||Create lag operator polynomial (LagOp) object|
||Apply lag operator polynomial to filter time series|
||Hodrick-Prescott filter for trend and cyclical components|
||Overlay recession bands on a time series plot|
Take a nonseasonal difference of a time series.
Apply both nonseasonal and seasonal differencing using lag operator polynomial objects.
Estimate long-term trend using a symmetric moving average function.
Deseasonalize a time series using a stable seasonal filter.
Apply seasonal filters to deseasonalize a time series.
Estimate nonseasonal and seasonal trend components using parametric models.
Use the Hodrick-Prescott filter to decompose a time series.
Create lag operator polynomial objects.
Understand the definition, forms, and properties of stochastic processes.
Determine which data transformations are appropriate for your problem.
Determine the characteristics of nonstationary processes.
Learn about splitting time series into deterministic trend, seasonal, and irregular components.
Some time series are decomposable into various trend components. To estimate a trend component without making parametric assumptions, you can consider using a filter.
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.
The Hodrick-Prescott (HP) filter is a specialized filter for trend and business cycle estimation (no seasonal component).