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