# Documentation

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# Data Preprocessing

Format, plot, and transform time series data

## Classes

 `LagOp` Create lag operator polynomial (LagOp) object

## Functions

 `hpfilter` Hodrick-Prescott filter for trend and cyclical components `price2ret` Convert prices to returns `ret2price` Convert returns to prices `recessionplot` Overlay recession bands on a time series plot `isStable` Determine stability of lag operator polynomial `reflect` Reflect lag operator polynomial coefficients around lag zero `toCellArray` Convert lag operator polynomial object to cell array

## Examples and How To

Nonseasonal Differencing

Take a nonseasonal difference of a time series.

Nonseasonal and Seasonal Differencing

Apply both nonseasonal and seasonal differencing using lag operator polynomial objects.

Moving Average Trend Estimation

Estimate long-term trend using a symmetric moving average function.

Seasonal Adjustment Using a Stable Seasonal Filter

Deseasonalize a time series using a stable seasonal filter.

Seasonal Adjustment Using S(n,m) Seasonal Filters

Apply seasonal filters to deseasonalize a time series.

Parametric Trend Estimation

Estimate nonseasonal and seasonal trend components using parametric models.

Using the Hodrick-Prescott Filter to Reproduce Their Original Result

Use the Hodrick-Prescott filter to decompose a time series.

Specify Lag Operator Polynomials

Create lag operator polynomial objects.

## Concepts

Stochastic Process Characteristics

Understand the definition, forms, and properties of stochastic processes.

Data Transformations

Determine which data transformations are appropriate for your problem.

Trend-Stationary vs. Difference-Stationary Processes

Determine the characteristics of nonstationary processes.

Time Series Decomposition

Learn about splitting time series into deterministic trend, seasonal, and irregular components.

Moving Average Filter

Some time series are decomposable into various trend components. To estimate a trend component without making parametric assumptions, you can consider using a filter.

Seasonal Filters

You can use a seasonal filter (moving average) to estimate the seasonal component of a time series.

Seasonal adjustment is the process of removing a nuisance periodic component. The result of a seasonal adjustment is a deseasonalized time series.

Hodrick-Prescott Filter

The Hodrick-Prescott (HP) filter is a specialized filter for trend and business cycle estimation (no seasonal component).