Data Transformations

FRED provides powerful transformation capabilities to prepare data for analysis. Learn how to apply transformations directly in your requests.

Transformation Types

Levels (lin)

Raw, untransformed data:

{
  "series_id": "GDP",
  "observation_start": "2020-Q1",
  "units": "lin"  // Default, can be omitted
}

Output:

[
  { "date": "2024-Q2", "value": "28647.8" },
  { "date": "2024-Q1", "value": "28435.1" }
]

Units: Billions of Dollars

Change (chg)

Absolute period-to-period change:

{
  "series_id": "GDP",
  "observation_start": "2020-Q1",
  "units": "chg"
}

Formula: x_t - x_{t-1} Output:

[
  { "date": "2024-Q2", "value": "212.7" },
  { "date": "2024-Q1", "value": "157.3" }
]

Use cases:

Quarterly GDP additions
Monthly employment changes
Period-over-period differences

Percent Change (pch)

Period-to-period percentage change:

{
  "series_id": "GDP",
  "observation_start": "2020-Q1",
  "units": "pch"
}

Formula: ((x_t / x_{t-1}) - 1) * 100 Output:

[
  { "date": "2024-Q2", "value": "0.75" },
  { "date": "2024-Q1", "value": "0.56" }
]

Use cases:

Month-over-month inflation
Quarter-over-quarter growth
Short-term momentum

Percent Change from Year Ago (pc1)

Year-over-year percentage change:

{
  "series_id": "CPIAUCSL",
  "observation_start": "2020-01-01",
  "units": "pc1"
}

Formula: ((x_t / x_{t-n}) - 1) * 100 where n = periods in a year Output:

[
  { "date": "2024-09-01", "value": "2.4" },
  { "date": "2024-08-01", "value": "2.5" }
]

Use cases:

Annual inflation rates
Year-over-year GDP growth
Annual wage growth

pc1 is the most common transformation for inflation and growth rates

Compounded Annual Rate of Change (pca)

Annualized growth rate:

{
  "series_id": "GDPC1",
  "observation_start": "2020-Q1",
  "units": "pca"
}

Formula: (((x_t / x_{t-1})^(n)) - 1) * 100 where n = periods per year Output:

[
  { "date": "2024-Q2", "value": "3.0" },
  { "date": "2024-Q1", "value": "1.4" }
]

Use cases:

Quarterly GDP at annual rates (official reporting)
Annualizing monthly growth

pca compounds the growth rate. A 0.75% quarterly growth becomes ~3% annual rate.

Change from Year Ago (ch1)

Absolute change from same period last year:

{
  "series_id": "PAYEMS",
  "observation_start": "2020-01-01",
  "units": "ch1"
}

Formula: x_t - x_{t-n} Output:

[
  { "date": "2024-09-01", "value": "2543" },
  { "date": "2024-08-01", "value": "2619" }
]

Use cases:

Year-over-year job gains
Annual change in levels

Continuously Compounded Rate (cch)

Log difference (percentage):

{
  "series_id": "SP500",
  "observation_start": "2020-01-01",
  "units": "cch"
}

Formula: (ln(x_t) - ln(x_{t-1})) * 100 Output:

[
  { "date": "2024-10-25", "value": "0.52" },
  { "date": "2024-10-24", "value": "-0.18" }
]

Use cases:

Financial returns analysis
Statistical modeling
Volatility calculations

Continuously Compounded Annual Rate (cca)

Log difference annualized:

{
  "series_id": "GDP",
  "observation_start": "2020-Q1",
  "units": "cca"
}

Formula: (ln(x_t) - ln(x_{t-n})) * 100 Use cases:

Academic research
Econometric modeling

Natural Log (log)

Logarithmic transformation:

{
  "series_id": "GDP",
  "observation_start": "2020-Q1",
  "units": "log"
}

Formula: ln(x_t) Output:

[
  { "date": "2024-Q2", "value": "10.2627" },
  { "date": "2024-Q1", "value": "10.2553" }
]

