Time Series Analysis

---
name: time-series-analysis
description: Analyze time-ordered data — decomposition, stationarity, forecasting models, changepoint detection, and proper temporal validation. Use when the order of observations matters.
category: ai-research
---

# Time Series Analysis

Time series data has memory: today's value depends on yesterday's. Analysis must respect that — 
in modeling (autocorrelation, seasonality, trends), in validation (never shuffle time), and in 
forecasting (uncertainty grows with horizon).

## Overview

Start by understanding the series: plot it, decompose into trend/seasonality/residuals, check 
stationarity. Model the structure you find — classical methods (ARIMA family, exponential 
smoothing) for well-behaved series, machine learning for complex patterns with enough data. 
Validate with time-based splits only: train on the past, test on the future, rolling forward. 
Forecast with intervals, because point forecasts without uncertainty are wishes.

## When to use

- Forecasting: demand, traffic, prices, sensor readings, resource usage.
- Detecting changes: changepoints, anomalies, regime shifts in temporal data.
- Understanding temporal structure: seasonality, trends, cycles, autocorrelation.
- Evaluating any model on time-ordered data (validation must respect time).

## Core concepts

- **Decomposition**: trend + seasonal + residual. Seeing the components separately reveals what to 
model — and what's just noise.
- **Stationarity**: constant mean/variance over time. Many methods assume it; differencing or 
detrending achieves it. Test (ADF/KPSS), don't assume.
- **Autocorrelation**: correlation with past values (ACF/PACF plots guide model order). Ignoring it 
leaves predictable structure on the table — or worse, in the residuals.
- **Classical models**: ARIMA/SARIMA for autocorrelated series with seasonality; exponential 
smoothing for trend/seasonal patterns; each with well-understood diagnostics.
- **ML approaches**: gradient boosting on lag features, deep models for long complex series. 
Powerful with enough data; hungry and opaque without it.
- **Temporal validation**: rolling-origin backtesting — train on past, predict future, roll 
forward. Random splits leak the future and lie about performance.

## Practical workflow

1. Plot the series; decompose; check stationarity and seasonality. Understand before modeling.
2. Establish baselines: naive (last value), seasonal naive, moving average. Many "advanced" models 
lose to these.
3. Fit candidate models; diagnose residuals — they should look like white noise. Structure left 
in residuals means structure unmodeled.
4. Backtest with rolling origins across multiple windows; compare on horizon-appropriate metrics 
(MAE, sMAPE, quantile loss).
5. Forecast with prediction intervals; communicate how uncertainty widens with horizon.
6. Monitor in production: detect drift and changepoints; retrain on a schedule, not on hope.

```text
Time series checklist:
[ ] Plotted + decomposed; stationarity tested
[ ] Naive/seasonal-naive baselines beaten
[ ] Residuals diagnosed (white noise?)
[ ] Rolling-origin backtest, multiple windows
[ ] Intervals reported, not just point forecasts
[ ] Retraining + drift monitoring planned
```

## Common pitfalls

- **Shuffled validation**: random train/test splits on time data. The model "predicts" the past 
from the future. Always split by time.
- **Skipping baselines**: complex models that lose to seasonal naive. Baselines first, always.
- **Ignoring residuals**: fitting without checking what's left. Residual structure is the model 
telling you what it missed.
- **Point forecasts only**: "demand will be 1,200." With what uncertainty? Intervals are the honest 
product.
- **Stationarity assumed**: applying ARIMA to a trending series without differencing. Test and 
transform.
- **Lookahead leakage**: features computed with future information (centered moving averages, 
full-series normalization). Every feature must be computable at forecast time.