Data Preprocessing

Format, plot, and transform time series data

Economic and financial time series data can require preprocessing or transforming before you can analyze or model them. While base MATLAB^® has general purpose and timetable functionality for preprocessing or cleaning data (for example, the log function removes an exponential trend from series and Data Cleaner enables you to clean messy data interactively), Econometrics Toolbox™ has specialized functionality for preprocessing financial time series. For example, you can obtain a common or desired time base by aggregating multiple series, convert price series to growth rates, or decompose series into additive trend and cyclical components.

Apps

Econometric Modeler

Analyze and model econometric time series

Classes

LagOp Create lag operator polynomial

Functions

expand all

Aggregate Time Series Data

`convert2daily`	Aggregate timetable data to daily periodicity (Since R2021a)
`convert2weekly`	Aggregate timetable data to weekly periodicity (Since R2021a)
`convert2monthly`	Aggregate timetable data to monthly periodicity (Since R2021a)
`convert2quarterly`	Aggregate timetable data to quarterly periodicity (Since R2021a)
`convert2semiannual`	Aggregate timetable data to semiannual periodicity (Since R2021a)
`convert2annual`	Aggregate timetable data to annual periodicity (Since R2021a)

Business Day Calendar

addBusinessCalendar Add business calendar awareness to timetables (Since R2020b)

Transform Time Series Data

`price2ret`	Convert prices to returns
`ret2price`	Convert returns to prices
`lagmatrix`	Create lagged time series data

Decompose Time Series Data

`hpfilter`	Hodrick-Prescott filter for trend and cyclical components
`bkfilter`	Baxter-King filter for trend and cyclical components (Since R2023a)
`cffilter`	Christiano-Fitzgerald filter for trend and cyclical components (Since R2023a)
`hfilter`	Hamilton filter for trend and cyclical components (Since R2023a)

Plot Recession Periods with Time Series Data

recessionplot Overlay recession bands on time series plot

Lag Operator Polynomial Operations

`filter`	Apply lag operator polynomial to filter time series
`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
`isEqLagOp`	Determine if two `LagOp` objects are same mathematical polynomial
`isNonZero`	Find lags associated with nonzero coefficients of `LagOp` objects
`minus`	Lag operator polynomial subtraction
`mldivide`	Lag operator polynomial left division
`mrdivide`	Lag operator polynomial right division
`mtimes`	Lag operator polynomial multiplication
`plus`	Lag operator polynomial addition

Topics

Interactive Workflows

Prepare Time Series Data for Econometric Modeler App
Prepare time series data at the MATLAB command line, and then import the set into Econometric Modeler.
Import Time Series Data into Econometric Modeler App
Import time series data from the MATLAB Workspace or a MAT-file into Econometric Modeler.
Plot Time Series Data Using Econometric Modeler App
Interactively plot univariate and multivariate time series data, then interpret and interact with the plots.
Transform Time Series Using Econometric Modeler App
Transform time series data interactively.
Analyze Time Series Data Using Econometric Modeler
Interactively visualize and analyze univariate or multivariate time series data.

Transform Time Series Data

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.
Econometric Modeling
Understand model-selection techniques and Econometrics Toolbox features.
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 Base Partitions for ARIMA Model Estimation
When you fit a time series model to data, lagged terms in the model require initialization, usually with observations at the beginning of the sample.

Decompose Time Series Data

Decompose Time Series Into Additive Trend Components
Estimate nonseasonal and seasonal trend components using parametric models.
Estimate Moving Average Trend Using Moving Average Filter
This example shows how to estimate long-term trend using a symmetric moving average function.
Seasonal Filters
You can use a seasonal filter (moving average) to estimate the seasonal component of a time series.
Seasonal Adjustment
Seasonal adjustment is the process of removing a nuisance periodic component. The result of a seasonal adjustment is a deseasonalized time series.
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.
Use Hodrick-Prescott Filter to Reproduce Original Result
Use the Hodrick-Prescott filter to decompose a time series.
Compare One-Sided and Two-Sided Hodrick-Prescott Filter Results
Smooth the U.S. GDP by applying the one-sided and two-sided Hodrick-Prescott filters, and compare the resulting smoothed trends.
Compare Hodrick-Prescott Filter Formulations
Compare two formulations of the Hodrick-Prescott filter: the closed-form solution of the programming problem and its state-space formulation, with a focus on how each formulation addresses missing observations.

Plot Recession Periods with Time Series Data

Compare Recession Indicators
Analyze time-varying local trends in carbon emissions data by building dynamic state-space models from series for coal, gas, and oil.

Lag Operator Polynomial Operations

Specify Lag Operator Polynomials
Create lag operator polynomial objects.

Related Information

When to Use the Hodrick-Prescott Filter

Featured Examples

Choose Time Series Filter for Business Cycle Analysis

Compare the performance of the two-sided Hodrick-Prescott filter, on performing business cycle analysis, against the Baxter-King, Christiano-Fitzgerald, one-sided Hodrick-Prescott, and Hamilton filters.

Open Live Script

Time Series Regression III: Influential Observations

Detect influential observations in time series data and accommodate their effect on multiple linear regression models. It is the third in a series of examples on time series regression, following the presentation in previous examples.

Open Live Script

Time Series Regression IV: Spurious Regression

Considers trending variables, spurious regression, and methods of accommodation in multiple linear regression models. It is the fourth in a series of examples on time series regression, following the presentation in previous examples.

Open Live Script

Time Series Regression V: Predictor Selection

Select a parsimonious set of predictors with high statistical significance for multiple linear regression models. It is the fifth in a series of examples on time series regression, following the presentation in previous examples.

Open Live Script