> ## Documentation Index
> Fetch the complete documentation index at: https://fred-mcp-server.amorelli.tech/llms.txt
> Use this file to discover all available pages before exploring further.

# Data Transformations

> Transform economic data for analysis and comparison

# 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 theme={null}
{
  "series_id": "GDP",
  "observation_start": "2020-Q1",
  "units": "lin"  // Default, can be omitted
}
```

**Output:**

```json theme={null}
[
  { "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 theme={null}
{
  "series_id": "GDP",
  "observation_start": "2020-Q1",
  "units": "chg"
}
```

**Formula:** `x_t - x_{t-1}`

**Output:**

```json theme={null}
[
  { "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 theme={null}
{
  "series_id": "GDP",
  "observation_start": "2020-Q1",
  "units": "pch"
}
```

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

**Output:**

```json theme={null}
[
  { "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 theme={null}
{
  "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 theme={null}
[
  { "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 theme={null}
{
  "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 theme={null}
[
  { "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 theme={null}
{
  "series_id": "PAYEMS",
  "observation_start": "2020-01-01",
  "units": "ch1"
}
```

**Formula:** `x_t - x_{t-n}`

**Output:**

```json theme={null}
[
  { "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 theme={null}
{
  "series_id": "SP500",
  "observation_start": "2020-01-01",
  "units": "cch"
}
```

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

**Output:**

```json theme={null}
[
  { "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 theme={null}
{
  "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 theme={null}
{
  "series_id": "GDP",
  "observation_start": "2020-Q1",
  "units": "log"
}
```

**Formula:** `ln(x_t)`

**Output:**

```json theme={null}
[
  { "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 theme={null}
    // Year-over-year (most common for news)
    { "units": "pc1" }

    // Annualized rate (GDP reporting)
    { "units": "pca" }
    ```
  </Tab>

  <Tab title="Trend Analysis">
    ```javascript theme={null}
    // Original levels
    { "units": "lin" }

    // Log transformation for exponential trends
    { "units": "log" }
    ```
  </Tab>

  <Tab title="Momentum Analysis">
    ```javascript theme={null}
    // Month-over-month
    { "units": "pch" }

    // Absolute changes
    { "units": "chg" }
    ```
  </Tab>

  <Tab title="Statistical Analysis">
    ```javascript theme={null}
    // 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 theme={null}
  {
    "series_id": "CPIAUCSL",
    "units": "pch"
  }
  // Shows monthly price changes
  ```

  ```javascript Year-over-Year theme={null}
  {
    "series_id": "CPIAUCSL",
    "units": "pc1"
  }
  // Standard inflation reporting
  ```

  ```javascript Annualized Monthly theme={null}
  {
    "series_id": "CPIAUCSL",
    "units": "pca"
  }
  // Monthly change at annual rate
  ```
</CodeGroup>

### GDP Growth

<CodeGroup>
  ```javascript Quarter-over-Quarter theme={null}
  {
    "series_id": "GDPC1",
    "units": "pch"
  }
  // Simple quarterly growth
  ```

  ```javascript Annualized (Official) theme={null}
  {
    "series_id": "GDPC1",
    "units": "pca"
  }
  // BEA's official reporting method
  ```

  ```javascript Year-over-Year theme={null}
  {
    "series_id": "GDPC1",
    "units": "pc1"
  }
  // Annual comparison
  ```
</CodeGroup>

### Employment Changes

<CodeGroup>
  ```javascript Monthly Change theme={null}
  {
    "series_id": "PAYEMS",
    "units": "chg"
  }
  // Net jobs added/lost (in thousands)
  ```

  ```javascript Year-over-Year theme={null}
  {
    "series_id": "PAYEMS",
    "units": "ch1"
  }
  // Annual job growth (in thousands)
  ```

  ```javascript Growth Rate theme={null}
  {
    "series_id": "PAYEMS",
    "units": "pc1"
  }
  // Percentage employment growth
  ```
</CodeGroup>

## Combining Transformations

### Compare Multiple Views

```javascript theme={null}
// 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 theme={null}
// 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 theme={null}
// 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 theme={null}
{
  "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 theme={null}
// 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 theme={null}
    { "series_id": "CPIAUCSL", "units": "pch" }  // Monthly
    { "series_id": "GDP", "units": "pch" }       // Quarterly
    ```

    ✅ **Do:** Use consistent frequencies

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

    ✅ **Do:** Use base series

    ```javascript theme={null}
    { "series_id": "GDPC1", "units": "pch" }  // Correct
    ```
  </Accordion>

  <Accordion title="Ignoring Units">
    ❌ **Don't:** Forget to check original units

    ```javascript theme={null}
    // 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 theme={null}
    { "series_id": "UNRATENSA", "units": "pch" }  // Seasonal distortion
    ```

    ✅ **Do:** Use SA data for comparisons

    ```javascript theme={null}
    { "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>