time-series-guide

Time Series Guide

A skill for applying time series econometric methods including ARIMA modeling, VAR systems, cointegration analysis, and unit root tests. Covers stationarity concepts, model selection, forecasting, and diagnostic checking for economic and financial data.

Stationarity and Unit Root Tests

Why Stationarity Matters

A time series is stationary when its statistical properties (mean, variance, autocorrelation) do not change over time. Most econometric methods require stationarity. Non-stationary series can produce spurious regressions.

Testing for Stationarity

from statsmodels.tsa.stattools import adfuller, kpss
import pandas as pd


def test_stationarity(series: pd.Series, name: str = "Series") -> dict:
    """
    Test for stationarity using ADF and KPSS tests.

    Args:
        series: Time series data
        name: Label for the series
    """
    # Augmented Dickey-Fuller test
    # H0: Unit root exists (non-stationary)
    adf_result = adfuller(series.dropna(), autolag="AIC")

    # KPSS test
    # H0: Series is stationary
    kpss_result = kpss(series.dropna(), regression="c", nlags="auto")

    return {
        "series": name,
        "adf": {
            "statistic": adf_result[0],
            "p_value": adf_result[1],
            "lags_used": adf_result[2],
            "conclusion": (
                "Stationary (reject unit root)"
                if adf_result[1] < 0.05
                else "Non-stationary (fail to reject unit root)"
            )
        },
        "kpss": {
            "statistic": kpss_result[0],
            "p_value": kpss_result[1],
            "conclusion": (
                "Non-stationary (reject stationarity)"
                if kpss_result[1] < 0.05
                else "Stationary (fail to reject stationarity)"
            )
        }
    }

Making a Series Stationary

Method 1: Differencing
  y_diff = y_t - y_{t-1}           (first difference)
  y_diff2 = delta(y_diff)          (second difference, rarely needed)

Method 2: Log transformation + differencing
  y_log = log(y_t)                 (stabilizes variance)
  y_return = log(y_t) - log(y_{t-1})  (log returns)

Method 3: Detrending
  Subtract a fitted trend (linear, polynomial, or HP filter)