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name: trend-analysis description: 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. license: MIT

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