---
title: Data Transformations
description: Transform economic data for analysis and comparison
icon: 'calculator'
---
# 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:
```javascript
{
"series_id": "GDP",
"observation_start": "2020-Q1",
"units": "lin" // Default, can be omitted
}
```
**Output:**
```json
[
{ "date": "2024-Q2", "value": "28647.8" },
{ "date": "2024-Q1", "value": "28435.1" }
]
```
<Note>
Units: Billions of Dollars
</Note>
### Change (chg)
Absolute period-to-period change:
```javascript
{
"series_id": "GDP",
"observation_start": "2020-Q1",
"units": "chg"
}
```
**Formula:** `x_t - x_{t-1}`
**Output:**
```json
[
{ "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:
```javascript
{
"series_id": "GDP",
"observation_start": "2020-Q1",
"units": "pch"
}
```
**Formula:** `((x_t / x_{t-1}) - 1) * 100`
**Output:**
```json
[
{ "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:
```javascript
{
"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:**
```json
[
{ "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
<Tip>
**pc1** is the most common transformation for inflation and growth rates
</Tip>
### Compounded Annual Rate of Change (pca)
Annualized growth rate:
```javascript
{
"series_id": "GDPC1",
"observation_start": "2020-Q1",
"units": "pca"
}
```
**Formula:** `(((x_t / x_{t-1})^(n)) - 1) * 100`
where `n` = periods per year
**Output:**
```json
[
{ "date": "2024-Q2", "value": "3.0" },
{ "date": "2024-Q1", "value": "1.4" }
]
```
**Use cases:**
- Quarterly GDP at annual rates (official reporting)
- Annualizing monthly growth
<Warning>
**pca** compounds the growth rate. A 0.75% quarterly growth becomes ~3% annual rate.
</Warning>
### Change from Year Ago (ch1)
Absolute change from same period last year:
```javascript
{
"series_id": "PAYEMS",
"observation_start": "2020-01-01",
"units": "ch1"
}
```
**Formula:** `x_t - x_{t-n}`
**Output:**
```json
[
{ "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):
```javascript
{
"series_id": "SP500",
"observation_start": "2020-01-01",
"units": "cch"
}
```
**Formula:** `(ln(x_t) - ln(x_{t-1})) * 100`
**Output:**
```json
[
{ "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:
```javascript
{
"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:
```javascript
{
"series_id": "GDP",
"observation_start": "2020-Q1",
"units": "log"
}
```
**Formula:** `ln(x_t)`
**Output:**
```json
[
{ "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
<Tabs>
<Tab title="Headlines & Reporting">
```javascript
// Year-over-year (most common for news)
{ "units": "pc1" }
// Annualized rate (GDP reporting)
{ "units": "pca" }
```
</Tab>
<Tab title="Trend Analysis">
```javascript
// Original levels
{ "units": "lin" }
// Log transformation for exponential trends
{ "units": "log" }
```
</Tab>
<Tab title="Momentum Analysis">
```javascript
// Month-over-month
{ "units": "pch" }
// Absolute changes
{ "units": "chg" }
```
</Tab>
<Tab title="Statistical Analysis">
```javascript
// Log returns
{ "units": "cch" }
// Log levels
{ "units": "log" }
```
</Tab>
</Tabs>
### 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
<CodeGroup>
```javascript Month-over-Month
{
"series_id": "CPIAUCSL",
"units": "pch"
}
// Shows monthly price changes
```
```javascript Year-over-Year
{
"series_id": "CPIAUCSL",
"units": "pc1"
}
// Standard inflation reporting
```
```javascript Annualized Monthly
{
"series_id": "CPIAUCSL",
"units": "pca"
}
// Monthly change at annual rate
```
</CodeGroup>
### GDP Growth
<CodeGroup>
```javascript Quarter-over-Quarter
{
"series_id": "GDPC1",
"units": "pch"
}
// Simple quarterly growth
```
```javascript Annualized (Official)
{
"series_id": "GDPC1",
"units": "pca"
}
// BEA's official reporting method
```
```javascript Year-over-Year
{
"series_id": "GDPC1",
"units": "pc1"
}
// Annual comparison
```
</CodeGroup>
### Employment Changes
<CodeGroup>
```javascript Monthly Change
{
"series_id": "PAYEMS",
"units": "chg"
}
// Net jobs added/lost (in thousands)
```
```javascript Year-over-Year
