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docs/source/notebooks/graded_intervention_time_series_single_channel_ols.ipynb

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"#### Introduction: Understanding the Problem\n",
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"**Autocorrelation** occurs when observations in a time series are correlated with their own past values. In causal inference with time series data, this creates a fundamental challenge:\n",
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"Autocorrelation occurs when observations in a time series are correlated with their own past values. In causal inference with time series data, this creates a fundamental challenge:\n",
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"**What is autocorrelation?**\n",
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"- Today's outcome is influenced by yesterday's (and last week's, and last month's...)\n",
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"Standard regression assumes **independent errors** — that the unexplained variation at time $t$ is unrelated to time $t-1$. When this assumption fails (as it almost always does in time series):\n",
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"1. **Coefficient estimates remain unbiased** ✓ (still correct on average)\n",
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"2. **Standard errors are WRONG** ✗ (typically too small, leading to overconfident inference)\n",
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"3. **Hypothesis tests are invalid** ✗ (false positives, misleading p-values)\n",
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"4. **Confidence intervals are too narrow** ✗ (underestimate true uncertainty)\n",
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"1. **Coefficient estimates remain unbiased:** still correct on average\n",
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"2. **Standard errors are WRONG:** typically too small, leading to overconfident inference\n",
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"3. **Hypothesis tests are invalid:** false positives, misleading p-values\n",
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"4. **Confidence intervals are too narrow:** underestimate true uncertainty\n",
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"This means you might conclude an intervention \"works\" when it actually doesn't, or claim high precision when you're actually quite uncertain!\n",
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"\n",

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