Use cases:

Identifying exponential trends
Statistical analysis requiring normality
Growth rate calculations

Transformation Selection Guide

By Use Case

Headlines & Reporting
Trend Analysis
Momentum Analysis
Statistical Analysis

// Year-over-year (most common for news)
{ "units": "pc1" }

// Annualized rate (GDP reporting)
{ "units": "pca" }

// Original levels
{ "units": "lin" }

// Log transformation for exponential trends
{ "units": "log" }

// Month-over-month
{ "units": "pch" }

// Absolute changes
{ "units": "chg" }

// Log returns
{ "units": "cch" }

// Log levels
{ "units": "log" }

By Data Frequency

Frequency	Common Transformations	Example
Daily	lin, pch, cch	Stock returns
Weekly	lin, pch, pc1	Initial claims
Monthly	pc1, pch, ch1	Inflation, employment
Quarterly	pca, pc1, log	GDP growth
Annual	pc1, chg	Demographics

Practical Examples

Inflation Analysis

{
  "series_id": "CPIAUCSL",
  "units": "pch"
}
// Shows monthly price changes

{
  "series_id": "CPIAUCSL",
  "units": "pc1"
}
// Standard inflation reporting

{
  "series_id": "CPIAUCSL",
  "units": "pca"
}
// Monthly change at annual rate

GDP Growth

{
  "series_id": "GDPC1",
  "units": "pch"
}
// Simple quarterly growth

{
  "series_id": "GDPC1",
  "units": "pca"
}
// BEA's official reporting method

{
  "series_id": "GDPC1",
  "units": "pc1"
}
// Annual comparison

Employment Changes

{
  "series_id": "PAYEMS",
  "units": "chg"
}
// Net jobs added/lost (in thousands)

{
  "series_id": "PAYEMS",
  "units": "ch1"
}
// Annual job growth (in thousands)

{
  "series_id": "PAYEMS",
  "units": "pc1"
}
// Percentage employment growth

Combining Transformations

Compare Multiple Views

// Original levels
const levels = {
  "series_id": "UNRATE",
  "observation_start": "2020-01-01",
  "units": "lin"
};

// Month-over-month change
const monthly = {
  "series_id": "UNRATE",
  "observation_start": "2020-01-01",
  "units": "chg"
};

// Year-over-year change
const annual = {
  "series_id": "UNRATE",
  "observation_start": "2020-01-01",
  "units": "ch1"
};

Growth Decomposition

// Nominal GDP growth
const nominal = {
  "series_id": "GDP",
  "units": "pc1"
};

// Real GDP growth
const real = {
  "series_id": "GDPC1",
  "units": "pc1"
};

// Implicit: Price change ≈ Nominal - Real

Advanced Techniques

Detrending

Remove long-term trends using logs:

// Step 1: Get log values
{
  "series_id": "GDPC1",
  "observation_start": "2000-Q1",
  "units": "log"
}

// Step 2: Calculate deviations from trend
// (done in analysis tool)

Volatility Measurement

Use continuous compounding for returns:

{
  "series_id": "SP500",
  "observation_start": "2023-01-01",
  "units": "cch"  // Daily log returns
}

// Calculate standard deviation for volatility

Real vs Nominal

Deflate nominal series:

// Nominal wages
const nominal_wages = {
  "series_id": "CES0500000003"
};

// CPI (for deflation)
const cpi = {
  "series_id": "CPIAUCSL"
};

// Real wages = (Nominal / CPI) * 100

FRED often provides pre-calculated real series (look for “Real” in title)

Common Pitfalls

Mixing Frequencies

❌ Don’t: Compare monthly % change with quarterly

{ "series_id": "CPIAUCSL", "units": "pch" }  // Monthly
{ "series_id": "GDP", "units": "pch" }       // Quarterly

✅ Do: Use consistent frequencies

{ "series_id": "CPIAUCSL", "units": "pc1" }  // Annual
{ "series_id": "GDP", "units": "pc1" }       // Annual

Transformation on Transformations

❌ Don’t: Apply transformations to already-transformed series

// Series ending in "CHG" or "PC1" are already transformed
{ "series_id": "GDPC1CHG", "units": "pch" }  // Wrong!