{
"series_id": "PAYEMS",
"units": "ch1"
}
// Annual job growth (in thousands)
```
```javascript Growth Rate
{
"series_id": "PAYEMS",
"units": "pc1"
}
// Percentage employment growth
```
</CodeGroup>
## Combining Transformations
### Compare Multiple Views
```javascript
// 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
```javascript
// 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:
```javascript
// 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:
```javascript
{
"series_id": "SP500",
"observation_start": "2023-01-01",
"units": "cch" // Daily log returns
}
// Calculate standard deviation for volatility
```
### Real vs Nominal
Deflate nominal series:
```javascript
// Nominal wages
const nominal_wages = {
"series_id": "CES0500000003"
};
// CPI (for deflation)
const cpi = {
"series_id": "CPIAUCSL"
};
// Real wages = (Nominal / CPI) * 100
```
<Note>
FRED often provides pre-calculated real series (look for "Real" in title)
</Note>
## Common Pitfalls
<AccordionGroup>
<Accordion title="Mixing Frequencies">
❌ **Don't:** Compare monthly % change with quarterly
```javascript
{ "series_id": "CPIAUCSL", "units": "pch" } // Monthly
{ "series_id": "GDP", "units": "pch" } // Quarterly
```
✅ **Do:** Use consistent frequencies
```javascript
{ "series_id": "CPIAUCSL", "units": "pc1" } // Annual
{ "series_id": "GDP", "units": "pc1" } // Annual
```
</Accordion>
<Accordion title="Transformation on Transformations">
❌ **Don't:** Apply transformations to already-transformed series
```javascript
// Series ending in "CHG" or "PC1" are already transformed
{ "series_id": "GDPC1CHG", "units": "pch" } // Wrong!
```
✅ **Do:** Use base series
```javascript
{ "series_id": "GDPC1", "units": "pch" } // Correct
```
</Accordion>
<Accordion title="Ignoring Units">
❌ **Don't:** Forget to check original units
```javascript
// Some series are in billions, others in thousands
{ "series_id": "GDP" } // Billions
{ "series_id": "PAYEMS" } // Thousands
```
✅ **Do:** Verify units in response
</Accordion>
<Accordion title="Seasonality Issues">
❌ **Don't:** Use NSA data for growth rates
```javascript
{ "series_id": "UNRATENSA", "units": "pch" } // Seasonal distortion
```
✅ **Do:** Use SA data for comparisons
```javascript
{ "series_id": "UNRATE", "units": "pch" } // Seasonally adjusted
```
</Accordion>
</AccordionGroup>
## Transformation Reference
### Quick Reference Table
| Code | Name | Formula | Period | Use Case |
|------|------|---------|--------|----------|
| lin | Levels | x_t | - | Raw data |
| chg | Change | x_t - x_{t-1} | Prior | Absolute change |
| ch1 | Change YoY | x_t - x_{t-n} | Year ago | Annual absolute change |
| pch | % Change | ((x_t/x_{t-1})-1)*100 | Prior | Growth rate |
| pc1 | % Change YoY | ((x_t/x_{t-n})-1)*100 | Year ago | Annual growth |
| pca | Compounded Annual | (((x_t/x_{t-1})^n)-1)*100 | Annual | Annualized rate |
| cch | Log Change | (ln(x_t)-ln(x_{t-1}))*100 | Prior | Log returns |
| cca | Log Change Annual | (ln(x_t)-ln(x_{t-n}))*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
<Steps>
<Step title="Start with Levels">
Always examine raw data first to understand scale and patterns
</Step>
<Step title="Match Use Case">
Choose transformation based on your analysis needs
</Step>
<Step title="Document Choices">
Note which transformations you applied for reproducibility
</Step>
<Step title="Verify Results">
Sanity-check transformed values against known economic facts
</Step>
</Steps>
## Next Steps
<CardGroup cols={2}>
<Card
title="Time Series Analysis"
icon="chart-line"
href="/examples/time-series-analysis"
>
Analyze transformed data
</Card>
<Card
title="Advanced Queries"
icon="magnifying-glass-chart"
href="/examples/advanced-queries"
>
Complex data retrieval
</Card>
<Card
title="Economic Indicators"
icon="chart-mixed"
href="/examples/economic-indicators"
>
Common indicator patterns
</Card>
<Card
title="API Reference"
icon="book"
href="/api-reference/fred-get-series"
>
Full transformation docs
</Card>
</CardGroup>
