From great-econometrics
Econometrics skill for time series analysis. Activates when the user asks about: "time series", "stationarity", "unit root test", "ADF test", "KPSS test", "ARIMA", "ARMA", "autocorrelation", "ACF", "PACF", "VAR model", "VECM", "Granger causality", "cointegration", "impulse response function", "forecast", "seasonal decomposition", "ARCH", "GARCH", "时间序列", "平稳性检验", "单位根", "自回归", "格兰杰因果", "协整", "脉冲响应", "预测", "向量自回归"
npx claudepluginhub zhouziyue233/great-econometrics --plugin econometricsThis skill uses the workspace's default tool permissions.
This skill provides guidance for univariate and multivariate time series analysis in empirical economics. It covers stationarity testing, ARIMA modeling, VAR/VECM systems, cointegration, and Granger causality.
Creates isolated Git worktrees for feature branches with prioritized directory selection, gitignore safety checks, auto project setup for Node/Python/Rust/Go, and baseline verification.
Executes implementation plans in current session by dispatching fresh subagents per independent task, with two-stage reviews: spec compliance then code quality.
Dispatches parallel agents to independently tackle 2+ tasks like separate test failures or subsystems without shared state or dependencies.
This skill provides guidance for univariate and multivariate time series analysis in empirical economics. It covers stationarity testing, ARIMA modeling, VAR/VECM systems, cointegration, and Granger causality.
Always test for unit roots before modeling. Preferred approach:
ADF vs KPSS Conflict Resolution: When ADF fails to reject (suggests unit root) but KPSS also fails to reject (suggests stationary), the tests disagree. Recommended approach: (a) check for structural breaks — a break can make a stationary series look like it has a unit root; (b) use Zivot-Andrews test to allow for one structural break; (c) examine the series visually and consider economic theory. When in doubt, err on the side of differencing to avoid spurious regressions.
# Python
from statsmodels.tsa.stattools import adfuller, kpss
# ADF test
adf_result = adfuller(series, autolag='AIC')
print(f"ADF stat: {adf_result[0]:.4f}, p-value: {adf_result[1]:.4f}")
print(f"Critical values: {adf_result[4]}")
# KPSS test
kpss_result = kpss(series, regression='c', nlags='auto')
print(f"KPSS stat: {kpss_result[0]:.4f}, p-value: {kpss_result[1]:.4f}")
# R
library(tseries); library(urca)
adf.test(series)
kpss.test(series, null = "Level")
* Stata
dfuller series, lags(4) regress
kpss series
# Python — auto order selection
from statsmodels.tsa.arima.model import ARIMA
import itertools
# Manual
model = ARIMA(series, order=(1, 1, 1)).fit()
print(model.summary())
# Forecast
forecast = model.forecast(steps=12)
# R
library(forecast)
model <- auto.arima(series, ic = "aic")
summary(model)
forecast(model, h = 12)
* Stata
arima series, arima(1,1,1)
predict yhat, xb
# Python
from statsmodels.tsa.api import VAR
model = VAR(data_matrix)
lag_order = model.select_order(maxlags=8)
print(lag_order.summary())
results = model.fit(lag_order.aic)
print(results.summary())
# Granger causality
results.test_causality('y1', ['y2'], kind='f')
# Impulse response
irf = results.irf(periods=10)
irf.plot(orth=True)
# R
library(vars)
VARselect(data_matrix, lag.max = 8, type = "const")
var_model <- VAR(data_matrix, p = 2, type = "const")
causality(var_model, cause = "y2")
irf(var_model, impulse = "y2", response = "y1", n.ahead = 10)
| Finding | Implication |
|---|---|
| All series I(0) | Estimate VAR in levels |
| All series I(1), no cointegration | Estimate VAR in first differences |
| All series I(1), cointegration found | Estimate VECM |
| Mixed orders of integration | Cannot use standard VAR/VECM; use ARDL bounds test |
# Python — Ljung-Box test for residual autocorrelation
from statsmodels.stats.diagnostic import acorr_ljungbox
# After fitting ARIMA model:
residuals = model.resid
lb_result = acorr_ljungbox(residuals, lags=[10, 20], return_df=True)
print(lb_result)
# If p-value > 0.05 at all lags → residuals are white noise (good)
# R — Ljung-Box test
Box.test(residuals(model), lag = 10, type = "Ljung-Box")
# p > 0.05 → no remaining autocorrelation
* Stata — Ljung-Box (portmanteau) test
* After arima estimation:
wntestq residuals, lags(10)
* Q-stat with p > 0.05 → white noise residuals
Use when residuals exhibit time-varying variance (heteroskedasticity that clusters over time). Common in financial and macroeconomic data.
# Python — GARCH(1,1) using arch library
from arch import arch_model
# First, fit mean model (e.g., AR(1)) and extract residuals
# Then model the conditional variance:
garch_model = arch_model(series, vol='GARCH', p=1, q=1, dist='normal')
garch_result = garch_model.fit(disp='off')
print(garch_result.summary())
# Extract conditional volatility
cond_vol = garch_result.conditional_volatility
# ARCH LM test for remaining ARCH effects:
from arch.unitroot import VarianceRatio
from statsmodels.stats.diagnostic import het_arch
lm_stat, lm_pval, _, _ = het_arch(garch_result.resid)
print(f"ARCH LM test p-value: {lm_pval:.4f}") # should be > 0.05
# R — GARCH(1,1) using rugarch
library(rugarch)
spec <- ugarchspec(
variance.model = list(model = "sGARCH", garchOrder = c(1, 1)),
mean.model = list(armaOrder = c(1, 0), include.mean = TRUE),
distribution.model = "norm"
)
fit <- ugarchfit(spec = spec, data = series)
show(fit)
# Test for remaining ARCH effects
# ArchTest(residuals(fit), lags = 10) # from FinTS package
* Stata — ARCH/GARCH
* First run mean model:
arima series, arima(1,0,0)
predict resid_mean, residuals
* ARCH LM test:
estat archlm, lags(1 2 5)
* Fit GARCH(1,1):
arch series, arch(1) garch(1) ar(1)
For cointegration tests (Johansen, Engle-Granger), VECM specification, and structural break tests, see references/time-series-reference.md.
# R — Zivot-Andrews test (allows break under stationarity alternative)
library(urca)
za <- ur.za(series, model = "both", lag = 4)
summary(za)
# If test statistic < critical value → reject unit root even with break
# za@teststat gives statistic; za@cval gives 1%, 5%, 10% critical values
# Python — Zivot-Andrews test
from statsmodels.tsa.stattools import zivot_andrews
za_stat, pval, cvdict, bpindex, baselag = zivot_andrews(series, maxlag=4, regression='ct')
print(f"ZA stat: {za_stat:.4f}, p-value: {pval:.4f}, break at index: {bpindex}")
# pval < 0.05 → series is stationary with one structural break