Detect long-term trends in time series data using parametric and non-parametric methods. Use when determining if a variable shows statistically significant increase or decrease over time.
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Trend analysis determines whether a time series shows a statistically significant long-term increase or decrease. This guide covers both parametric (linear regression) and non-parametric (Sen's slope) methods.
Linear regression fits a straight line to the data and tests if the slope is significantly different from zero.
from scipy import stats
slope, intercept, r_value, p_value, std_err = stats.linregress(years, values)
print(f"Slope: {slope:.2f} units/year")
print(f"p-value: {p_value:.2f}")
Sen's slope is robust to outliers and does not assume normality. Recommended for environmental data.
import pymannkendall as mk
result = mk.original_test(values)
print(result.slope) # Sen's slope (rate of change per time unit)
print(result.p) # p-value for significance
print(result.trend) # 'increasing', 'decreasing', or 'no trend'
| Method | Pros | Cons |
|---|---|---|
| Linear Regression | Easy to interpret, gives R² | Sensitive to outliers |
| Sen's Slope | Robust to outliers, no normality assumption | Slightly less statistical power |
| p-value | Interpretation |
|---|---|
| p < 0.01 | Highly significant trend |
| p < 0.05 | Significant trend |
| p < 0.10 | Marginally significant |
| p >= 0.10 | No significant trend |
import pandas as pd
import pymannkendall as mk
# Load annual precipitation data
df = pd.read_csv('precipitation.csv')
precip = df['Precipitation'].values
# Run Mann-Kendall test
result = mk.original_test(precip)
print(f"Sen's slope: {result.slope:.2f} mm/year")
print(f"p-value: {result.p:.2f}")
print(f"Trend: {result.trend}")
| Issue | Cause | Solution |
|---|---|---|
| p-value = NaN | Too few data points | Need at least 8-10 years |
| Conflicting results | Methods have different assumptions | Trust Sen's slope for environmental data |
| Slope near zero but significant | Large sample size | Check practical significance |
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Create or update AgentSkills. Use when designing, structuring, or packaging skills with scripts, references, and assets.
Create or update AgentSkills. Use when designing, structuring, or packaging skills with scripts, references, and assets.
Set up and use 1Password CLI (op). Use when installing the CLI, enabling desktop app integration, signing in (single or multi-account), or reading/injecting/running secrets via op.
CLI to manage emails via IMAP/SMTP. Use `himalaya` to list, read, write, reply, forward, search, and organize emails from the terminal. Supports multiple accounts and message composition with MML (MIME Meta Language).