to persist or the speed at which economies recover from disturbances.
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