tomevault-io Trend Analysis Guide
Overview
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.
Parametric Method: Linear Regression
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}")
Assumptions
- Linear relationship between time and variable
- Residuals are normally distributed
- Homoscedasticity (constant variance)
Non-Parametric Method: Sen's Slope with Mann-Kendall Test
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'
Comparison
| 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 |
Significance Levels
| 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 |
Example: Annual Precipitation 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}")
Common Issues
| 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 |
Best Practices
- Use at least 10 data points for reliable results
- Prefer Sen's slope for environmental time series
- Report both slope magnitude and p-value
- Round results to 2 decimal places
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