✅ Do: Use base series

{ "series_id": "GDPC1", "units": "pch" }  // Correct

Ignoring Units

❌ Don’t: Forget to check original units

// Some series are in billions, others in thousands
{ "series_id": "GDP" }      // Billions
{ "series_id": "PAYEMS" }   // Thousands

✅ Do: Verify units in response

Seasonality Issues

❌ Don’t: Use NSA data for growth rates

{ "series_id": "UNRATENSA", "units": "pch" }  // Seasonal distortion

✅ Do: Use SA data for comparisons

{ "series_id": "UNRATE", "units": "pch" }  // Seasonally adjusted

Transformation Reference

Quick Reference Table

Code	Name	Formula	Period	Use Case
lin	Levels	x_t	-	Raw data
chg	Change	x_t - x_	Prior	Absolute change
ch1	Change YoY	x_t - x_	Year ago	Annual absolute change
pch	% Change	((x_t/x_)-1)*100	Prior	Growth rate
pc1	% Change YoY	((x_t/x_)-1)*100	Year ago	Annual growth
pca	Compounded Annual	(((x_t/x_)^n)-1)*100	Annual	Annualized rate
cch	Log Change	(ln(x_t)-ln(x_))*100	Prior	Log returns
cca	Log Change Annual	(ln(x_t)-ln(x_))*100	Annual	Annual log returns
log	Natural Log	ln(x_t)	-	Log levels

Frequency Multipliers (n)

Frequency	n (per year)
Daily	365 (business) / 260 (trading)
Weekly	52
Monthly	12
Quarterly	4
Semi-annual	2
Annual	1

Best Practices

Start with Levels

Always examine raw data first to understand scale and patterns

Match Use Case

Choose transformation based on your analysis needs

Document Choices

Note which transformations you applied for reproducibility

Verify Results

Sanity-check transformed values against known economic facts

Next Steps

Time Series Analysis

Analyze transformed data

Advanced Queries

Complex data retrieval

Economic Indicators

Common indicator patterns

API Reference

Full transformation docs

​Data Transformations

​Transformation Types

​Levels (lin)

​Change (chg)

​Percent Change (pch)

​Percent Change from Year Ago (pc1)

​Compounded Annual Rate of Change (pca)

​Change from Year Ago (ch1)

​Continuously Compounded Rate (cch)

​Continuously Compounded Annual Rate (cca)

​Natural Log (log)

​Transformation Selection Guide

​By Use Case

​By Data Frequency

​Practical Examples

​Inflation Analysis

​GDP Growth

​Employment Changes

​Combining Transformations

​Compare Multiple Views

​Growth Decomposition

​Advanced Techniques

​Detrending

​Volatility Measurement

​Real vs Nominal

​Common Pitfalls

​Transformation Reference

​Quick Reference Table

​Frequency Multipliers (n)

​Best Practices

​Next Steps

Time Series Analysis

Advanced Queries

Economic Indicators

API Reference

Data Transformations

Transformation Types

Levels (lin)

Change (chg)

Percent Change (pch)

Percent Change from Year Ago (pc1)

Compounded Annual Rate of Change (pca)

Change from Year Ago (ch1)

Continuously Compounded Rate (cch)

Continuously Compounded Annual Rate (cca)

Natural Log (log)

Transformation Selection Guide

By Use Case

By Data Frequency

Practical Examples

Inflation Analysis

GDP Growth

Employment Changes

Combining Transformations

Compare Multiple Views

Growth Decomposition

Advanced Techniques

Detrending

Volatility Measurement

Real vs Nominal

Common Pitfalls

Transformation Reference

Quick Reference Table

Frequency Multipliers (n)

Best Practices

Next Steps